SZENT ISTVÁN UNIVERSITY

Transcription

1 SZENT ISTVÁN UNIVERSITY BLOCK-ORIENTED MODELING OF SOLAR THERMAL SYSTEMS Thei of the dotoral (Ph.D.) diertation Jáno Buzá Gödöllő 2009

2 Dotoral hool denomination: Mehanial Engineering PhD Shool iene: Energeti of Agriulture head of hool: Prof. Dr. Itván Farka Dr. of Tehnial Siene Faulty of Mehanial Engineering Szent Itván Univerity, Gödöllő, Hungary upervior: Prof. Dr. Itván Farka Dr. of Tehnial Siene Intitute for Environmental Sytem Faulty of Mehanial Engineering Szent Itván Univerity, Gödöllő, Hungary.. affirmation of head of hool.. affirmation of upervior

3 CONTENTS NOTATION INTRODUCTION AND AIMS Signifiane of the reearh Aim of the reearh MATERIAL AND METHOD Phyial baed model of the flat plate olletor Solar torage tank model Storage tank model with built in heat exhanger oil Storage tank model without built in heat exhanger External heat exhanger model Solar thermal ytem for verifiation meaurement RESULTS Determination of the flat plate olletor tranfer funtion Solving of olletor model with blok-oriented imulation Identifiation of the overall heat lo oeffiient of the olletor Solar thermal ytem imulation with internal heat exhanger Simulation of olar thermal ytem with external heat exhanger Controller model of olar thermal ytem Monitoring and imulation of wimming pool water heater olar thermal ytem NEW SCIENTIFIC RESULTS CONCLUSIONS AND SUGGESTIONS SUMMARY PUBLICATIONS RELATED TO THE RESEARCH

4 NOTATION A - aborber urfae of olletor (m 2 ) A - external boundary urfae of torage tank (m 2 ) - peifi heat apaity of fluid in the olletor (J kg -1 K -1 ) - peifi heat apaity of fluid in the torage tank (J kg -1 K -1 ) C - heat apaity of fluid in the olletor (J K -1 ) F' - heat tranfer fator between the aborber and fluid (dimenionle) k - heat lo oeffiient of torage tank (W m -2 K -1 ) I - irradiane on olletor plate (W m -2 ) m& - ma flow rate of fluid in the olletor (kg -1 ) T 1 - outlet fluid temperature from heat exhanger oil ( C) T ab - olletor aborber temperature ( C) T av - average olletor fluid temperature ( C) T a - olletor ambient temperature ( C) T i - olletor inlet fluid temperature ( C) T o - olletor outlet fluid temperature ( C) T d - torage tank inlet upplied old water temperature ( C) T ha - external heat exhanger ambient temperature ( C) T hi - torage outlet water temperature to external heat exhanger ( C) T ho - external heat exhanger outlet water temperature return to torage ( C) T hhi - heat exhanger hot ide inlet temperature return from olletor ( C) T hho - heat exhanger hot ide outlet temperature return to olletor ( C) T - water temperature in the torage tank ( C) T a - torage tank ambient temperature ( C) T i - heat exhanger oil inlet heat tranfer medium temperature ( C) U - heat lo oeffiient of olletor (W m -2 K -1 ) U L - overall heat lo oeffiient of the olletor (W m -2 C -1 ) v& - volumetri flow rate of olletor and built in heat exhanger oil (m 3-1 ) v& l - volumetri flow rate of extrated hot water from the torage tank (m 3-1 ) v& - flow rate of loop between torage and external heat exhanger (m 3-1 ) V - het tranfer fluid volume in the olletor (m 3 ) V - torage tank volume (m 3 ) η 0 Greek ymbol - optial effiieny of the olletor (dimenionle) ρ - denity of fluid in olletor and the olletor loop (kg m -3 ) ρ - denity of fluid in torage and torage ide of heat exhanger (kg m -3 ) τ - time ontant of the olletor () 4

