Fraunhofer. Institut Umwelt-, Sicherheits-, Energietechnik UMSICHT

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1 IUSE Fraunhofr Institut Umwlt-, Sichrhits-, Enrgitchnik UMSICHT Nam: Dipl.-Ing. Michal Wigbls; Dr.-Ing. Wilhlm Althaus; Dipl.-Ing. Michal Lucht Institution: Fraunhofr Institut für Umwlt-, Sichrhits- und Enrgitchnik UMSICHT Addrss: Ostrfldr Straß 3; D Obrhausn; Grmany Tl.: Fax: mail: Rport Titl: Nonlinar Optimisation in CHP Applications Rport No. 1 1 Introduction At th Fraunhofr Institut UMSICHT a nonlinar modl has bn dvlopd facilitating th dynamic optimisation 1 of combind hat and powr production systms. Th stratgy calld dynamic supply tmpratur optimisation is a vry promising approach to us th DH-ntwork itslf as a larg hat storag causing no additional invstmnt cost. Th piplin systm of a district hating systm has a hug potntial for th storag of nrgy. Espcially for th application of rnwabl nrgis th optimal us of ths storag capabilitis will incras th ovrall fficincy. In particular for CHP systms with fixd hat and powr coupling (back prssur turbins), this approach could nabl a rduction of oprating hating plants and th displacmnt of xpnsiv pak powr plants. It will rduc lctrical powr paks and nabls a bttr utilisation of tariffs. Th supply tmpratur optimisation aims at finding th oprating point at which th powr rquirmnts (hat and lctrical nrgy) of th consumrs can b covrd with minimum oprating cost. In ordr to dtrmin th optimal valus of th variabls, th systm prformanc as wll as th tchnical and contractual rstrictions hav bn considrd in th mathmatical optimisation modl. Ths ar.g. th nrgy purchas contracts, th charactristics of th nrgy convrsion plants, th powr rquirmnt of th consumrs and th dynamic bhaviour of th DH ntwork. Ths connctions hav bn dscribd by quations and inquations, in which optimisation variabls and modl cofficints ar linkd togthr. On th basis of configuration and calculation data an optimisation modl has bn formulatd undr application of modrn optimisation procdurs. As rsults of ths optimisation modl th optimal courss of th supply tmpraturs of th individual supplirs, th lctrical and thrmal input powrs as wll as th storag powrs tc. can b rcivd. 2 Scintific and tchnical objctivs Sinc th volum of th DH-ntwork of a CHP systm is oftn mor than m 3, th piplin systm in particular nabls th storag of hat without additional invstmnt costs. In a DHntwork a tim of som minuts to svral hours passs btwn th input of hat at th production 1 In this contxt not th dynamic programming but th optimisation ovr a crtain tim priod is mant

2 plant and th output of this hat at particular consumr stations. In othr words, aftr incrasing th hat input thr is a tim priod in which th hat is stord in th DH-ntwork. Th maximal storag tim dpnds upon th distanc btwn th production plant and th consumr and th vlocity of th DH-watr. Thrfor, th charactristics of th nrgy supply systm s opration hav to b considrd to valuat th potntial for hat storag procsss. gnration and purchas simplifid ntwork load forcasts and unit commitmnt Fig. 2-1: Hat storag optimisation modl gnration and distribution costs ful consumption combind production purchas lctricity ara load covring pumping powr hat losss hat storag thrmohaydraulic tim charactristic critical prssurs nonlinar optimization modl load dispatch supply tmpratur profils C costs T v =f(t) dcras of pak loads lss powr purchas bttr utilization of tariffs h In ordr to dtrmin th optimisation potntial of hat storag procsss in th DH-ntwork of a DH or CHP systm, an algorithm for th dynamic optimisation has bn dvlopd. As input data, th tchnical and conomical structur of th nrgy production facilitis, th nrgy purchas as wll as th DH-ntwork including hat accumulators and th prognoss of th thrmal and lctrical powr rquirmnts of th consumrs is ndd (s figur abov). This prognoss data must b providd for th tim priod considrd for th optimisation. Basd on this data an appropriat optimisation modl has to b gnratd which nabls th considration of th dynamic thrmo-hydraulic bhaviour of DH and CHP systms du to dynamic nrgy production, distribution and dmand. Th dynamic pumping powr rquirmnt along with th hat loss has to b modlld. Spcial considration must b takn towards a suitabl mathmatical formulation for th complx dynamic procsss in th transport systm sinc this is ssntial whn modlling th hat storag procsss in th DH-systm. Th unit commitmnt, th load dispatch as wll as th opration of th bypasss and spcially th supply tmpraturs in all hat production plants must b considrd to facilitat th full potntial of th nrgy supply systm du to its optimisation by th hat storag procsss. 2.1 Mathmatical modl In th mathmatical modl Fraunhofr UMSICHT distinguishs btwn nrgy supply and DH ntwork. Th nrgy supply consists of systms for th nrgy convrsion, th contracts for th xtrnal supply of hat and lctrical powr as wll as th lctricity ntwork. Thy hav to b st up in such a way that th supply tmpratur is dclard as optimisation variabl. Th DH-ntwork is th most important part of th mathmatical modl. In this modl th thrmo-hydraulically dynamic bhaviour of th DH ntwork has to b modlld. This submodl is basd on mthods of th thrmo-hydraulic ntwork simulation.

