Heat demand forecasting for concrete district heating system


 Christiana Malone
 2 years ago
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1 Hea demand forecaing for concree diric heaing yem Bronilav Chramcov Abrac Thi paper preen he reul of an inveigaion of a model for horerm hea demand forecaing. Foreca of hi hea demand coure i ignifican for horerm planning of hea producion and i i mo imporan for echnical and economic conideraion. Weaher foreca are an imporan inpu o many hea demand forecaing model. In hi paper we propoe he foreca model of hea demand baed on he aumpion ha he coure of hea demand can be decribed ufficienly well a a funcion of he oudoor emperaure and he weaher independen componen (ocial componen). Time of he day affec he ocial componen. The ime dependence of he load reflec he exience of a daily hea demand paern, which may vary for differen week day and eaon. Foreca of ocial componen i realized by mean of BoxJenkin mehodology. We have udied halfhourly hea demand daa, covering a hree (four) monh period in wo concree diric heaing yem (DHS) of he Czech Power and Heaing company. Comparion of accuracy of he predicion model wih incluion and wihou incluion of oudoor emperaure for 12 and 24 hourahead foreca are preened. Keyword BoxJenkin, Conrol algorihm, Diric Heaing Conrol, Predicion, Time erie analyi. conumpion. I expre hea energy, which i he cuomer upplied in a pecific ime inerval (generally day or year). The coure of hea demand and hea conumpion can be demonraed by mean of hea demand diagram. The mo imporan one are: Daily Diagram of Hea Demand (DDHD) which demonrae he coure of requiie hea oupu during he day. (See Fig. 1) duraion hea demand diagram  Ycoordinae repreen hea demand and diance from zero repreen duraion of correponding hea demand. Daily and yearly duraion hea demand diagram are currenly known. Hea demand [/hod] I. INTRODUCTION T HE paper deal wih he uilizaion of ime erie predicion for conrol of echnological proce in real ime. An improvemen of echnological proce conrol level can be achieved by ime erie analyi in order o predicion of heir fuure behavior. We can find an applicaion of hi predicion alo by he conrol in he Cenralized Hea Supply Syem (CHSS), epecially for he conrol of ho waer piping hea oupu [2]. In order o improve he conrol level of diric heaing yem, i i neceary for he energy companie o have reliable opimizaion rouine, implemened in heir organizaion [11]. However, before a plan of hea producion, a predicion of he hea demand fir need o be deermined. Due o he large operaional co involved, efficien operaion conrol of he producion ource and producion uni in a diric heaing yem i deirable. Knowledge of hea demand i he bae for inpu daa for operaion preparaion of CHSS. Term hea demand i inananeou required hea oupu or inananeou conumed hea oupu by conumer. Term hea demand relae o erm hea Dae Fig. 1: DDHD for he concree localiy Thee diagram are mo imporan for echnical and economic conideraion. Therefore foreca of hee diagram coure i ignifican for horerm and longerm planning of hea producion. I i poible o judge he queion of peak ource and namely he queion of opimal diribuion loading beween cooperaive producion ource and producion uni inide hee ource according o ime coure of hea demand. The foreca DDHD i ued in hi cae. II. PROBLEM FORMULATION Mo forecaing model and mehod for load predicion have already been uggeed and implemened wih varying degree of ucce. They may be claified ino wo broad caegorie: claical (or aiical) approache and arificial inelligence baed echnique. The aiical mehod foreca he curren value of a Iue 4, Volume 4,