5 1.1. Signifiane of the reearh 1. INTRODUCTION AND AIMS Analyze the tendeny of energy prie it ould be determined that the rie in prie up to preent and the expeted inreae in prie foreat the eonomi energy utilization. Similarly to the developed ountrie, the appliation of the deentralized energy prodution unit will alo inreae in Hungary, whih enure partial autonomy for onumer. Beide thi, another quite important apet the preading out of uh environmental friendly energy prodution tehnologial olution, whih redue the environmentally damaging pollution emiion, ome from burning traditional foil fuel. One poible olution i: growing appliation of renewable energy oure that fulfil the requirement with the above-mentioned apet. One form to ue renewable energy i the ative thermal utilization of olar energy. Today olar thermal tehnologie are effiient and highly reliable, providing olar energy for a wide range of appliation from dometi hot water and pae heating in reidential and ommerial building, to wimming pool heating, olar aited ooling, olar aited ditrit heating, indutrial proe heat and dealination. The total olar thermal apaity in operation at the end of 2007 reahed 15,4 GW th (22 million m 2 of olletor area) in the member tate of the European Union. Hungary ha advantage in the olar thermal utilization apability ompare to many European ountrie. At preent in Hungary everal oure ontain different data in referene to intalled olar thermal in operation and the annually intalled olletor area. Aording to etimation in thouand m 2 total intalled olletor area wa in Hungary, while in 2006 the market tatiti publihed by the European Solar Thermal Indutry Federation ontain m 2 olletor area in operation and in one year later aording to tatiti m 2 olletor area wa in Hungary. For omparion in Autria in 2007 the total olletor area in operation wa m 2. The olar thermal ytem with fluid working medium i exepted to be ued manly in dometi hot water heating, indutrial proe heat, wimming pool heating and in leer proportion in heating in reidential and ommerial building in Hungary. An average family approximately 55-60% of annual total hot water onumption ould be produed a olar thermal ytem with 3-4 m 2 olletor area and 150 l olar torage tank. Herewith energy ould be ubtituted whih produed from foil or nulear fuel, additionally the aompaniment harmful emiion of energy prodution ould alo be redued. 5

6 1.2. Aim of the reearh The aim of the reearh were modeling and imulating of heat tranfer proee of olar thermal ytem for hot water heating and meaurement and monitoring on the available olar thermal ytem for validate the model reult. The heat prodution unit of the olar thermal ytem operating with fluid working medium i the olar olletor. Apply the relevant literature the aim i to work out uh a phyial baed model whih able to deribe the heat balane of flat plate olletor with fluid working medium repet to irradiane, ambient temperature, inlet olletor fluid temperature and ma flow rate. The heat produed by the olar olletor for later uage hould be alloated in to the torage. In ae of two loop ytem the heat tranfer proe between the olletor loop and the torage implemented by a heat exhanger. There are two main ontrution in olar thermal ytem one i the internal heat exhanger when a heat exhanger oil i built into the torage tank and the other way i when no heat exhanger in the torage tank, but an external heat exhanger i intalled. Hene it i important to develop uh phyial model, whih deribe the heat tranferred by fluid tream from the olletor through the heat exhanger oil get into the torage tank water or get into the fluid tream flowing on the old ide of external heat exhanger from the torage tank. The energy prodution period of olar thermal ytem and the energy demand of the onumer motly different in time. Aordingly the funtion of torage tank i to tore the heat aumulated by the olletor and upply it by the need of the onumer. Therefore phyial baed model are neeary to deribe the inlet and outlet fluid and heat team of the torage tank. The heat flux between olletor and torage unit in olar thermal ytem regulate by the ontroller. In onnetion the modeling of ontroller model are neeary for the entire ytem imulation to regulate the heat tranfer fluid tream in the ytem baed on outlet olletor temperature and the torage tank temperature. The aim i to develop ontroller model with the ame operation a the intalled ontroller in the ytem ued model validation meaurement during the reearh. Baed on the ubytem model deribe the operation of the main omponent of olar thermal ytem uh a olar olletor, heat exhanger, torage tank and ontroller, the integrated model of the entire ytem an be developed. The aim i to develop uh a imulation model whih an be ued to alulate the hot water temperature in the torage tank repetively etimate the heat prodution of the olar thermal ytem baed on the input variable a irradiation, ambient temperature, upplied old water temperature and the hot water onumption. 6