3 Th mathmatical modl is basd on th sparation of th optimisation priod into quidistant tim stps with th tim incrmnt t. Th tim stps ar chronologically numbrd. Th starting point of th optimisation priod is th first tim stp. To gt a clarr formulation of th modl th first tim stp is dfind as zro point of th tim axis. Basd on this discrt rprsntation th modl is dividd into thr sctions for th dscription of th thrmo-hydraulical dynamic bhaviour of th DH ntwork: stady stat hydraulic modl stady stat thrmal modl dynamic thrmal modl. Du to th assumption of a quasi stady stat hydraulic bhaviour of th systm th stady stat hydraulic modl has to b st up for ach tim stp. Th stady stat thrmal modl srvs for th dfinition of a clar starting point for th dynamic optimisation. Du to th convctiv hat transport and th larg dlay tims in som pips a dynamic thrmal modl has to b dvlopd for ths componnts, which dscribs th dlay tim charactristic of th ntwork. For th othr componnts of th DH ntwork th dlay tim bhaviour can b nglctd. For ach lmnt of th DH-ntwork a adquat nonlinar modl has bn dvlopd. All sparat lmnts ar st up to an ovrall systm of linar and nonlinar rstrictions. It can b distinguishd btwn: Powr plants (Hating unit, CHP Unit of diffrnt typs) linar Hat xchangr nonlinar Valvs nonlinar Pumps nonlinar Pips nonlinar Consumr linar Purchas contracts linar To mak this systm solvabl th quations hav to b continuously diffrntiabl. For xampl th massflow dirction in pips can chang from on to anothr timstp what is an discontinuous procss. Thrfor, som modls do not fulfil this critrion. Th problm is solvd by approximation of th discontinuous modls by continuous functions. Th nxt diagram shows for xampl th approximation of th absolut function: y x + y y-appr ( = 0,5) y-appr ( = 2) y x Fig. 2-2: Approximation of continuously not diffrntiabl functions Th solution of th complt optimisation modl can b controlld by th approximation paramtr ; A bttr approximation usually lads to a problm which is mor difficult to solv.

4 2.2 Objctiv function Solving conomic qustions th attainabl profit oftn rprsnts th quality of a dcision. Howvr, th incoms of th nrgy supply company cannot b influncd by th opration mod and thrfor thy rprsnt a constant in th contxt of oprational planning. That is why instad of th profit th oprating costs ar usd for th valuation of th quality of an opration mod. Th costs of th nrgy purchas as wll as of th ful supply for th production systms ar th only costs influncd by th opration mod of th powr supply systm. Thrfor, th total costs K for th nrgy purchas and th ful supply ar formulatd as objctiv function of th optimisation problm. GHWK With K + K + K + K + K = 0 GTHWK SB HW WB GHWK: GTHWK: HW: SB: WB: St of production units with backprssur turbins St of production units with gasturbins St of production units with hat only boilrs (HOB) St of lctricity purchas contracts St of hat purchas contracts Targt of th oprational planning is th dtrmination of th opration mod with th minimum oprating costs. All th othr quations rprsnt constraints of th optimisation problm, which hav to b kpt. 3 Optimisation rsults Aftr svral tsts with virtual and small ral DH-systms th softwar prototyp for th nonlinar optimisation was tstd for th Vinna CHP-systm. Th actual CHP-systm of th Austrian DHcompany Frnwärm Win GmbH is dsignd for a total hat production and transport of 2790 MW, th maximum load of th yar 1999 was 1605 MW. In th sam yar 4540 GWh hat was supplid to thir customrs. Th hat supply taks plac in 11 powr units. Th basic load by wast incinration plants (21% of total hat production), in th man load by combind hat and powr production (73%) as wll as from gas/oil hat only boilrs (6%). Th actual transport and distribution ntwork covrs a total lngth of 974 km with a total volum of 76,000 m³ in th main transport ntwork. Thr ar 5030 substations attachd. By which 202,000 housing customrs and 4,400 big customrs ar supplid. Th DH-ntwork is dsignd on 25 bar/160 C and/or. 6 bar/90 C. Th dtaild ntwork topology is rprsntd in fig. 3.1 (lft). To carry out th nonlinar dynamic optimisation procss a highly simplifid DH-ntwork of th Vinna supply systm had to b dsignd by th simplification stratgy of DH-systms dscribd abov. Fig. 3-1 (right) shows th simplifid modl of th DH-systm in Vinna. Th numbr of substations and pips has dcrasd by almost 99 %. Th avrag rrors in trms of prssur and tmpratur diffrncs tc. ar lss than 5 %. Th simplification lvl is suitabl to carry out th optimisation procss and th accuracy is sufficint to guarant maningful rsults.