2 variable by uing a mahemaical combinaion of he previou value of ha variable and previou or curren value of exogenou facor, pecially weaher and ocial variable. Thee include linear model, olving by mean of nonlinear model, pecral analyi mehod, ARMA model, BoxJenkin mehodology ec. In recen ime, much reearch ha been carried ou on he applicaion of arificial inelligence echnique. Thee echnique are baed on proceing ma daa. Thee include exper yem, neural nework, fuzzy neural model ec. However, he model ha have received he large aenion are he arificial neural nework [7], [12], [13]. Mo applicaion in he ubjec conider he predicion of elecricalpower load. Neverhele wa creaed everal work, which olve he predicion of DDHD and i ue for conrol of DHS. A number of hee work are baed on ma daa proceing [7], [9]. Bu hee mehod have a big diadvanage. I coni in ou of dae of real daa. From hi poin of view i available o ue he foreca mehod according o aiical mehod. The baic idea of hi approach i o decompoe he load ino wo componen, wheher dependen and wheher independen. The weaher dependen componen i ypically modeled a a polynomial funcion of emperaure and oher weaher facor. The weaher independen componen i ofen decribed by a Fourier erie, ARMA model, BoxJenkin mehodology or explici ime funcion. Previou work on hea load forecaing [1], [6], how ha he oudoor emperaure, ogeher wih he ocial behavior of he conumer, ha he greae influence on DDHD (wih repec o meeorological influence). Oher weaher condiion like wind, unhine ec. have le effec and hey are par of ochaic componen. In hi paper we propoe he foreca model of DDHD baed on he previou approach. The model i baed on he aumpion ha he coure of DDHD can be decribed ufficienly well a a funcion of he oudoor emperaure and he weaher independen componen (ocial componen). We have udied hea demand daa in wo concree DHS of he Czech Power and Heaing company. Comparion of accuracy of he predicion model i preened and ome concluion are given. Many oher work olve he queion of economical hea producion and diribuion in DHS. Some mehod able o predic dynamic hea demand for pace heaing and domeic warm waer preparaion in DHS, uing imeerie analyi wa preened [10]. Oher work preen one ep ahead predicion of waer emperaure reurned from agglomeraion baed on inpu waer emperaure, flow and amopheric emperaure in pa 24 hour [14]. III. FORECAST MODEL OF HEAT DEMAND A menioned above, he model i baed on he aumpion ha he coure of DDHD can be decribed ufficienly well a a funcion of he oudoor emperaure and he weaher independen componen (ocial componen). Time of he day affec he ocial componen. The ime dependence of he load reflec he exience of a daily hea demand paern, which may vary for differen week day and eaon. Foreca of ocial componen i realized by mean of BoxJenkin mehodology [3]. Thi mehod work wih fixed number of value, which are updae for each ampling period. For incluion of oudoor emperaure influence in calculaion of predicion of DDHD wa propoed general plan pecified in Secion 3.2. A. The BoxJenkin mehod Thi mehodology i baed on he correlaion analyi of ime erie and i work wih ochaic model, which enable o give a rue picure of rend componen and alo of periodic componen. Becaue hi mehod achieve very good reul in pracice, i wa choen for predicion of ocial componen of DDHD. The coure of ime erie of DDHD conain moly wo periodic componen (daily and weekly period). Bu general model according o BoxJenkin enable o decribe only one periodic componen. We can propoe wo evenual approache o calculaion of foreca o decribe boh periodic componen [5]. The mehod ha ue he model wih double filraion The mehod uperpoiion of model Fir we inroduce implified form (2) of general model according o BJ for he nex uing, when here i ued ubiuion in he form (1). We can find more deailed analyi of general model in work [3]. 