7 2. MATERIAL AND METHOD The harateriti of the operation of olar dometi hot water ytem are tranient, time varying proee. For the deription of the proee uh a onentrated parameter ordinary differential equation were ued whih able to deribe the time varying heat tranfer proee with the required auray. For the olution of the equation blok-oriented imulation oftware the MATLAB+Simulink wa ued. Beyond the modeling of the given phyial proee the oftware able to model and examine the regulation and ontrol funtion of the ytem a well. Mot of the olar thermal ytem in Europe intalled with gla owered flat plate olletor. Thi i alo true for the Hungarian intallation. Hene the diertation deal with the modeling of flat plate olletor. For modeling phyial baed approah wa applied. The phyial baed mathematial model an be ued to parameter enitivity analyi, imulation and ontrol aim in addition to allow of the appliation of ytem analyi method widely ued in the ontrol theory to determine the tranfer feature Phyial baed model of the flat plate olletor Aume the flat plate olletor in Figure 1 the model deribe the outlet fluid temperature of the olletor T o (t) a a funtion of input variable and parameter. In ae of the teady tate of the olletor the inlet heat amount of the olletor equal with the outlet heat amount of the olletor. Thu the amount of heat arry from the olletor by the heat tranfer medium flowing through and warming up in the olletor i equal with the differene of the heat gain of the olletor from the olar radiation and the heat lo of the olletor to the ambient. A T a (t) I (t) U T i (t) T o (t) m& (t) Fig. 1. Sheme of the olletor The tate equation of the olletor arranged to the firt order differential of the outlet fluid temperature: dt A η U A v& o 0 L = I ( T T ) + ( T T ( t )), (1) av a i o dt C C V where C = ρ V, m& (t) = v& (t) ρ and T av (t) i the average olletor temperature: T + T i o T =. (2) av 2 7

8 2.2. Solar torage tank model For modeling of hot water torage tank numerou appliable method an be found in the related literature whih are very differing from eah other. The onentrated parameter model onern to thermally ompletely mixed torage tank. The mathematial model i an ordinary differential equation deribe the torage tank temperature varying in time. In thi ae the model valid only with a ondition whih aume no temperature ditribution in the torage tank o the temperature pae onidered homogeneou. In the oure of reearh I applied thi modeling method Storage tank model with built in heat exhanger oil In the pratie in mall-ale olar thermal intallation approximately up to 500 liter torage tank volume ommonly apply torage tank with built in heat exhanger oil. In thi ae the heat tranfer fluid returning from the olletor going through the heat exhanger oil built in the lower part of the torage tank (Fig. 2.). Aumption: uniform temperature ditribution or thermally ompletely mixed torage tank and T d (t)=t d i ontant. The model doe not take into aount the heat lo between the torage tank and ambient. For the blok-oriented imulation of the torage tank the differential equation deribing the energy balane of the torage tank arranged to the firt order differential of the torage tank temperature T (t): dt v& l = ( T dt V d v& T ) + ( V T T i (t) T 1 (t), v& (t) T (t), T (t) v& l (t) T d (t) Fig. 2. Storage tank with built in heat exhanger oil i ( t ) T ( t )) 1. (3) The outlet heat tranfer fluid temperature of the heat exhanger oil an be alulated a follow: v& ( t ) ρ ( T T ) e + T ( ) T = t 1 i UA, (4) where ρ i the denity of the fluid in the heat exhanger oil, i the heat apaity of the fluid in the heat exhanger oil, U i the heat tranfer oeffiient of the heat exhanger, A i the urfae of the heat exhanger oil. 8

