Multi-zone buildings thermo-hygrometric analysis: a novel dynamic simulation code based on adaptive control

Transcription

1 Muli-zon buildings hrmo-hygromric analysis: a novl dynamic simulaion cod basd on adapiv conrol Annamaria Buonomano Dparmn of Indusrial Enginring, Univrsiy of Napls Fdrico II, Ialy annamaria.buonomano@unina.i Umbro Monanaro Dparmn of Indusrial Enginring, Univrsiy of Napls Fdrico II, Ialy umbro.monanaro@unina.i Adolfo Palombo Dparmn of Indusrial Enginring, Univrsiy of Napls Fdrico II, Ialy adolfo.palombo@unina.i Sfania Sanini Dparmn of Elcrical Enginring and Informaion chnology, Univrsiy of Napls Fdrico II, Ialy sfania.sanini@unina.i Absrac his papr prsns a novl dynamic simulaion modl for h analysis of muli-zon buildings hrmal rspons and h assssmn of building nrgy prformanc and indoor comfor. In his nw rlas of h cod, calld DEEC.3, wo imporan innovaions ar implmnd. hy rgard h simulaion modl of muli-zon buildings, consising of hrmal zons oally nclosd in ohrs, and h dsign of a novl mpraur-humidiy conrol algorihm. h dvlopd innovaiv conrol sragy is basd on a rfrnc adapiv conrol schm for h onlin adapaion of h conrol gains, wih h aim of ovrcoming h wllknown problms of classical fixd gain conrol algorihms. his faur will b a ky ool for h nx gnraion of building prformanc simulaion cods (also oward NZEB analyss). Boh h innovaions mbddd in h cod can b xploid o simula spcial indoor nvironmns of hospials / laboraoris, rooms or musum halls. Wih h aim of showing h faurs and h ponialiis of h simulaion cod coupld wih h nw conrol schm, a suiabl cas sudy rlad o an xpo indoor spac of a musum building, including a display cas wih an accura clima conrol, was dvlopd. Dails abou haing and cooling dmands and loads ar providd. Good racking prformanc for boh h mpraur and humidiy conrol ar obaind hrough h prsnd conrol schm. 1. Inroducion A crucial challng for h nx gnraion of buildings is h capabiliy o ovrcom h radoff bwn low nrgy dmands and high hrmal and hygromric comfor lvls. h growing anion o hs issus has ld h rsarch inrs oward h us of building managmn sragis wih h aim of improving boh building nrgy fficincy and occupans comfor. In his rgard, Building Enrgy Prformanc Simulaion (BEPS) ools play a ky rol. In h las yars, rcn advancs in h numrical analysis basd on compuaional mhods, as wll as compur calculaion powr, providd significan opporuniis for dvloping and/or improving a nw gnraion of BEPS cods. Hr, paricular anion was paid o: i) invsigaing nw building nvlop chnologis and innovaiv HVAC sysms, ofn suppord by rnwabl nrgis; ii) implmning advancd conrol algorihms and sysms (Shaikh P. H. al. 14). h prsnd papr focuss on his spcific framwork. In paricular, h aricl dscribs h nw faurs includd in DEEC.3, which updas a prvious rlas (DEEC. (Buonomano A. and Palombo A. 14)) validad by mans of h BESES procdur. Spcifically, DEEC.3 nabls h simulaion of mulihrmal zons (in paricular of zons oally nclosd in ohrs). Furhrmor, i implmns advancd hrmo-hygromric conrol acions abl 19