5 In ordr to tst th optimisation procdur a tim horizon of 24 hours has bn rgardd. For th hat and powr dmand profils wr givn in 2 hour incrmnts. This day can b charactrisd as a high load dmand day with hat load paks of up to 1300 MW and a total hat production of approx. 26 GWh. Th targt was to rciv an optimisd control rgim for th hat and powr units for that day. Mainly th hat and powr input and th supply tmpraturs of all activ input plants wr of intrst. Fig. 3-1: Dtaild (lft) and simplifid modl (right) of th Vinna DH-Systm Th optimisation procss took 9 hours using th solvr CONOPT on a SUN-sparc2-station with 400 MHz. It is obvious that this tim should b dcrasd highly by using mor modrn softwar and hardwar. It was possibl to rach a local optimum for th 24 hours optimisation horizon. Th following figurs show som rsults of th optimisation. On th lft sid of fig. 3-2 th total hat balanc for th DH-systm is illustratd. It can b sn that th two hat load paks at 6 am and at 4 pm ar shavd by taking hat from th DH-ntwork. Whil th hat load is lowr th DH-ntwork is loadd, so th DH-ntwork is usd as a big hat storag. Th hat load paks ar dcrasd by 150 MW and 40 MW, undrlining th big potntial of this control rgim. Espcially for companis with rigid hat and powr production and powr purchas contracts with powr costs dpndnt on th pak load this offrs a grat cost saving potntial. But also companis oprating cost ffctiv CHP-plants and cost intnsiv pak powr plants can bnfit by rplacing th lattr in pak tims using th DH-ntwork as a hat storag having bn loadd by th formr Q [MW] 600 T [ C] t [h] Hat Input Hat Load Hat Losss Hat Storag Hat Losss + Hat Load t [h] Si_3 Lo_GuD OMV Fig. 3-2: Optimizd ovrall hat balanc (lft) and supply tmpraturs of som powr units (right)

6 Th right sid of fig. 3-2 shows xmplary th supply tmpraturs of 3 powr units. Th production costs of th units Lo_GuD and Si_1 ar dpndnt from th supply tmpratur th units ar oprating. That is why th supply tmpraturs of this units ar kpt at a low lvl. Th costs of th powr unit OMV ar indpndnt from th supply tmpratur. Thrfor this powr unit is usd to initiat th loading procss of th DH-ntwork by incrasing it s supply tmpratur. Th rsults of th optimisation tsts carrid out in a coopration btwn Frnwärm Win GmbH and Fraunhofr UMSICHT show that thr might b som potntial for cost savings by an improvd control rgim using th DH-ntwork as a hat storag. As a nxt stp it is pland to vrify wathr th optimisd control rgim also in ral world opration lads to lowr oprating costs. 4 Litratur [1] Lown A.: Entwicklung ins Vrfahrns zur Aggrgation komplxr Frnwärmntz. Dissrtation, Univrsity of Dortmund [2] Lown A., Wigbls M., Althaus W. t. al.: Strukturvrinfachung komplxr Frnwärmsystm - Rproduzirbar mathmatisch Rduktion von Ntzrchnmodlln - Til 1 Eurohat & Powr; Frnwärm intrnational, Vol. 30, pp , May ISSN X [3] Lown A., Wigbls M., Althaus W. t. al.: Strukturvrinfachung komplxr Frnwärmsystm - Rproduzirbar mathmatisch Rduktion von Ntzrchnmodlln - Til 2 Eurohat & Powr; Frnwärm intrnational, Vol. 30, pp , Jun ISSN X [4] Althaus, W., Lucht, M., Tröstr, S.: Bssr Ausnutzung von Frnwärmanlagn - Dynamisch Vorlauftmpraturoptimirung. Statusbricht '97 Rationll Enrgivrwndung - Frnwärm, Forschungszntrum Jülich (Hrsg.), Jülich [5] Tröstr, S.: Zur Btribsoptimirung in Kraft-Wärm-Kopplungssystmn untr Brücksichtigung dr Spichrfähigkit ds Frnwärmntzs; Dissrtation, Univrsität Dortmund, 1999 [6] GAMS Dvlopmnt Corporation; 1217 Potomac Strt, N.W., Washington, DC 20007, USA [7] CONOPT ARKI Consulting and Dvlopmnt; Bagsvardvj 246A, DK-2880 Bagsvard; Dnmark [8] ProCom Systmhaus und Ingniuruntrnhmn GmbH; Luisnstraß 41; Aachn; Grmany