9 Storage tank model without built in heat exhanger Larger ale olar thermal ytem frequently intalled with external heat exhanger, o the torage tank doe not ontain built in heat exhanger. The heme of the torage tank hown in Figure 3. The developed model doe not take into aount the heat apaity derived from the torage tank ontrution. Aumption: the temperature pae i homogeneou in the torage tank and the hot water temperature in the torage i the ame a the outlet temperature toward to the external heat exhanger T hi (t)=t (t). Thu the tate equation of the torage tank: dt v& l = ( T dt V d v& T ) + ( T V 2.3. External heat exhanger model ho T(t) T ho (t), v& (t ) T hi (t) T(t) T a (t) T d (t), & (t) Fig. 3. Storage tank without heat exhanger A k T ) ( T T ) a. (5) ρ V Larger ale olar thermal ytem often deigned with external heat exhanger. Among the olar thermal ytem whih were available for verifiation meaurement alo had thi kind of ontrution. I have developed a model for external heat exhanger. The keth of heat exhanger an be een in Fig. 4. The variable and parameter on the hot ide or olletor loop ide of heat exhanger are: fluid temperature in hot ide of heat exhanger T 1 (t), hot ide volume of heat exhanger V 1 and the volumetri flow rate in the olletor loop & (t) onneted to the hot ide of heat exhanger. v Variable and parameter on the old ide or torage loop ide of heat exhanger are: fluid temperature in old ide of heat exhanger T 2 (t), old ide volume of heat exhanger V 2 and the volumetri flow rate in the torage loop v& (t) onneted to the old ide of heat exhanger. T hhi (t) T hi (t) ρ,, v& (t), V 1, T 1 (t) ρ,, v& (t), V 2, T 2 (t) Tha(t) T hho (t) v l T ho (t) Fig. 4. External heat exhanger Auming homogeneou temperature ditribution on both ide of the heat exhanger (aume thermally mixed fluid) and introduing the following: T 1 (t)=t hho (t), T 2 (t)=t ho (t), V 1 =V 2 =V. The energy balane equation of the heat exhanger hot ide: 9

10 dthho ρ v& = dt C + ρ V h1 ( T hhi T hho ) C h1 Aa ka / 2 C + ρ V h1 A k ( T + ρ V ( T hho hav T T ho ha ) ). The energy balane equation of the heat exhanger old ide: dtho ρ v& A k = ( T T ) + ( T T ) hi ho hho ho dt C + ρ V C + ρ V h2 h2 (7) Aa ka / 2 ( T T ). hav ha C + ρ V h2 The average heat exhanger temperature: T + T hho ho T =. (8) hav 2 Further parameter of the heat exhanger model are: heat tranfer urfae between the hot and old ide A, heat tranfer oeffiient between the hot and old ide k, external boundary urfae of the heat exhanger A a, heat tranfer oeffiient between the heat exhanger and ambient k a. The heat apaity of the hot and old ide of the heat exhanger onerning to the deign C h1 =C h2 =( h m h )/2, where h i the peifi heat apaity of the heat exhanger material and m h i the ma of the heat exhanger without fluid Solar thermal ytem for verifiation meaurement In the oure of reearh the experiment and meaurement onerning to the modeling and imulation were arried out on two olar thermal ytem. One of the ytem developed in the Department of Phyi and Proe Control, Szent Itván Univerity (SZIU). The ytem intalled with a 1,65 m 2 flat plate olletor and a 150 l eletri water-heater whih wa adopted for the olar thermal appliation. To onnet the olletor loop to the torage tank ha two option, one i through a built in heat exhanger oil or the other i a ompat brazed external heat exhanger. The monitoring of the ambient and ytem operation parameter and the pump and valve regulation wa arried out a omputer ontrolled miroontroller baed modular data logging ytem. The other olar thermal ytem intalled in the ampu of SZIU Gödöllő. It ontain 33,3 m 2 urfae of olletor field with 23,31 kw th thermal apaity. The ytem inlude two plate heat exhanger with kw apaity. One i for wimming pool water heating with 1 m 2 heat tranfer urfae and the other i for heating kindergarten hot water with 2 m 2 heat tranfer urfae. The pool loop onnet the pool heat exhanger and the 700 m 3 wimming pool, while the kindergarten loop operating between the kindergarten heat exhanger and the 2000 l olar torage. A data logging and monitoring ytem alo intalled. (6) 10