2 Annamaria Buonomano, Umbro Monanaro, Adolfo Palombo, Sfania Sanini o auomaically adap o h variaions of h simulad sysm and is surrounding nvironmn. h cod, purposly dvlopd by h auhors for rsarch aims, is concivd as a rliabl hrmo-hygromric calculaion ool for building nrgy dsign and prformanc analysis. DEEC allows on o dynamically calcula haing and cooling dmands of muli-zon buildings and o assss h bnfis of diffrn and advancd building nvlop chniqus (PCM, BIPV, BIPV/, sunspac, c.). hus, dsigns of high-prformanc buildings can b obaind. I is worh noing ha ofn svral rsarch opics canno b analysd by commrcial BEPS cods (.g. rcn prooypal chnologis, non-sandard opraing iions, paricular sysm schduling, c.). Such inninc can b xcdd by dvloping in-hous cods such as DEEC. Hr, updaing and modificaions of h includd modls can b carrid ou by auhors for all h occurring rsarch nds. h aim of his papr is o show h ffcivnss of h cod in prdicing h bhaviour of building hrmal zons wih rigid hrmo-hygromric consrains. Such a goal is achivd by xploiing h faurs of h adapiv conrol schm mbddd ino in DEEC.3, basd on a nw opimal modl rfrnc schm (namd L- EMAC, Linar uadraic Exndd Modl frnc Adapiv Conrol). h major advanag of his conrol chniqu is h conrol of h hrmo-hygromric variabls for indoor spacs in uncrain iions, wihou rquiring an a priori knowldg of h building dynamics. o his aim, diffrn from sandard fixd gains chniqus such as, for xampl, h PI approach implmnd in h prvious DEEC. rlas, h implmnd conrol algorihm is abl on-lin o auomaically vary is gains valus o conrac abrup and unknown changs in h building bhaviour and/or is faurs and xrnal iions. h ida bhind his approach is o achiv gra conrol flxibiliy and robusnss in ordr o guaran, a h sam im, opimaliy wih rspc o a crain cos funcion subjc o som consrains. h L-EMAC approach xnds and fuss h classical Modl frnc Adapiv Conrol (MAC) schm ha has bn provd o b ffciv in conrolling uncrain plans (Di Brnardo M. al. 8), wih an L algorihm, ypical in h opimal conrol hory. A suiabl cas sudy is hr dvlopd in ordr o show h ffcivnss of h adopd approach. In paricular, i rfrs o an indoor hall of a musum building wih an includd glass display cas. Hr, an accura clima conrol (rigid consrains of mpraur and humidiy of h cas indoor air) is rquird. As is wll known, such an occurrnc is mandaory in cas of paricular xhibid ims conaind in musum glass cass (.g. archival arifacs, papr-basd objcs, c.). Hr, prsrvaion chniqus mus b mphasizd in ordr o avoid any irrvrsibl damag. h cas sudy building is locad in h Mdirranan wahr zon of Napls, souhrn Ialy. o h bs of h auhors knowldg, his is h firs amp in liraur o modl in BEPS cods: i) conrol by mans of advancd schms (abl o guaran rigorous consrains of mpraurs and humidiy, simulanously); ii) hrmal zons oally includd ino ohrs.. hrmodynamic modl In his papr, a suiabl rsisiv-capaciiv (C) hrmal nwork simulaion modl (assuming 1D ransin ha ransfr) for h hrmo hygromric analysis of wo hrmal zons (on opionally complly nclosd in h ohr on) is dscribd. I is mbddd in h nw rlas of DEEC (Buonomano A. and Palombo A. 14). hrough such a modl, h assssmn of h dynamics of mpraurs and humidiy, as wll as of haing and cooling loads and dmands, can b carrid ou. A skch of h modlld C hrmal nwork is shown in Fig. 3. h calculaion procdur concrns h ha flows bwn: i) h oudoor nvironmn and h main modlld hrmal zon (zon 1 in Fig. 3); ii) h zon 1 and h rlad includd hrmal zon (Fig. 3). h following modl simplificaions ar considrd: i) h indoor air of ach hrmal zon is uniform and modlld as a singl indoor air mpraur nod; ii) h building nvlop of zon 1 is subdividd ino M muli-layr lmns (adoping a high ordr C hrmal nwork); iii) h 11