1 P 1 ( B ) (B) Θ ( B ) θ ( B) D d F = Φ φ (1) a p Q z = F (2) where: z i real value of hea demand in ime, a i whie noie proce, B i backward hif operaor, eaonal period, ΦP ( B ), ΘQ ( B ) are polynomial in B of degree P and Q of he eaonal AR and MA procee, φ (B) θ ( B) ( B ) Θ ( B ) q p, ΦP, are polynomial in B of degree p and q of he Q AR and MA procee, of order D, D i he eaonal difference operaor d i he difference operaor of order d The mehod ha ue model wih double filraion We can decribe model wih double filraion hrough he ubiuion (1). The model in he form (3) i he reul of i. * D z = F * a (3) where: D degree of eaonal difference daily (in equaion 1), D*  degree of eaonal difference weekly, eaonal period  daily (in equaion 1), *  eaonal period  weekly q Iue 4, Volume 4,
3 I i imporan o adhere o hi general plan for uing he mehod ha ue model wih double filraion for calculaion of DDHD predicion. a) The filraion of ime erie i execued for he reaon of eliminaion of weekly periodic componen. b) Thi filered ime erie can be decribed by mean of general model according BJ and hen calculaion of foreca by mean of coure can be execued; ha i provided in work [3]. c) I i imporan o do back ranformaion ha i invere o he poin a), becaue we have execued eliminaion of weekly periodic componen. The model in he form (3) enable o decribe he DDHD coure (i.e. i decribe daily periodic componen and alo weekly one). I can be ued for analyi and predicion of following regular influence of calendar (Saurday, Sunday). The mehod uperpoiion of model We can ue econd mehod i.e. uperpoiion of model for eliminaion of regular influence of calendar. Thi mehod wa publihed in he work [5]. Thi mehod i being ued on wo model in he form (2). Thee model are dicerned by mean of ymbol * and **. The ime erie incribed wih ymbol *, i erie of value of DDHD oupu in every ampling period (e.g. 1 hour, 30 minue, 15 minue, ec.). And he ime erie incribed by mean of ymbol ** i erie of value of hea demand per day (he ampling period i 1 day). The plan of calculaing predicion by mean of he mehod of uperpoiion of model i hown on he Fig. 2. We can find more deailed analyi in work [5]. Fig. 2: Superpoiion of model  plan of calculaing predicion 1) Idenificaion of BoxJenkin model Idenificaion of ime erie model parameer i he mo imporan and he mo difficul phae in he ime erie analyi. Idenificaion proce firly include deerminaion of a degree of differencing. Afer differencing he ime erie, we have o idenify he order of auoregreive proce AR(p) and order of moving average proce MA(q). In our cae, he Akaike Informaion Crierion (AIC) in he form (4) i ued for eing. Adequacy of he model wa eed [4] by mean of Pormaneau e. 2 AIC( p, q) = n ln ˆ σ a + 2( p + q) (4) where: p, q i order of AR and MA proce repecively, 2 σ i a variance of reidual, n i a number of reidual. ˆ a B. Foreca algorihm for incluion of oudoor emperaure Above menioned mehod do no decribe udden flucuaion of meeorological influence. In hi cae we have o include hee influence in calculaion of predicion. For incluion of oudoor emperaure influence in calculaion of predicion of DDHD wa propoed hi general plan: a) The influence of oudoor emperaure filer off from ime erie of DDHD by mean of heaing characeriic (funcion ha decribe he emperauredependen par of hea conumpion) b) Predicion of DDHD by mean of BoxJenkin mehod for hi filered ime erie c) Filraion of prediced value for he reaon of incluion of oudoor emperaure influence (on he bae of weaher foreca) From he previou plan i eviden ha he principal aim i o derive an explici expreion for he emperauredependen par of he hea demand. I i obviou ha he emperaure dependence i nonlinear. For relaively high oudoor emperaure, he emperaure ha le influence. For example, he load will almo be he ame for 25 C and 27 C. A correponding concluion i alo rue for relaively low emperaure, e.g. wheher he oudoor emperaure i 28 C or 30 C doe no maer, he producion uni will produce a heir maximum rae anyway. * Legend o he Fig. 2: z i real value of hea demand in * ** every ampling period, z i value of hea demand per day, ** ** r h i raio of ranformaion, ** z * i ranformed real value of * r+ hea demand in every ampling period, z * i prediced value * * + of ranformed ime erie, z i prediced value of hea * ** + demand (afer back ranformaion), z i prediced value of ** ** + daily hea demand, h i raio of ranformaion for prediced ** value of daily hea demand,. Fig. 3: The ample of heaing characeriic (cubic funcion) Iue 4, Volume 4,
