Bi-level Optimization Method of Air-conditioning System Based on Office Building Energy Storage Characteristics

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1 IOP Cnference Seres: Materals Scence and Engneerng PAPER OPEN ACCESS B-level Optmzatn Methd f Ar-cndtnng System Based n Offce Buldng Energy Strage Characterstcs T cte ths artcle: Qngze Wang et al 017 IOP Cnf. Ser.: Mater. Sc. Eng Related cntent - Cmfrt ar temperature nfluence n heatng and clng lads f a resdental buldng C Stancu, I rga, A T Gherghan et al. - A B-Level Partcle Swarm Optmzatn Algrthm fr Slvng Unt Cmmtment Prblems wth Wnd-EVs Crdnated Dspatch Le Sng and B Zhang - System slutn t mprve energy effcency f HVAC tems L Chreten, R Becerra, N P Salts et al. Vew the artcle nlne fr updates and enhancements. Ths cntent was dwnladed frm IP address n 4/11/017 at 1:44

2 017 nd Asa Cnference n Pwer and Electrcal Engneerng (ACPEE 017) IOP Publshng IOP Cnf. Seres: Materals Scence and Engneerng (017) d: / x/199/1/01093 B-level Optmzatn Methd f Ar-cndtnng System Based n Offce Buldng Energy Strage Characterstcs Qngze WANG 1, Xngyng CHEN 1,, a, L JI 1,, Yngchen LIAO 1, and Kun YU 1,3 1 Cllege f Energy and Electrcal Engneerng, Hha Unversty, Nanjng 11100, Chna Jangsu Engneerng Research Center fr Dstrbutn & Utlzatn and Energy Effcency, Nanjng 11100, Chna 3 Nanjng Heha Scence and Technlgy Ltd, Nanjng 10098, Chna a Crrespndng authr : xychen@hhu.edu.cn Abstract. The ar-cndtnng tem f ffce buldng s a large pwer cnsumptn termnal equpment, whse unreasnable peratn mde leads t lw energy effcency. Realzng the ptmzatn f the ar-cndtnng tem has becme ne f the mprtant research cntents f the electrc pwer demand respnse. In ths paper, n rder t save electrcty cst and mprve energy effcency, b-level ptmzatn methd f ar-cndtnng tem based n TOU prce s put frward by usng the energy strage characterstcs f the ffce buldng tself. In the upper level, the peratn mde f the ar-cndtnng tem s ptmzed n rder t mnmze the uses electrcty cst n the premse f ensurng user cmfrt accrdng t the nfrmatn f utdr temperature and TOU prce, and the clng lad f the ar-cndtnng s utput t the lwer level; In the lwer level, the dstrbutn mde f clng lad amng the mult chllers s ptmzed n rder t maxmze the energy effcency accrdng t the characterstcs f each chller. Fnally, the expermental results under dfferent mdes demnstrate that the strategy can mprve the energy effcency f chllers and save the electrcty cst fr users. 1. Intrductn Wth the develpment f ecnmy, the number f ffce buldngs n cty s ncreasng, whle the arcndtnng tem s the hghest energy cnsumer n a buldng. Ar-cndtnng lad has accunted fr 30%~50% f the summer peak lad n sme large and medum-szed ctes[1]. The water cled central ar-cndtnng tem s usually used n ffce buldng, whch has gd clng effect, and s manly cnsst f clng twer, chllers, ar treatment unt, ar supply ppe et al.[]. Amng them, the pwer cnsumptn prprtn f chllers s the bggest, whch can reach mre than 80% f the arcndtnng tem[3]. There are tw man reasns fr the hgh pwer cnsumptn f the current ffce buldng ar-cndtnng tem: 1) The unreasnable settng temperature; ) The unreasnable lad rate dstrbutn amng the mult chllers[4][5]. Therefre, t mprve energy effcency f arcndtnng tem and save the electrcty cst fr users, hw t take c-ptmzatn between the settng temperature and lad rate dstrbutn, has mprtant sgnfcance. Ar-cndtnng lad belngs t a temperature cntrl lad (TCL), wth the energy cnversn and strage characterstcs[6]. Many schlars have carred n related researches n the ptmzatn f arcndtnng tem. The research n [7] measured and analyzed the effect f pre-clng and ndr Cntent frm ths wrk may be used under the terms f the Creatve Cmmns Attrbutn 3.0 lcence. Any further dstrbutn f ths wrk must mantan attrbutn t the authr(s) and the ttle f the wrk, jurnal ctatn and DOI. Publshed under lcence by IOP Publshng Ltd 1