3 Muli-zon buildings hrmo-hygromric analysis: a novl dynamic simulaion cod basd on adapiv conrol consrucion nvlop of zon is lumpd in a singl nod; iv) ach m-h muli-layr building lmn of zon 1 is subdividd in N sub-layrs (of diffrn hicknsss), whr hrmal masss and uciviis ar uniformly discrisd; v) N+ capaciiv and surfac nods ar accound for ach m-h nvlop componn of zon 1, whil 1 nod is rfrrd o is indoor air; vi) nods ar modlld for zon, ach on for h lumpd nvlop and h indoor air. For zon 1, in ach -h im sp and for ach n-h capaciiv nod (j = 1,..., N) of h m-h lmn (m = 1,..., M), h diffrnial quaion dscribing h nrgy ra of chang of ach mpraur nod of h building nvlop is: n+1 dmn,, m, j - m,n Cmn d q j=n-1 m, j (1) whr C and ar h hrmal capacianc and mpraur of h nod, rspcivly. mj, is h sum of h halvs sub-layrs hrmal rsisancs mj, (ha links h n-h nod o hir nighbours, Fig. 3). For non-capaciiv our (n = ) and innr (n = N+1) surfac boundary nods, h algbraic quaion dscribing h ha ransfr is: 1,, n m j m n, cv mn jn1 mj, cv m, j is ihr a civ (xrnal inrnal m,n+1 q () m, or m,n ) or a uciv rsisanc ( ), dpnding on h sid layr of h considrd nod (Fig. 3). m, and nods o hos rlad o h m,n+1 connc non capaciiv oudoor air mpraur (ou) and o h indoor air on (in,1), rspcivly. In cas of floor lmns, ou and cv m, j ar rplacd wih h ground mpraur (gr) and an quivaln hrmal uciv rsisanc ( ). h modlld forcing funcion mn, includs h incidn solar and h long-wav radiaion xchang acing on our and innr surfacs of zon 1 (Buonomano A. and Palombo A. 14). A simplifid approach is adopd for zon. Hr, h diffrnial quaion dscribing h nrgy ra of chang of h mpraur nod of h zon nvlop (w,) is calculad as: k gr dw,, in j w, Cw, d j=1 j (3) whr Cw, is h nvlop lumpd hrmal capacianc, whos indoor air mpraur is in,; j is a al hrmal rsisanc ha aks ino accoun all h ha ransfr ffcs. For zon 1, 1 is calculad by adding h half sub-layr uciv hrmal rsisanc of h zon nvlop nod o h quivaln civ and radiaiv hrmal rsisanc (modlld by a combind linarizd civ-radiaiv hrmal rsisanc). A simplifid approach is considrd for zon. Hr, h radiaiv xchang only aks ino accoun h long-wav fracion vs. h zon 1. hus, for zon, h quivaln al hrmal rsisanc ( and cion phnomna only. ) includs combind ucion h diffrnial quaions on h hrmal nwork nods rlad o h indoor air of zon 1 and zon mus b solvd simulanously wih h sysm of qs. (1), () and (3). h snsibl nrgy ra of chang of zon 1 and zon indoor air masss (a in,1 and in,, rspcivly) can b calculad as: d - -, M in,1 m,n in,1 w, in,1 ou in,1 in, in,1 C in 1 + g, 1 AC,1 d m=1 m,in 1 v v, zns din, w, in, in,1 in, Cin, g, AC, d v, zns (4) (5) whr h hrmal rsisancs v and v,zns dscrib h air vnilaion and infilraion hrmal loads: v links h indoor air nod of zon 1 o h xrnal on (oudoor air a ou), v,zns links h indoor air nod of zon o h on rlad o zon

4 Annamaria Buonomano, Umbro Monanaro, Adolfo Palombo, Sfania Sanini ou sky rad sky x I m m, m, m,1 m,1 C m,1 m,1 m,1 m-h building lmn (xrnal wall, roof, ciling, floor, inrior wall, window) Zoom of ZONE includd in ZONE 1 mn, mn, C m,n Linkd o air nod of ZONE 1 mn, mn, 1 w, C W, Zon in I m rad mm, Fig. 3 Skch of h C hrmal nwork rad m,1 rad m, m,n+1 gr C in, M, N+1 rad m,m -1 Zon 1 in, m,n +1 AC, Zon 1 g, in,1 v, C in,1 M-1,N+1 1,N+1 AC,1 Excp for h hrmal load du o h solar radiaion ransmid hrough h windows and incidn on h indoor surfacs, includd in mn,, in ( I m, Fig. 3), all h rmaining snsibl ha gains ar considrd as civ lumpd ha sourc rms, nworkd o h indoor air nods only. hy includ: i) h hrmal zon inrnal gains du o occupans, lighs and quipmn, g,1 and g, ; ii) h snsibl ha o b supplid o (or rmovd from) h building spac by an idal HVAC sysm, aiming a mainaining h indoor air a h dsird s poin mpraur, AC, 1 and AC,. hrfor, h whol