4 Regarding o previou conideraion we can ued he emperauredependen par of hea demand in he form (5). Example of he coure of heaing characeriic for conan x1 = 0.002, x2 = 3.5 i hown in he Fig. 3. The prediced value are neceary o filrae afer predicion calculaion of filering off ime erie for he reaon of incluion of oudoor emperaure influence (on he bae of weaher foreca). We can define hi operaion in he form (8). z 3 = x T x2 T (5) 1 filr + + z = z + z (8) where: z i correcion value of hea demand in ime including oudoor emperaure influence, T i real value of oudoor emperaure in ime, x 1, x 2 are conan. The emperaure dependen par can aumed o vary a a piecewie linear funcion [5], ee he illuraing example in Fig. 4. Here a funcion wih five egmen i ued, bu he number of egmen can of coure be choen arbirarily. filr where: z + i prediced value of filer off ime erie of hea demand in ime, z i correcion value of hea demand + in ime including oudoor emperaure influence, z i prediced value of hea demand in ime. The value + z i obained by applicaion of he equaion filr (5) or (6) for hi operaion. We ue weaher foreca (emperaure foreca). Fig. 4: The ample of heaing characeriic (piecewie linear funcion) IV. CALCULATION OF FORECAST FOR SPECIFIC LOCALITY Puruan o he menioned heory and lieraure a program wa creaed in Malab, which enable o chooe available mahemaical aiical model for calculaion of predicion of DDHD coure. All eing i baed on lo of real daa. Thee daa were obained in pecific localiy and hey are proceed for nex uing in ex file form (ee Fig. 5). The program i drawn in uer menu and by help of ha i i poible o chooe many parameer of foreca calculaion (ee Fig. 6). Given he number of egmen a a N. and he emperaure level a τ i, i = 1,2, N+1. The parameer of heaing characeriic are changed in hee emperaure level. Now we can conider he emperauredependen par of hea demand in he form (6). z i = α T τ < T < τ i + β, i i+ 1, i = 1,..., N (6) where: z i correcion value of hea demand in ime including oudoor emperaure influence, T i real value of oudoor emperaure in ime, α i i he lope of ih egmen, β i i abolue equaion erm of ih egmen Conan (x 1, x 2 and,α i, β i ) have o be deermined for concree localiy empirically. Filraion ime erie of DDHD ha inpu in predicion model i defined in he form (7). z filr = z z (7) where: filr z i hea demand in ime wih filering off he influence of oudoor emperaure, z i correcion value of hea demand in ime including oudoor emperaure influence, z i real value of hea demand in ime Fig. 5: The ample of ex file Selecion of calculaion mehod of predicion of DDHD coure i a oher poibiliy of ubmied program. We can realize he calculaion of predicion by mean of he mehod ha ue model wih double filraion and he mehod uperpoiion of model. Afer chooing one of he mehod he calculaion of predicion i ared. A fir in he coure of calculaion i i earched for he mo uiable model, i i for opimum number of auoregreion parameer and opimum number of parameer of moving average proce. Afer following calculaion of predicion, reuling graphic window i diplayed. The example of hi window i preened in he Fig. 9, Fig. 10, Fig. 12 and Fig. 13. In hi window here i drawn coure of DDHD, coure of prediced daa and probabiliy Iue 4, Volume 4,