3 017 nd Asa Cnference n Pwer and Electrcal Engneerng (ACPEE 017) IOP Publshng IOP Cnf. Seres: Materals Scence and Engneerng (017) d: / x/199/1/01093 temperature resettng strategy appled t a medum densty ffce and fund the pwer lad f arcndtnng decreased a lt wthut causng peple s dscmfrt. The research n [8] analyzed the effect f the demand respnse cntrl strategy n the whle buldng energy cnsumptn, and the results shwed that the pre-clng strategy can reduce by 10~0% f the verall cst. The research n [9] made a research n shftng strategy f ar-cndtnng by usng actual measurement and fast evaluatn sftware fr demand respnse and the results shwed that the pre-clng strateges f ndex-type and step-type are mre effectve. These researches are manly based n the actual measurement and buldng energy cnsumptn sftware, whch lack f ar-cndtnng tem energy cnsumptn mdel and neglect the perfrmance dfferences f chllers t ptmze the clng lad dstrbutn. TOU prce, as an mprtant measure f demand respnse, has been gradually ppularzed and prmted. The ar-cndtnng tem cntrller wth the functn f advanced cmputng capablty s prpsed n [10], whch can prvde the best rat f cmfrt / cst and reduce the energy cnsumptn. In[11], accrdng t the predcted value f the utdr temperature and the electrcty prce sgnals t cntrl the ar-cndtnng tem, the mult-bjectve ptmzatn methd s ffered n ths paper. Based n the abve cnsderatns, the ffce buldng s used as energy strage devce n ths paper. The b-level ptmzatn methd f central ar-cndtnng tem s put frward cnsderng TOU prce. In the upper level mdel, t mnmze the cst f ffce buldng, the pre-clng tme and settng temperature f ar-cndtnng tem s ptmzed. In the lwer level mdel, the lad rate f each chller s ptmzed t maxmze the COP (Ceffcent f Perfrmance). At last, the case verfes the effectveness f the prpsed strategy.. Energy cnsumptn mdel f ar-cndtnng tem.1. Clng lad calculatn f ffce buldng In ths paper, the heat balance methd s used t establsh the energy cnsumptn mdel f arcndtnng tem t descrbe the relatnshp between ar-cndtnng clng lad and ndr temperature, utdr temperature[1]. q Ah ( T T ) mc ( T T ) E 0 (1) p T MCm Ah ( T T ) Ah ( T T ) 0 () t Where, q s the clng lad sent t the ndr by ar-cndtnng n rder t cunteract the heat; Ah ( T T ) s cnvectn heat frm the external heat strage materal t the ndr ar, where A s the area f the surface f the external heat strage materal, h s the cnvectn ceffcent between external heat strage materal and ndr ar, T s temperature f ndr ar and T s temperature f external heat strage materal. mc ( T T ) s the heat that nfltrates nt the ndr p 1/n thrugh the dr, cracks etc. Where m al P, P s pressure dfference nsde and utsde the envelpe, n s ar-tghtness ceffcent, asscated wth the degree f tghtness drs and wndws and s between 1 and. The gd ar-tghtness s clse t, the wrse ar-tghtness s clse t 1. l s the gap length f drs and wndws. a s leakage ceffcent f unt length gap. C s the specfc heat rat f the ar. E s the ttal heat generated by the nternal heat surce f the buldng, whch s T assumed t be a cnstant. MCm s the heat change caused by temperature change f external heat t strage materal, where M s qualty f external heat strage materal, and C m s specfc heat rat f external heat strage materal; Ah ( T T ) s cnvectn heat frm external heat strage materal p