sysm including zon 1 and zon is modlld hrough a hrmal nwork of (M x N) + 5 nods. h diffrnial and algbraic quaions dscribing h sysm hrmal bhaviour ar: (1), (), (3), (4) and (5). h assssmn of h lan nrgy o b addd o (or subracd from) boh h hrmal zons 1 and (for mainaining h slcd rlaiv humidiy spoin of h indoor air) is carrid ou by adoping a dcoupld approach (Ghiaus C. 14). For ach indoor spac h moisur balanc is calculad by nglcing h moisur xchang bwn h air nod and h surrounding building surfacs. In ach τ-h simulaion im sp and for ach hrmal zon (z = 1, ), h adopd moisur balanc is: g,1 v,1,n+1 1 w, Zon, la din z AC,, *,,,, z in z mv z ou z in z mwg z d hvs whr Ωin in is h indoor dry air mass; air vnilaion mass flow ra; (6) m v is h m wg is h inl war vapour mass flow ra o h hrmal zon (du o occupans); ωou* and ωin ar h xrnal and indoor air spcific humidiy, rspcivly (no ha h xrnal air spcific humidiy is rfrrd o h: i) oudoor air for zon 1; ii) zon 1 air for zon ); hvs is h war lan vaporaion ha a C..1 ducd ordr modl For conrol aims, a linar simplifid modl was drivd. Such a modl sms from h abov prsnd high ordr on (of (M x N) + nods (qs. (1) and ()) rlad o zon 1) which has bn simplifid ino a linar and s-ordr modl, xploid for h rfrnc modl dsign, whr: i) h hrmal capaciy of h whol building nvlop of zon 1 is lumpd in a singl nod; ii) h inpu signals acing on h hrmal nwork nods ar: ou, x I, gr and g,1 ; iii) an quivaln hrmal rsisanc of h building nvlop for inrnal and xrnal surfacs is adopd; iv) wighd avrag hrmal propris ar assumd. hus, qs. (1) and () bcom: d x -1 w,1 ou -w,1 I hou in,1 -w,1 gr -w,1 C w,1 = d q q q q x x in gr As a consqunc, quaion (4) bcoms: d - - ou -in,1 in, -in,1 in,1 w,1 in,1 w, in,1 C in,1 = q g,1 ± AC,1 d in 1 v v,zns (7) (8) As an xampl, for h snsibl load calculaion, h following vcors and marics ar considrd: i) mpraurs vcor of h lumpd nvlop and indoor air hrmal capaciancs of boh h zons, x = w,1 in,1 w, in, ; ii) vcor of snsibl ha o b supplid or rmovd from h building spac, u = AC,1 AC, ; iii) h upl (A, B, C) of dynamic marix A, inpu and h oupu vcors B -1-1 and C (.g. B = Cin,1 C in, and C= 1 1 for h snsibl load calculaion), s Scion 3. 11

5 Muli-zon buildings hrmo-hygromric analysis: a novl dynamic simulaion cod basd on adapiv conrol 3. h nhancd opimal L-MAC algorihm In ordr o conrol h hrmo-hygromric bhaviour, a nw conrol schm ha nhancs h classical Modl frnc Adapiv Conrol (MAC) sragy proposd by Landau (Landau I. D. (1979)) is adopd. h novl conrol algorihm (namd Linr-uadraic Enhancd Modl frnc Adapiv Conrol, L-EMAC) includs addiional conrol acions o improv h closdloop prformanc wih rspc o hos providd by h mor classical MAC approach. Furhrmor, i mbds as a rfrnc modl a rough plan modl conrolld via an L sragy (Andrson B.D.O. and Moor J.B. 1971). his implis ha closd-loop dynamics, opimal wih rspc o a givn prformanc indx, ar imposd o h plan undr invsigaion via h adapiv acion. Mor prcisly, h rfrnc modl is a rough simaion of plan dynamics: x = A x + B u, y = C x (9) (whr x n is h plan sa, uy, ar h conrol inpu and h sysm oupu, rspcivly, A n n is h dynamic marix, and B n, C 1 n ar h inpu and h oupu marics, rspcivly, wih n bing h sa spac dimnsion) drivn by a full sa opimal fdback conrol acion as: op op uop K x K r bing (1) op 1n op K, K som fixd conrol paramrs. From Opimal Conrol hory, i follows ha h conrol signal in (1) minimizs a quadraic funcional of h form: + J = y()- r y()- r +u ()u() d (11) (whr r is h s-poin o impos o h plan oupu, is h iniial im insan, and ar som posiiv marics). As a rsul, h closd-loop opimal dynamics o b imposd o h plan ar h soluions, xm, of h following opimally-conrolld im-invarian sysm: x A x B r (1) m m m m bing op Am A B K and B BK op m. Dails on h conrol algorihm and h conrol gains adapaion mchanism can b found in h following Appndix. 