11 3. RESULTS 3.1. Determination of the flat plate olletor tranfer funtion Applying the method of Laplae tranform I have determined the tranfer funtion of flat plate olletor. The olletor equation (1) an be onidered a linear if the fluid flow rate in the olletor i aumed & (t) = ontant. I have defined the time ontant of the olletor a follow: 1 τ = (9) U A v& L + 2C V The tranfer funtion for the ertain input variable an be found. Conidering linear olletor equation beaue of the aumed ontant flow rate the priniple of the uperpoition an be ued. Aording to thi priniple the repone of the output variable aued by the input variable an be alulated a the um of the individual repone aued by the individual input. At the determination of the tranfer funtion of an individual input variable the reminder input and the initial value of the outlet olletor temperature T o (0)=0 are equal to zero. Applying Laplae tranform the time-domain variable igned by top line in - domain. Denote the tranfer funtion by W(). The tranfer funtion of the olletor onerning to the olar irradiane: To ( ) ( τ Aη 0 ) / C W1 ( ) = =. (10) I ( ) τ + 1 The tranfer funtion regarding to the olletor inlet heat tranfer medium temperature: T ( ) τ v& U A o L W ( ) = = 2. (11) T ( ) τ + 1 i V 2C The tranfer funtion referring to the olletor ambient temperature: To ( ) ( τ U L A ) / C W3( ) = =. (12) T ( ) τ + 1 a Finally the effet of the initial value of the olletor outlet heat tranfer medium temperature T o (0) an alo be determined. The outlet medium temperature repone aued by the initial value an be given a follow: ( τ W ) = 0. (13) τ + 1 Aording to the uperpoition priniple the aggregation of the tranfer funtion defined by equation (10-13) gave the overall tranfer funtion v 11

12 onerning to the olletor outlet heat tranfer medium temperature. The individual input auing effet on the output thorough their tranfer funtion. The equation onerning to the outlet heat tranfer medium temperature with tranfer funtion if the initial value of outlet olletor temperature T o (0) 0: T ) = W ( ) T (0) + W ( ) I ( ) + W ( ) T ( ) W ( ) T ( ) (14) o ( 0 o 1 2 i + 3 a 3.2. Solving of olletor model with blok-oriented imulation For the alulation of the olletor outlet heat tranfer medium temperature I applied the Simulink whih i the imulation toolbox of MATLAB oftware and upport the model baed dynami ytem imulation. The blok ytem ha been ontruted baed on equation (1) and (2). Figure 5 how the reult of the imulation. Temperature, C T o imulated T o meaured T a ambient T i inlet Time, hour Figure 5. Meaured and imulated olletor outlet temperature The average differene between the meaured and imulated olletor outlet temperature wa 8,6 C. The minimum of the differene -3,6 C and the maximum wa 72,1 C, while the tandard deviation wa 16,4 C. The error i influened by more fator. The model take into aount only the heat apaity of the heat tranfer fluid (C ) in the olletor, o the heat apaity of the aborber plate, the fluid arrier pipe and the additional trutural part of the olletor are negleted. The applied optial effiieny value (η 0 ) and the heat lo oeffiient of the olletor (U L ) were hoen baed on the relevant literature whih i approximately ould be typial baed on the experiene of pratie but of ure it i not idential with the value of the teted olletor Identifiation of the overall heat lo oeffiient of the olletor The differene between the meaured and imulated olletor outlet temperature an be redued by parameter identifiation. Baed on the meaured olletor outlet temperature the model parameter value an be refined. For intane thi kind of parameter i the overall heat lo oeffiient of the olletor (U L ). For the identifiation more type of ot funtion an be 12