4 017 nd Asa Cnference n Pwer and Electrcal Engneerng (ACPEE 017) IOP Publshng IOP Cnf. Seres: Materals Scence and Engneerng (017) d: / x/199/1/01093 t the utdr ar, where h s the cnvectn ceffcent between external heat strage materal and utdr ar, and T s utdr temperature. Frm the research, the trgnmetrc functn curve can be ftted well by the utdr temperature varatn, suppsed that the utdr temperature s T T T sn( t ). The temperature change f the heat strage materal and the change f the clng lad s shwn as (3) and (4), respectvely. T T t T T sn( t )+ C e 1 t 1 1 t E mc ( T T ) p { 1 + P v C Pqv CPqv q t C q T T T sn t C e Where, C 1 s cnstant; 1 tan ( / ( )), whse value s frm 0 t / ; = / 4h ; MC / C q s tme cnstant based n ventlatn rate durng the nght, where s ar densty; m p v h A / C q s the ceffcent f cnvectve heat transfer between heat strage materal and p v utdr ar; h A / C q s the ceffcent f cnvectve heat transfer between heat strage p v materal and ndr ar. The pre-clng perd s tp ~ t 1, the nternal heat gan s 0, where there s ar nfltratn, and the clng lad s btaned frm the heat balance equatn: mc ( T T ) p { P v Cq P v q t C q T T T sn t φ C e 1 1 } t Durng t ~ tp 4, the nternal heat gan s 0, ar-cndtnng tem s ff, ventlatn rate f ventlatn tem s q v, as a cnstant, and ar nfltratn heat can be neglected. The wall temperature can be gt frm the heat balance equatn, as (6): 1 1 (1 ) sn t T T t T + T t C e (6).. Pwer calculatn f ar-cndtnng tem In rder t ensure the clng capacty f the ar-cndtnng tem, ffce buldngs are usually equpped wth multple chllers. Suppse that the number f chllers s n, clng capacty f central ar-cndtnng can be calculated as fllws: n cl N, 1 } L ( t) COP ( t) ( t) P (7) Where, () t s the lad rate f the th chller at tme t ; P N, s rated pwer f the th chller; COP reflects the peratn cndtn f chllers, and s the mprtant ndex f energy effcency f arcndnng. The relatnshp between COP and lad rate s: COP ( t) a b ( t) c[ ( t)] (8) Where, a, b and c are ceffcent, whch s related t the characterstcs f chller. Durng the wrkng tme, the frmula (9) can be establshed frm the heat balance equatn. (3) (4) (5) 3

5 017 nd Asa Cnference n Pwer and Electrcal Engneerng (ACPEE 017) IOP Publshng IOP Cnf. Seres: Materals Scence and Engneerng (017) d: / x/199/1/01093 q ( t) L ( t) (9) Where, s dsspatn factr, generally 0.8~0.9, and 0.8 s taken n ths paper. Frmula (10) can be btaned frm the frmula(7), (8)and(9). cl n 3 ( ) ( ( ) [ ( )] [ ( )] ) N, 1 q t a t b t c t P (10) Pwer cnsumptn f ar-cndtnng tem can be btaned frm frmula(10). n P ( t) ( t) P (11) ar N, 1.3. Calculatn f thermal cmfrt In ths paper, the PMV-PPD ndex n ISO 7730 s used t descrbe and evaluate the thermal cmfrt f human. The PMV ndex s dvded nt seven levels. The relatnshp between temperature sense and PMV ndex s as shwn n Table1. Table 1. The relatnshp between temperature sense and PMV ndex temperature sense ht warm slghtly warm neutral slghtly cl cl cld PMV ndex In Chna, the range f PMV s -1 PMV +1 accrdng t desgn cndtns f ar-cndtnng tem n <Standard fr desgn f heatng ventlatn and ar-cndtnng> (GB ). The calculatn f PMV s very cmplex. T smplfy the calculatn, the PMV value s calculated by the dmensnless ndex f evaluatng thermal envrnment prpsed n [13]. PMV K T 0.13K T 5.97 (1) Where, K A A A j s the area f j th surface f the rm. (13) j j1 j0 5 j0 3. B-level ptmzatn mdel f ar-cndtnng tem j j K A A (14) 3.1. B-level ptmzatn mdel The B-level ptmzatn mdel f ar-cndtnng tem s as shwn n Fgure 1.In the upper level mdel, the buldng s used as energy strage devce. And durng the perd f lw prce, arcndtnng can pre-cl thermal mass, whle durng the perd f hgh prce, the cld can be released t rm t reduce the clng lad f ar-cndtnng tem cnsderng the TOU prce. In the lwer level mdel, the dstrbutn mde f clng lad amng the mult chllers s ptmzed n rder t maxmze the energy effcency accrdng t the characterstcs f each chller. Offce buldng Lw prce Pre-cl Thermal mass (Cld strage) hgh prce Released t rm P 1 :Optmzng peratn mde f ar-cndtnng tem clng lad Chllers Chller 1 Chller Chller n P :Optmal dstrbutn f clng lad amng mult chllers Fgure 1. The B-level ptmzatn mdel f ar-cndtnng tem 4