4. Cas sudy and dsign of h L- EMAC algorihm h prsnd cas sudy rfrs o a musum indoor spac in which wo hrmal zons ar modlld. In paricular, h firs zon rfrs o a musum hall whil h s on (oally includd in h firs zon) o a glass display cas wih an accura clima conrol (rigid consrains of mpraur and humidiy of h cas indoor air) ncssary o prsrv collcd xhibis such as: pains, woods, paprs and lahrs (which rquir suiabl iions of indoor air mpraur and rlaiv humidiy, simulanously). h skch of h wo-zon building is shown in Fig. 3. h simulaion, carrid ou by DEEC.3, rfrs o h wahr zon of Napls (souhrn Ialy), by using a Monorm hourly daa fil. For zon 1, a ypical Ialian building nvlop is akn ino accoun, wih lngh, widh and high qual o, 1 and 3.5 m, rspcivly. h building s longiudinal axis is as ws orind and a souh-facing windows (4-6-4 air filld doubl-glazd sysm) of 3 m is akn ino accoun. h hicknss of h building s walls and floor/ciling ar 5 and 3 cm, rspcivly. hir sraigraphy is dsignd by concr bricks (λ =.51 W/mK, ρ = 14 kg/m 3, c = 1 J/kgK) and hrmal insulaion (λ =.4 W/mK, ρ = 15. kg/m 3, c = 14 J/kgK). No ha ach building lmn is subdividd in 1 sub layrs of qual hicknss. h dirc solar radiaion ransfrrd hrough h windows o h insid zon is assumd o b absorbd by h floor wih an absorpion facor of.3. h absorpion and mission facors of inrior surfacs ar assumd o b qual o.15 and.9, rspcivly. For such a zon, a vnilaion ra qual o 1 Vol/h and a crowding indx of.1 prson/m ar akn ino accoun. A cubic shapd zon wih a 1 m lngh sid is considrd. In paricular, a glass nvlop of 3 cm hicknss, wih an occurring air infilraion of l/h is modlld. h simulaion sars on : of January 1 s and nds a 4: of Dcmbr 31 s. h haing/cooling sysm of h hrmal zon 1 is swichd on from 7: o 18:, from Novmbr 1 s o March 31 s (haing mod) and from Jun 1 s o Spmbr 3 h (cooling mod). h haing and cooling s poins 113

6 Annamaria Buonomano, Umbro Monanaro, Adolfo Palombo, Sfania Sanini indoor air mpraur ar s a 19 and 5 C, rspcivly. h rlaiv humidiy of h zon 1 indoor air is conrolld a 5%. h haing/cooling sysm of h hrmal zon is swichd on 4/7 o accuraly consrv h cas xhibid ims. Hr, h indoor air mpraur and rlaiv humidiy ar conrolld hroughou h yar a C and 65%, rspcivly. h L-EMAC has bn implmnd o conrol h air mpraur and humidiy, simulanously, of boh h modlld hrmal zons. In paricular, following a dcnralizd conrol approach (ach conrol variabl is usd o impos h dynamic bhaviour of only on variabl o b conrolld, s Pdro A. and Sala A. (4)), four diffrn and indpndn adapiv conrollrs ar synhsizd. In ordr o dsign h L-EMAC conrol, h simplifid modls (s Scion.1) wr adopd as nominal modls o b opimizd via h L approach, by sing o zro h disurbanc acing on h plan dynamics. No ha h choic of hs simplifid modls rducs h complxiy of h conrol dsign, wihou jopardizing h closd-loop prformanc. No ha h opimaliy and robusnss of h closd-loop conrol is guarand by h adapiv acions, whos gains volv o compnsa any paramr mismach and/or prsnc of unmodlld dynamics (s Appndix), and o assur h minimizaion of a quadraic cos funcion, for indoor air mpraur and humidiy racking rrors and snsibl and lan loads. hus, h minimizaion