13 ontruted. One of the motly ued funtion i alulate the um of the quare differene between the meaured and alulated olletor outlet temperature. The ot funtion an be given by equation (15). Thu the identifiation mean the minimization of the ot funtion. J ( U L n ) = ( T i= 1 o ( t ) Tˆ i o ( t )) i 2 min. (15) In equation (15) J denote the um of the quare differene between the meaured and alulated olletor outlet temperature in the examined time interval. T o (t i ) i the meaured value in the i-th ampling time point and Tˆ (t o i) i the alulated value for the i-th ampling time point and n i the number of meaured value. The reult of the identifiation i the value of the overall heat lo oeffiient of the olletor aroe to U L =35,0 W m -2 C -1. The imulation arried out with the identified value the average differene between the meaured and imulated olletor outlet temperature wa -0,3 C. The minimum of the differene -15,8 C and the maximum wa 14,6 C, while the tandard deviation wa 3,4 C Solar thermal ytem imulation with internal heat exhanger One of the mot urrent verion from the olar thermal ytem ontrution applied in the pratie i the deign with heat exhanger built in the torage tank. The developed and previouly introdued olletor and torage tank model with internal heat exhanger an be ued to ompoe the blok-oriented model of the entire olar thermal ytem hown in Figure 6. T o (t) T (t), & (t) v l T a (t) I (t) T (t) A U L T i (t) T i (t) T 1 (t), v& (t) Fig. 6. Solar thermal hot water ytem with internal heat exhanger built in the torage tank I have ued blok-oriented imulation tehnique for imulate the entire ytem ontaining olletor and torage tank with built in heat exhanger by uing the formerly detailed ub model. The meaured input variable for the imulation were the olletor loop flow rate v& (t), the olar irradiane intenity I(t), the ambient temperature T a (t), the torage tank inlet old water temperature T d (t) T d (t) 13

14 and the flow rate of the hot water extration v& l (t) from the torage tank. In the oure of imulation the alulated output variable are the olletor outlet fluid temperature To(t) and the torage tank temperature T (t) Simulation of olar thermal ytem with external heat exhanger Beide the ytem ontrution introdued in the previou hapter the other mot frequently applied olar thermal ytem ontrution i the ue of external heat exhanger. Thi verion mainly ued uh ytem whih ha large olletor field and large ize torage or more torage tank are intalled in the ytem. I have ued equation (1) and (2) for the alulation of the olletor outlet fluid temperature. The meaured input variable of the olletor model are the olar irradiane intenity on olletor plate I (t), the olletor ambient temperature T a (t) and the heat tranfer fluid flow rate v& (t) through the olletor. The output variable of the model i the outlet olletor temperature To(t). The blok-oriented olution of equation (6) and (7) relating to the hot and old ide of external heat exhanger i hown in Fig. 7. The model alulate the heat exhanger hot and old ide outlet temperature (T hho (t), T ho (t)). 1 in_2 2 in_1 3 in_3 4 in_4 5 in_5 Thhi v' Tha Thi v' Mux Mux Mux Mux1 f(u) Fn Heat exhanger hot ide [ C/] Eq. (6) f(u) Fn Heat exhanger old ide [ C/] Eq. (7) 1/ Integrator Thho(0) [ C] 1/ Integrator Tho(0) [ C] 1 out_1 Thho [ C] 2 out_2 Tho [ C] Sine the torage Fig. 7. Blok-orientid external heat exhanger model tank and the onneted external heat exhanger intalled in the ame room thu the heat exhanger ambient temperature T ha (t) and the torage tank ambient temperature T a (t) wa the ame in the oure of imulation. The blok-oriented olution of the torage tank energy balane equation (5) an be een in Figure 8. The torage tank model alulate the tored water temperature T (t). 14

15 1 in_1 2 in_2 3 in_3 4 in_4 5 in_5 v'l Td Tho Ta v' Mux Mux1 u[1]/v*(u[2]-u[6])+u[5]/v*(u[3]-u[6])-(a*k)/(ro**v)*(u[6]-u[4]) Fn Storage tank [ C/] Eq. (5) 1/ Integrator T(0) [ C] Figure 8. Blok-oriented torage tank model baed on equation (5) 1 out_1 T [ C] Combined the developed ubytem model I have reated the model of the entire olar thermal ytem intalled with external heat exhanger. Uing the blok-oriented imulation tehnique the model of the omplete ytem built on different ubytem model hown in Figure 9. 1 Inport 2 Inport1 v'l Td 3 Inport2 4 Ta I Pipe Ti To=Thhi [ C] Thho [ C] Inport3 5 Inport4 6 Pump On/Off Tha=Ta v' Pump_1 Colletor loop Colletor Heat exhanger Tho [ C] Storage tank T=Thi [ C] 1 Outport T [ C] Inport5 v' Pump_2 Storage loop Fig.9. Blok-oriented model of the olar thermal ytem with external heat exhanger In the oure of the imulation for modeling the irulation pump operation the meaured "on" and "off" tate of the pump wa ued in the olletor loop and the torage loop. During the meaurement the pump in the olletor and torage loop wa ontrolled baed on the temperature differene between the meaured olletor outlet temperature T o (t) and the torage tank temperature T (t). The upper and lower dead band temperature differene wa 3 C. The flow rate ontrol in the olletor loop operated a follow: ,9 10 m, when To( t) T + 3 v& = m, when To( t) T