6 017 nd Asa Cnference n Pwer and Electrcal Engneerng (ACPEE 017) IOP Publshng IOP Cnf. Seres: Materals Scence and Engneerng (017) d: / x/199/1/ Upper level ptmzatn mdel Objectve functn. T save electrcty cst, the ar-cndtnng tem shuld adjust the settng temperature value dynamcally accrdng t the change f uter temperature t ensure the users cmfrt. S the electrcty cst and users thermal cmfrt shuld be cnsdered n the bjectve functn. tt * * mn f mn p( t) Par ( t) (1 ) PMV ( t) ttp (15) P ( t) P ( t) P (16) * ar ar ar, B PMV * (t) PMV ( t) PMV B (17) Where, s the weght ceffcent f electrcty cst and thermal cmfrt; P ar, B s reference pwer f ar-cndtnng tem; PMV s reference value f thermal cmfrt; And the reference B value s determned n the case f ndr temperature and heat strage materal temperature f Cnstrants.1) PMV shuld meet the requrement f standard. 1 PMV 1 (18) ) Settng temperature f ar-cndtnng tem Tmn T n Tmax (19) Where, T mn, T max are the lwer and upper lmt f settng temperature, respectvely. 3) Electrc pwer fr ar-cndtnng tem 0 P( t) P (0) Where, P max s the allwable maxmum electrc energy cnsumptn f ar-cndtnng tem Lwer level ptmzatn mdel Objectve functn. The gal f the lwer level mdel s t make the verall energy effcency f all chllers hghest, s the bjectve functn s: Where, n s the number f the chllers. n 1 max max COP ( t ) (1) e Cnstrants. Suppse that the expected lad rate f th chller s () t at t mment and the e expected ptmzatn s.the relatnshp between them s: e (t) a ( ) ( ) e ( ) f W t t t W () The expected ptmzatn capacty f each chller s: e a W ( t) ( t) W ( t) (3) 1) The expected ptmzatn needs t meet the requrements f the target ptmzatn: n W ( t) q ( t) (4) 1 Where, q () t s the bjectve ptmzatn capacty at t mment btaned frm the upper level. ) Lad rate cnstrants f chller e The expected lad rate () t f th chller cant be lwer than the lwest lmt f lad rate: 0 e ( ) 1 (5) t 5

7 Temperature( C) 017 nd Asa Cnference n Pwer and Electrcal Engneerng (ACPEE 017) IOP Publshng IOP Cnf. Seres: Materals Scence and Engneerng (017) d: / x/199/1/ Case study 4.1. Basc nfrmatn Buldng nfrmatn. The ffce buldng lcates n Nanjng, Chna. The buldng area s 1780m, buldng sze s 48m 30m 36m, the thckness f wall s 40mm, the densty s 600kg/m 3, specfc heat s 0.96kJ/(kg K), the cnvectn heat transfer ceffcent frm external wall t external ar n summer s h =4.74W/(m K) and the cnvectn heat transfer ceffcent t nternal ar s h =.46W/(m K).The sze f the rm s 8m 6m 3m, the ventlatn rate durng nght s q v =450m 3 /h and the nternal heat gan s E =500W. ΔP s 6.4kg/m, n s 1 and l s m.the ar densty s 1.9kg/m 3 and specfc heat s 1.005kJ/ (kg K) The central ar-cndtnng tem nfrmatn. The buldng s equpped wth water cled central ar-cndtnng, wth 3 chllers that has the same rated capacty but dfferent COP curve. The rated capacty s 400kW, and lad rate lwer lmt s 60%. The COP functn respectvely s: COP a a COP a 14.69a COP a a Weather nfrmatn. The utdr temperature s ftted by the sne functn and the fluctuatn s T 3.85, the average s T sn t 10 / 1.The curve f utdr temperature s as shwn n