of haing and cooling dmands can b also achivd. In so doing, diffrn from classical fixd gains algorihms lik PI (implmnd in h prvious DEEC rlas), h proposd approach allows on o impos, on h sysm undr conrol, a dynamic bhaviour ha can also b opimal from h nrgy dmand poin of viw. h wigh marics ( and, which dfin h cos funcion in q. (11)) wr s in ordr o impos: i) a sling im of 5 minus for zon 1 and 1 minus for zon ; ii) absnc of ovrshoos for any sp variaion of h rfrnc signal. h choic of h rlaxaion im of zon 1 is don according o (Ghiaus C. and Hazyuk I. 1), wih h aim o nsur a smooh daily ransiion during h ransin opraion oward h rgim s-poin (conrol sysm is swichd on from 7: o 18:). Conrarily, a fasr ransin rquirmn is imposd on h sling im of zon bcaus of is rigorous hrmo hygromric rquirmns. Finally, h rfrnc inpu signals (r in Scion 3) dpnds on h slcd mpraur and humidiy s poins. No ha h humidiy conrol is obaind hrough h inpu rfrnc s poin of indoor air spcific humidiy (ωsp), in ordr o achiv h slcd rlaiv humidiy s-poin (φsp). 5. suls and discussion In h following, h rsuls rlad o h ffcivnss assssmn of h novl DEEC conrol approach, in imposing rfrnc indoor air mpraur and humidiy dynamics, ar shown. h analysis rfrs o boh h invsigad hrmal zons 1 and. As mniond abov, mpraur and humidiy ar conrolld daily from 7: o 18: in zon 1 and 4/7 in zon (for prsrvaion purposs of h xhibid ims). Fig. 4 shows h dynamic rnd of zon 1 indoor air mpraur, for wo sampl winr days (January 13 h and 14 h, i.. h 13 h and 14 h days of h yar) and for wo sampl summr days (July 5 h and 6 h, i.. h 6 h and 7 h days of h yar). Hr, a saisfacory prformanc of h dvlopd closdloop conrol schm can b obsrvd (coincidn rfrnc and obaind mpraur profils). No ha h s poin mpraur shifs from 19 C (for h winr sason) o 5 C (for h cooling sason). In Fig. 5 h im hisory of h indoor air mpraur during h ransin HVAC sysm rgim (sling im from 7: o 8:3) is shown for January 13 h. Also hr h obaind mpraur profil ovrlaps h dsird rfrnc on. ( C) Fig. 4 Zon 1 - Conrolld indoor air mpraur (rd solid lin for January 13 h and 14 h and blu dashd lin for July 5 h and 6 h ) and rfrnc mpraurs (grn dashd lin). 114

7 Muli-zon buildings hrmo-hygromric analysis: a novl dynamic simulaion cod basd on adapiv conrol ( C) 17 (kw) im (h) Fig. 5 Swichd on HVAC sysm in zon 1 in January 13h - im hisory of h indoor air mpraur (rd solid lin), rfrnc mpraur (grn dashd lin), s poin mpraur (black dashd lin). Fig. 6 shows h dynamic rnd of zon 1 indoor air humidiy for July 5 h and 6 h (Fig. 6a) and h lan load (dhumidificaion) rsuling from h conrol acion (Fig. 6b). Hr, h spcific humidiy s poin is 1 g/kg, corrsponding o a rlaiv humidiy of 5%. As in Fig. 5, Fig. 6c shows h im hisory of h indoor air humidiy during h sling im, for July 6 h. No ha h obaind humidiy profils ovrlap h dsird rfrnc ons. In Fig. 7, h snsibl hrmal load ( AC, 1), calculad according o h mpraur conrol of Fig. 4, is rpord. A similar bhaviour is obaind la for AC, 1 (no shown for sak of brviy). (g/kg) a) c) im (h) (W) (g/kg) - b) Fig. 6 Zon 1: a) conrolld indoor air humidiy (grn solid lin), b) lan hrmal load (grn dashd lin), c) humidiy im hisory during h sling im (grn solid lin) - frnc humidiy (rd dashd lin) Fig. 7 im hisory of zon 1 snsibl hrmal load (rd lin haing mod - January 13 h and 14 h, blu lin for cooling mod - July 5 h and 6 h ) - AC,1. Wih h hlp of hs simulaion rsuls, som conclusions can b highlighd, such as: i) mpraur and humidiy s poins (conrol aim) ar