5 i ha ypical day load of abou MW. Thee ime erie conain beide ime and ype of he day, he value of hea demand and oudoor emperaure for every 30 minue. Meaured daa of period November, 2008 February, 2009 for he localiy MoKomořany and period January, 2004 March, 2004 for localiy Lioměřice were available. In Fig. 7 meaured value of hea demand and oudoor emperaure in he localiy MoKomořany for 3 week of January, 2009 are preened. In Fig. 8 meaured value of hea demand and oudoor emperaure in he localiy Lioměřice for 2 week of February, 2004 are preened. Fig. 6: Uer menu of calculaion program limi. The reul can be repreened in concree value form. Thee value are followed by calculaion and hey can be diplayed in reuling window. The example of hi window i hown on Fig. 11 and Fig. 14. In hi window i i poible o find alo opimum number of auoregreion parameer and opimum number of parameer of moving average proce. A. Daa for experimen I i neceary o re ha he real daa are ued for all experimen and e of propoed foreca model. The real daa were obained due o cloe cooperaion of our reearch workplace wih energy plan operaion. In our cae i i cloe cooperaion wih company MST a.. Power and Heaing plan Olomouc, Power and Heaing Plan Orokovice, a.. and company Unied Energy a..  Power and Heaing plan Mo Komořany. Meaured daa from wo diric heaing yem in he region Mo, Czech Republic are ued in our experimen. The larger yem i iuaed o localiy MoKomořany. Thi yem ha a ypical day load (winer day) of abou MW. The maller yem i iuaed o localiy Lioměřice and Hea Demand Oudoor Temperaure [ C] ,0 22,0 20,0 18,0 16,0 14,0 12,0 10,0 8,0 6,0 4,0 2,0 0,02,04,06,08,010,0 Fig. 8: Hea demand and Oudoor Temperaure (doed line) for yem in he localiy Lioměřice The coure of boh previou ime erie of DDHD diplay only one periodic componen (daily period). Therefore general model according o BoxJenkin i ued for foreca of ocial componen. B. Reul of hea demand foreca in concree localiy The model were eed on daa from he localiy Lioměřice from wo following week ( ) and on daa from he localiy MoKomořany from wo following week ( ). 24 hourahead and 12 hourahead foreca were made wice a day a 6.00 AM and 6.00 PM. The model wih incluion of oudoor emperaure and wihou incluion of oudoor emperaure wa ued. Accuracy of he foreca i analyzed and ummarized by mean of Mean Abolue Percen Error (). i defined in he form (9) and i can be ued o compare differen predicion [8]. Roo Mean Squared Error () i defined in he form (10) and i i he quare roo of he arihmeic mean of he um of he quare of he predicion error [8]. 100 = n n i= 1 ei z i (9) Fig. 7: Hea demand and Oudoor Temperaure (doed line) for yem in he localiy MoKomořany = n 1 2 e (10) n i i= 1 Iue 4, Volume 4,
6 where: e i i he difference beween he acual value of ime erie z i and he foreca value, n i he number of forecaed value Table 1. preen reul of hea demand predicion wih incluion of oudoor emperaure for he localiy Mo Komořany. Accuracy of hea demand foreca wihou incluion of oudoor emperaure i preened in Table 2. The ample of he graphic oupu of hee foreca are hown in he Fig. 9 and Fig. 10. Table 1: Accuracy of he foreca model for 24, 12 hour ahead foreca wih incluion of oudoor emperaure for he localiy Mo Komořany Dae, Time 24 hourahead foreca 12 hourahead foreca , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM Average value Table 2: Accuracy of he foreca model for 24, 12 hour ahead foreca wihou incluion of oudoor emperaure for he localiy MoKomořany Dae, Time 24 hourahead foreca 12 hourahead foreca , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM Average value Fig. 9: 24 hour ahead foreca (wih incluion of oudoor emperaure) of hea demand on :00 AM in he localiy MoKomořany Fig. 10: 24 hour ahead foreca (wihou incluion of oudoor emperaure) of hea demand on :00 AM in he localiy MoKomořany Iue 4, Volume 4,