16 The flow rate ontrol in the torage loop operated a follow: ,9 10 m, when To T + 3 v& = m, when To T Controller model of olar thermal ytem In thi hapter three different ontroller model are introdued what I have developed. The blok-oriented model of the ontroller operated on the ame way a it i ued in the pratie for irulation pump ontrol in the olletor loop of olar thermal ytem. I have developed the model of differential ontroller operating with the ame upper and lower dead bend temperature differene. The ontroller model i hown in Figure in_1 2 in_2 To T Mux Mux u[1]>=u[2]+5 Fn Figure 10. Simulink model of differential ontroller operating with ame "on" and "off" dead band temperature On the bai of the ontroller ued in the olar thermal ytem for wimming pool water and dometi hot water heating I have developed the differential ontroller model operating with diimilar "on" and "off" dead band temperature. In the ontroller model developed for entire olar thermal ytem imulation different upper and lower dead band temperature value an be et. The blok-oriented model of the ontroller an be een in Figure 11. Sum Relay 1 out_1 1 in_1 Colletor field outlet temperature, To, C 2 in_2 Storage tank temperature, T, C Mux Mux u[1]>=u[2]+5 Fn Sum Relay out_1 u[1]>=u[2]+2 On (1) / Off (0) Fn1 Figure 11. Blok-oriented realization of the diimilar upper and lower dead band differential ontroller The third developed ontroller model type beide the on/off ontrol of the pump i appropriate for flow rate ontrol during the irulation pump operation. Thi ontroller model i inlude the feature of the previouly diued differing on and off dead bend differential ontroller. The ontroller withe on the pump if the olletor outlet temperature T o (t) ompared with the torage tank temperature i higher than the adjuted value for upper dead band 16

17 temperature (dte). During the irulation if the dereaing temperature differene reahe the et point value for lower dead band (dta) the ontroller withe off the pump. Comparing thi ontroller to the previouly diued two type thi i able to ontrol the flow rate of the irulation pump operating in olletor loop. With that the outlet olletor temperature ould be kept on an optimal temperature. The ontroller alulate the optimal olletor outlet temperature a it i hown below: TKO=T +1/2(dTE+dTA), where TKO i the optimal olletor outlet temperature and T i the torage tank temperature. The blok-oriented ontroller model hown in Figure in_1 To, C 2 in_2 T, C Mux Mux u[1]>u[2]+dte + Sum 1 out_1 Mux u[2]/u[1] 2 Fig. 12. Model of the olletor loop irulation pump flow rate ontroller The irulation pump peed orretion fator alulated by the above ontrol model appear in out port 2. Thi orretion oeffiient linked to the in port 2 in the model of the olletor loop pump, illutrated by Figure 13. Finally the flow rate appear on the output of the irulation pump model. The introdued flow rate ontrol model and the variable fluid tranport rate irulation pump model an be ued to ontrol the heat tranfer medium flow rate in the olletor loop whih ait the realization of tabilized operation of olar thermal ytem. 1 in_1 2 in_2 Pump peed orretion e-5 Contant v, m3/ (Pump On) 0 Contant v, m3/ (Pump Off) Fn dte=20 C u[1]>=u[2]+dta Fn1 dta=2 C Swith Figure 13. Model of the variable flow rate olletor loop pump 3.7. Monitoring and imulation of wimming pool water heater olar thermal ytem In the oure of reearh I have arried out monitoring and imulation tak on a wimming pool water and dometi hot water heater olar thermal ytem. Relay u[1]+1/2*(dte+dta) Fn1 TKO Mux Mux u[1]/u[2] Fn Mux1 Saturation Fn1 TKO/TK out_2 3 out_3 1 out_1 v, m3/ 17