always saisfacorily achivd for any iniial indoor air mpraur and humidiy and vry disurbanc; ii) ypical xponnial bhaviours of asympoically sabl linr-im-invarian sysms (wih uni gain, ral ignvalus and a sling im of abou on hour) occur for boh h mpraur and humidiy conrols during h ransin HVAC rgims; iii) smooh dynamic rnds of h conrolld variabls and corrsponding haing and cooling dmands (conrol acions) ar obaind. I is noworhy o rmark ha a good racking prformanc of h closd-loop conrols is achivd. Vry low roo man squard rrors ar obaind (.4 C and g/kg for h air mpraur and humidiy conrol, rspcivly). In Fig. 8, for zon (whr a coninuous conrol of boh h mpraur and humidiy is rquird), h obaind rgulaion rror for h indoor air mpraur is shown (from April 9 h o May nd ). Such conrol rror is boundd wihin.1 C, dspi h significan oscillaion of h yarly indoor air mpraur of zon 1 (which rang from h minimum winr mpraur of 1 C and h maximum summr on of 3 C). In all hs figurs, h gry shadd rgions rfr o unoccupid hours, during which h HVAC sysm is swichd off and fr floaing hrmohygromric iions and null conrol acions occur. 115

8 Annamaria Buonomano, Umbro Monanaro, Adolfo Palombo, Sfania Sanini.1 Zon mpraur rror ( C) Zon 1 indoor air mpraur (W) Fig. 8 gulaion mpraur rror wihin zon and indoor air mpraur of zon 1 (up-righ cornr). Corrspondingly, h humidiy conrol rror vs. h slcd s poin in zon is lowr han 1-8 for h nir simulad yar, dspi a significan zon 1 humidiy variaion (from 4o 15g/kg), as clarly dpicd in FFig. 9. (-) 1 x x 1-8 Zon humidiy rror Zon 1 humidiy Fig. 9 gulaion humidiy rror wihin zon and indoor air mpraur of zon 1 (up-righ cornr). Obviously, boundd conrol acions ar h rsul of boundd conrol gains, as clarly shown in Fig. 1. Hr, as an xampl, h dynamic rnd of h snsibl hrmal load of zon ( AC, ), rsuling from h conrol of h indoor air mpraur from April 9 h o May nd (s also Fig. 8) is rpord. As xpcd, h zon hrmal loads ar much smallr han hos in zon 1. No ha, in Fig. 1, haing and cooling loads (as wll as humidificaion and dhumidificaion dmands) ar dcd, bcaus of h coninuous hrmo-hygromric conrol (i.. no gry shadd rgions occur in figur). F Fig. 1 im hisory of zon snsibl hrmal load - AC,. Finally, in Fig. 11 for boh h invsigad hrmal zons, h calculad haing and cooling (snsibl and lan) yarly uniary dmands, ar shown. Hr, i can b obsrvd ha h cooling dmands ar rmarkably highr han h haing ons (according o h high inrnal gains assumd for zon 1 and o h simulad wahr iions). In addiion, i is worh noing ha for zon h humidificaion and dhumidificaion dmands vs. h snsibl ons ar proporionally highr han hos occurring in zon 1. [kwh/m y] - -4 Zon 1 Zon Snsibl Haing Humidificaion Snsibl Cooling Dhumidificaion Fig. 11 Haing and cooling snsibl and lan dmands. his rsul is du o h coninuous humidiy conrol of zon and o h considrd indoor air mpraur and rlaiv humidiy s poins (in, = C, φsp = 65%). Noic ha, during h haing and cooling priods slcd for h hrmal zon 1, h humidificaion and dhumidificaion rquirmns of zon ar abou 78 and 89% of h rlad yarly calculad dmands, rspcivly. 6. Conclusion In his papr, nw faurs of h in-hous dvlopd compur cod (calld DEEC.3) for h building dynamic nrgy prformanc simulaion ar prsnd. h cod, dvlopd for 116