Fgure T and (6) 5 0 actual temperature fttng temperature :00 :00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:0011:00 1:0013:00 14:0015:00 16:0017:00 18:0019:00 0:001:00 :00 3:00 Tme/h Fgure. The curve f utdr temperature Electrcty prce nfrmatn. The TOU prce nfrmatn s as shwn n Table. Table. The TOU prce perd prce/(yuan/kwh) Valley perd(1:00-8:00 the next day) 0.6 Peak perd(8:00-1:00) Result analyss The weght ceffcent f electrcty cst and thermal cmfrt s 0.5. The PSO algrthm s used t slve b-level ptmzatn mdel and takng the randmness f the PSO algrthm nt accunt, the average value f the 10 calculatn results s as the fnal slutn. The fllwng wll be analysed frm three aspects f electrcty cst, thermal cmfrt, energy effcency. 6

8 Settng Temperature( C) PMV Value 017 nd Asa Cnference n Pwer and Electrcal Engneerng (ACPEE 017) IOP Publshng IOP Cnf. Seres: Materals Scence and Engneerng (017) d: / x/199/1/ The analyss f electrcty cst. In rder t explan the effect f pre-clng strategy under TOU prce, the results f the cnstant temperature mde and the mde wthut pre-clng strategy, are cmpared, as shwn n Table 3. Table 3. Smulatn results under dfferent peratn mdes The dfferent peratn mdes electrcty cst(yuan) PMV The mde f cnstant temperature The mde wthut pre-clng strategy The mde wth pre-clng strategy It can be knwn frm Table 3 that the electrcty cst s the hghest but thermal cmfrt s the best when ar-cndtnng perates n the mde f cnstant temperature. Cmpared wth the cnstant temperature mde, the ptmzatn f settng temperature n the mde wthut pre-clng strategy makes the electrcty cst decreased by 7.79%. The users thermal cmfrt ndex has been reduced, but dd nt affect the users thermal cmfrt. Cmpared wth the mde f cnstant temperature and the mde wthut pre-clng strategy, the mde wth pre-clng strategy makes the electrcty cst decreased by 9.08% and 1.39%, respectvely. The reasn s that the TOU prce and buldng strage characterstcs are cnsdered n the mde wth pre-clng strategy. Thermal mass s pre-cled durng perd f the lw prce and the cld s stred n the thermal mass n advance; whle durng perd f the hgh prce, the cld stred n the thermal mass s released t the rm, thereby reducng the pwer cnsumptn f the arcndtnng tem The analyss f thermal cmfrt. The settng temperature and PMV s as shwn n Fgure 3 n the dfferent mdes The mde f cnstant temperature The mde wthut pre-clng strategy The mde wth pre-clng strategy Fgure 3. The settng temperature and PMV n dfferent peratn mdes It can be knwn frm Fgure 3 that the settng temperature s bascally flatng up and dwn at 6.5 n the mde wthut pre-clng strategy, whle the settng temperature s flatng up and dwn at 6.7. Althugh the settng temperature turn up, but the PMV ndex s stll wthn the scpe f the prvsns, whch wll nt cause the bdy uncmfrtable. The pre-clng strategy makes the settng temperature turn up, because the ar-cndtnng tem pre-cled the thermal mass durng the perd f lw prce and the cld wll be released nt rm s as t reduce the clng lad f arcndtnng tem durng the wrkng perd. In addtn, the PMV curve f three peratn mdes are relatvely stable, whch demnstrates that the ndr staff d nt feel smetmes ht and smetmes cld. Althugh the ptmzatn strategy reduces the PMV ndex slghtly, the ptmzed settng temperature s stll able t meet the thermal cmfrt requrements The analyss f energy effcency. The expected lad rate f every chller and the verall COP by slvng the b-level ptmzatn mdel, are shwn n Table 4. Tme 8:00 9:00 10:00 11:00 1:00 13:00 14:00 15:00 16:00 17:00 18:00 Tme/h Table 4. The relatnshp between temperature sense and PMV ndex Lad rate Chller 1 Chller Chller 3 0 Overall COP 7