7 , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM Average value Fig. 11: Reul window for 24 hour ahead foreca of hea demand on :00 in he localiy MoKomořany From he reul, we conclude ha he predicion model wih incluion of oudoor emperaure achieve for he localiy MoKomořany very good reul. for he e period i a any ime le han 10 percen and eldom exceed he value of 10MW. Average value of in he e period i approximaely 5% and average value of i approximaely 6 MW. Obviouly, we alo oberve ha he value of and are lower for a half a day ahead foreca han for a day ahead foreca. Furher, he reul of hea demand predicion wih incluion of oudoor emperaure for he localiy Lioměřice are preened in Table 3. Accuracy of hea demand foreca wihou incluion of oudoor emperaure i preened in Table 4. The ample of he graphic oupu of hee foreca are hown in he Fig. 12 and Fig. 13. Table 3: Accuracy of he foreca model for 24, 12 hour ahead foreca wih incluion of oudoor emperaure for he localiy Lioměřice Dae, Time 24 hourahead foreca 12 hourahead foreca , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM Fig. 12: 24 hour ahead foreca (wih incluion of oudoor emperaure) of hea demand on :00 AM in he localiy Lioměřice Fig. 13: 24 hour ahead foreca (wihou incluion of oudoor emperaure) of hea demand on :00 AM in he localiy Lioměřice Fig. 14: Reul window for 24 hour ahead foreca of hea demand on :00 in he localiy Lioměřice Table 4: Accuracy of he foreca model for 24, 12 hour ahead foreca wihou incluion of oudoor emperaure for he localiy Lioměřice Dae, Time 24 hourahead foreca 12 hourahead foreca , 6:00 AM , 6:00 PM Iue 4, Volume 4,
8 , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM , 6:00 AM , 6:00 PM Average value From he experimen for he localiy Lioměřice, we conclude ha he predicion model wih incluion of oudoor emperaure achieve again very good reul. for he e period i a any ime le han 10 percen and eldom exceed he value of 3 MW. Average value of in he e period i approximaely 7% and average value of i approximaely 2 MW. Obviouly, we alo oberve ha he value of and are lower for a half a day ahead foreca han for a day ahead foreca. C. Review of he reul Realized experimen for boh diric heaing yem demonrae poibiliy of uing of foreca model wih incluion of oudoor emperaure for improvemen of hea demand predicion. Reul in he Table 5 ae o hi fac. Average value of and for all experimen of he boh diric heaing yem are preened in he Table 5. From he reul, we conclude ha he for predicion wih incluion of oudoor emperaure i approximaely 3% le han wihou incluion of oudoor emperaure. Likewie, he i approximaely 3 MW (localiy Mo Komořany) or 1 MW (localiy Lioměřice) lower han for predicion wihou incluion of oudoor emperaure. The accuracy of predicion (expreed by ) i beer for diric heaing yem in he localiy MoKomořany. Thi fac i due o higher ypical day load ( MW) han he ypical day load (2835 MW) in he maller yem (localiy Lioměřice). Table 5: Overview of reul of all experimen for he boh diric heaing yem 24 hour ahead foreca wih incluion of oudoor emperaure 24 hour ahead foreca wihou incluion of oudoor emperaure 12 hour ahead foreca wih incluion of oudoor emperaure 12 hour ahead foreca wihou incluion of oudoor emperaure MoKomořany Lioměřice A deeper analyi of he reul how ha he wore predicion wa achieved on he day of weekend. A concluding remark i ha accuracy of weaher forecaing can have a grea impac on he accuracy of hea demand forecaing. V. CONCLUSION Thi paper preen he BoxJenkin mehodology for building up he foreca model of ime erie of DDHD and he poibiliy of improvemen of hi foreca model wih help of incluion of oudoor emperaure influence. The propoed foreca mehod wa uccefully applied o real daa from concree diric heaing yem. The effecivene of propoed foreca model wa demonraed hrough a comparion of he real hea demand daa wih horerm (24, 12 hour) forecaed value. In