9 Muli-zon buildings hrmo-hygromric analysis: a novl dynamic simulaion cod basd on adapiv conrol rsarch purposs, nabls h auhors o modl and analys nw prooypal chnologis, nonsandard opraing iions, paricular sysm schduling, c., which canno b dal wih (or simulanously akn ino accoun) hrough commrcial BEPS cods. From his poin of viw, anohr advanag of DEEC is h possibiliy o upda and modify all h includd modls for ach occurring rsarch nd. Wih h hlp of h prsnd cod rlas, muli-zon buildings, consising of hrmal zons oally nclosd ino ohrs, can b modlld. In addiion, all h simulad zons can b govrnd by rigid assignd hrmo-hygromric consrains. his is accomplishd hrough an innovaiv adapiv conrol sragy (calld L-EMAC). Hr, h onlin adapaion of h conrol gains is achivd in ordr o assur h minimizaion of a quadraic cos funcion, which wighs boh h mpraur / humidiy racking rror and h snsibl / lan nrgy dmand. h conrol algorihm was dsignd on a simplifid fourh ordr modl. hn, i was sd and applid on h original and daild DEEC on, basd on mor han 7 diffrnial quaions. In his papr, h ffcivnss of h proposd novl building simulaion ool was vrifid hrough a suiabl cas sudy in which wo hrmal zons of a musum building ar modlld. Hr, a glass display cas wih a rigid mpraur / humidiy micro-clima conrol (for prsrving aims) is nclosd in a larg indoor spac. Simulaion rsuls show vry good racking prformanc of air mpraur and humidiy, simulanously, in boh h simulad hrmal zons. Boundd conrol gains and haing and cooling loads (during h ransin rgim) ar obaind. suls also confirm h robusnss of h dvlopd conrol approach for unmodlld dynamics. Appndix h L-EMAC conrol acion is: u( ) umac ( ) ui ( ) ue( ) (13) wih umac K( ) x( ) K( ) r( ), ue KE sgn y, and xi x() d. h im-varying u K x I I I conrol gains (adapiv gains) ar compud as: K( ) y ( ) x ( ) d y ( ) x ( ) K ( ) y ( ) r( ) d y ( ) r( ) I I d I K ( ) y ( ) x ( ) y ( ) x ( ) K () y d E whr,,, n, wih (14) n bing h nn subspac of diagonal marics in and,, ar som adapiv wighs wih h op sam sign of K assumd o b known (Ioannou P. and Fidan B. 6). h oupu rror y is compud as y C x, bing x ( ) x ( ) x( ) and C B P wih P soluion of h Lyapunov m quaion (Andrson B.D.O. and Moor J.B. (1971), PA A P M, M >. m m Nomnclaur Symbols C hrmal capacianc (J/K) h civ ha ransfr coff. (W/m K) hvs war lan vaporaion ha (J/g) I irradianc (W/m ) m flow ra (g/s) hrmal load (W) ω Ω hrmal rsisanc (K/W) mpraur (K) im (s) air spcific humidiy (g/g) dry air mass (g) Subscrips/Suprscrips AC q x g gr in in la ou rfrrd o h HVCAC sysm ucion cion quivaln xrnal inrnal gain al ground indoor air inrnal lan oudoor air m 117

10 Annamaria Buonomano, Umbro Monanaro, Adolfo Palombo, Sfania Sanini v vnilaion w nclosd zon nvlop wg war vapour frncs Andrson B.D.O. and Moor J.B. (1971). Linar Opimal Conrol, Englwood Cliff NJ, Prnic Hall. Buonomano A. and Palombo A. (14). "Building nrgy prformanc analysis by an in-hous dvlopd dynamic simulaion cod: An invsigaion for diffrn cas sudis." Applid Enrgy 113(): Di Brnardo M. al. (8). "Novl hybrid MAC- L conrol schms: synhsis, analysis and applicaions." Inrnaional Journal of Conrol 81(6): Ghiaus C. (14). "Linar algbra soluion o psychomric analysis of air-iioning sysms." Enrgy 74(): Ghiaus C. and Hazyuk I. (1). "Calculaion of opimal hrmal load of inrminly had buildings." Enrgy and Buildings 4(8): Ioannou P. and Fidan B. (6). Adapiv Conrol uorial: Advancs in Dsign and Conrol, SIAM. Landau I. D. (1979). Adapiv Conrol, h modl rfrnc approach, Springr-Varlag. Pdro A. and Sala A. (4). Mulivariabl Conrol Sysms: An Enginring Approach, Springr. Shaikh P. H. al. (14). "A rviw on opimizd conrol sysms for building nrgy and comfor managmn of smar susainabl buildings." nwabl and Susainabl Enrgy viws 34():