9 017 nd Asa Cnference n Pwer and Electrcal Engneerng (ACPEE 017) IOP Publshng IOP Cnf. Seres: Materals Scence and Engneerng (017) d: / x/199/1/ : : : : : : : : : : : It can be knwn frm Table 4 that lad rates frm hgh t lw are chller, chller 1, chller 3, and the dstrbutn f lad s accrdng t the degree f new r ld. The lad rate f relatvely ld chller 3 s always lwer than that f the chller 1 and chller. The relatvely new chllers take mre lad, whch makes the verall COP maxmum and mprves the energy effcency f ar-cndnng tem. 5. Cnclusn Ar-cndtnng tem, as ne f the largest pwer cnsumptn f ffce buldngs, s ne f the mprtant means t acheve the demand respnse f ffce buldng users based n the TOU prce. The b-level ptmzatn methd put frward n ths paper cnsders utdr temperature, prce nfrmatn, users cmfrt and the perfrmance f chllers, and takes t mnmze users electrcty cst and maxmze the COP f chllers fr the target. Cmpared wth the cnstant temperature cntrl, the results shw that the prpsed methd can effectvely mprve the effcency f chllers and reduce the users electrcty cst. Acknwledgement Ths wrk s supprted by the Natnal Natural Scence Fundatn f Chna (N ), State Grd Crpratn f Chna (key technlgy research and applcatn fr dynamc ptmzatn f publc buldngs electrcty cnsumptn pattern) and Natnal Develpment and Refrm Cmmssn (the research, develpment and ndustralzatn fr ntegrated management f smart dstrbutn grd & utlzatn and enhancng energy effcency technlgy based n nternet f thngs). References [1] The buldng energy-savng Center f Tsnghua Unversty. Annual research reprt n the develpment f buldng energy savng n Chna 013[M]. Bejng: Chna archtecture and buldng press, 013. [] LI Canbng, SHANG Jncheng, ZHU Shuzhen, et al. An analyss f energy cnsumptn caused by ar temperature-affected accumulatve effect f the ar-cndtnng lad [J], Autmatn f Electrc Pwer Systems, 010, 34(0): [3] SONG Hngkun, TANG Guqng, LU Y, et al. Summer ar-cndtnng lad analyss and demand sde management measures n Jangsu prvnce [J]. Pwer System Technlgy, 006, 30 (17): [4] Yrdanva S, Merazchev D, Jan L. A Tw-Varable Fuzzy Cntrl Desgn Wth Applcatn t an Ar-Cndtnng System[J]. IEEE Transactns n Fuzzy Systems, 015, 3(): [5] SUN Xayu, LI Ru. Smulatn and analyss f jnt peratn strategy f chller [J]. Buldng Energy Effcency, 015 (4): [6] ZHOU Le, LI Yang, GAO Cwe. Ar-cndtnng lad plymerzatn temperature cntrl methd and mprved cntrl strategy f [J], Prceedngs f the CSEE, 014, 31: 16. [7] Xu P, Haves P, Pette M A, et al. Peak demand reductn frm pre-clng wth zne temperature reset n an ffce buldng[j]. Lawrence Berkeley Natnal Labratry, 004. [8] Mrgan S, Krart M. Impact f electrcty rate structures n energy cst savngs f pre-clng 8

10 017 nd Asa Cnference n Pwer and Electrcal Engneerng (ACPEE 017) IOP Publshng IOP Cnf. Seres: Materals Scence and Engneerng (017) d: / x/199/1/01093 cntrls fr ffce buldngs[j]. Buldng and envrnment, 007, 4(8): [9] YIN Rngxn. Calfrna ht clmates peak strateges f large cmmercal buldngs [D]. Tngj Unversty, a masters degree thess, 009. [10] Thmas A G, Jahangr P, Wu D, et al. Intellgent Resdental Ar-Cndtnng System Wth Smart-Grd Functnalty[J]. IEEE Transactns n Smart Grd, 01, 3(4): [11] ZHANG Yanyu, CENG Peng, LI Zhngwen, et al. Mult bjectve ptmzatn cntrl algrthm fr ar cndtnng tem n smart grd envrnment [J]. Pwer System Technlgy, 014, 38 (7): [1] Thmas A G, Jahangr P, Wu D, et al. Intellgent Resdental Ar-Cndtnng System Wth Smart-Grd Functnalty[J]. IEEE Transactns n Smart Grd, 01, 3(4): [13] YE Ha, WEI Runb. A smple methd fr bjectve evaluatn f the thermal envrnment [J]. Ergnmcs, 004, 10 (3):