erm of he average in he e period our approach achieved 5% and 7% error repecively. Hea demand foreca play an imporan role in power yem operaion and planning. Accurae hea demand predicion ave co by improving economic load dipaching, uni commimen, ec. Model decribed hould prove ueful for he conrol in he Cenralized Hea Supply Syem (CHSS), epecially for he qualiaivequaniaive conrol mehod of howaer piping hea oupu he Baláě Syem [2]. ACKNOWLEDGEMENT: Thi work wa uppored in par by he Miniry of Educaion of he Czech Republic under gran No. MSM and Naional Reearch Programme II No. 2C REFERENCES: [1] L. Arvaon, Sochaic modeling and operaional opimizaion in diricheaing yem, Lund, Docoral hei. Lund Univeriy, Cenre for Mahemaical Science. ISBN [2] J. Baláě, Deign of Auomaed Conrol Syem of Cenralized Hea Supply, Brno, Thei of DrSc (Docor of Science) Work. TU Iue 4, Volume 4,
9 Brno, Faculy of Mechanical Engineering. [3] G. E. Box and G. M. Jenkin, Time erie analyi: forecaing and conrol. Rev. ed. San Francico: HoldenDay, ISBN [4] B. Chramcov and J. Baláě, Time Serie Analyi of Hea Demand, In Proceeding of 22nd European Conference on Modelling and Simulaion, ClermonFerrand: European Council for Modelling and Simulaion, ISBN [5] P. Doál, Machine Proceing of Daily Diagram Coure Predicion of Loading he Cenralized Hea Supply Syem, Brno, Docoral hei. TU Brno, Faculy of Mechanical Engineering. [6] E. Dozauer, Simple model for predicion of load in diricheaing yem, Applied Energy, NovemberDecember 2002, Volume 73, Iue 34, ISSN [7] H. S. Hipper, C. E. Pedreira and R. C. Souza, Neural nework for horerm load forecaing: a review and evaluaion, IEEE Tranacion on Power Syem, February 2001, Volume 16, Iue 1, ISSN [8] IPredic [online]. 2004, La modified: 8/11/2010 [ci ]. Timeerie Forecaing Error Saiic. Available: <hp://www.ipredic.i/errorsaiic.apx>. [9] O. Lehorana, J. Seppälä, H. Koivio and H. Koivo, Adapive diric hea load forecaing uing neural nework, In. Proceeding of Third inernaional Sympoium on Sof Compuing for Indury, Maui, USA, June, [10] D. Popecu, F. Ungureanu and E. Serban, Simulaion of Conumpion in Diric Heaing Syem, In Environmenal problem and developmen: Proceeding of he 1 WSEAS Inernaional Conference on Urban Rehabiliaion and Suainabiliy (URES 08), Buchare: WSEAS Pre, ISBN , ISSN [11] J. Torkar; D. Goricanec and J. Krope, Economical hea producion and diribuion, In Proceeding of 3rd IASME/WSEAS In. Conf. on Hea Tranfer, Thermal Engineering & Environmen, Corfu: WSEAS, ISBN [12] A. C. Takoumi e al., Applicaion of Neural Nework for Shor Term Elecric Load Predicion, WSEAS Tranacion on Syem, July 2003, Volume 2, Iue 3, ISSN [13] G. J. Tekoura e al., Shor Term Load Forecaing in Greek Inerconinenal Power Syem uing ANN: a Sudy for Inpu Variable, In Recen advance in Neural Nework: Proceeding of he 10h WSEAS Inernaional Conference on Neural Nework, Prague: WSEAS Pre, ISBN , ISSN [14] P. Vařacha, Impac of Weaher Inpu on Heaing Plan  Aglomeraion Modeling, In. Recen Advance in Neural Nework: Proceeding of he 10h WSEAS Inernaional Conference on Neural Nework, Prague: WSEAS Pre, ISBN , ISSN Bronilav Chramcov wa born in Uherké Hradišě, Czech Republic, in He udied Auomaizaion and conrol echnology a he Faculy of Technology in Zlin of he Univeriy of Technology in Brno, and he ook hi degree in In 2006 he graduaed hi docoral degree from he Faculy of Applied Informaic of Thoma Baa Univeriy in Zlin. Hi docoral hei wa focued on he uilizaion of ime erie predicion for conrol of echnological proce. He i working now a a lecurer a he Faculy of Applied Informaic of Thoma Baa Univeriy in Zlin. Hi reearch aciviie are focued on Conrol Algorihm for Diric Heaing Syem, Time Serie Foreca in Energy or Uing of Fuzzy Logic for Time Serie Foreca. Iue 4, Volume 4,
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