18 After the evaluation of meaured data of the intalled data logging ytem the monthly ditribution of the olar inolation on olletor field, the heat generated by the olletor field and the utilized amount of heat i hown in Figure 14. kwh/month 4000 Solar irradiation on 33.3 m2 olletor area Solar energy ued for wimming-pool heating Heat generated by the olar olletor Solar energy ued for hot water heating Jan Feb Mar Apr May Jun Jul Aug Sep Ot Nov De Jan Feb Mar Apr May Figure 14. Monthly ditribution of the olar irradiation on olletor field and the utilized olar energy During the monitored period of January 2004 and July 2006 the olar thermal ytem heated the wimming-pool water with 3,5 MWh thermal energy, while the olar energy utilized for kindergarten hot water heating wa 7,2 MWh. In the evaluated period 0,34 kwh/m 2 day utilized thermal energy pertained for 1 m 2 olletor field area. Figure 15 how the blok-oriented model of the entire olar thermal ytem. Jun Jul Aug Sep Ot Nov De Jan Feb Mar Apr May Jun Jul Td (torage tank inlet old water temp.) temp.mat From File Meaured temperature, C flow.mat Demux Demux1 Ta (olletor ambient temperature) Tha (heat exhanger ambient temp.) Ta (torage tank ambient temp.) vi (hot water onumption) I (global radiation on olletor plate) Model of the entire olar thermal ytem T (meaured) To (meaured) T (imulated) To (imulated) Mux Mux reult.mat To File Simulation reult From File Meaured hot water onumption, vl, m 3 / rad.mat [t x y]=linim('ompll4',[ ],[ ],[1e-3 1 1]); From File Meaured olar irradiation, I, W/m 2 Figure 15. Blok-oriented model of the olar thermal ytem 18

19 The imulation wa arried out for the period of May 14-20, The meaured and imulated outlet temperature of the olletor and the torage tank temperature are hown in Figure a/ Storage tank temperature, May 14-20, 2002 Temperature, o C imulated meaured Time, hour b/ Colletor field outlet temperature, May 14-20, 2002 imulated meaured Temperature, o C Time, hour Figure 16. Comparion of the meaured and imulated temperature The average differene between the meaured and imulated olletor outlet temperature wa 4,26 C, while the average olar torage tank temperature differene wa 1,91 C. To improve the model further meaurement and invetigation i needed. Baed on the meaured data the parameter value, the heat tranfer oeffiient of the omponent more preiely an be identified with thi the auray of the imulation expetedly ould be improved. 19

20 4. NEW SCIENTIFIC RESULTS In referene to the reearh of olar thermal hot water ytem the related new ientifi reult an be ummarized a follow: 1. For the deription of the main omponent of liquid working medium olar thermal ytem a flat plate olletor, heat exhanger and torage tank, applying the phyial baed modeling approah, I have developed onentrated parameter model with ordinary differential equation. I applied the blok-oriented modeling tehnique to olve the energy balane equation deribing the heat and ma tranfer proee of the ertain omponent. The elaborated dynami model baed on the input variable are appropriate for the thermal imulation and the omputation of the time varying output variable of the individual ubytem. 2. I have determined the tranfer funtion of flat plate olletor onerning to the irradiane intenity, the inlet fluid temperature, the ambient temperature and the initial value of olletor outlet temperature a input variable. Knowing the tranfer funtion of the input, allow a eparation in the analyi of the input variable effet on outlet olletor temperature. Thu, in the ene of input variable it an by analyzed the effet of ontrution parameter of flat plate olletor baially determined the tranfer propertie. I have defined the overall tranfer funtion of flat plate olletor a a linear uperpoition of the individual tranfer funtion onerning to different input variable. 3. I have elaborated an experimental identifiation method for the determination of the overall heat lo oeffiient value for flat plate olletor. By mean of thi method utilizing meaured data I have determined the overall heat lo oeffiient value for flat plate olletor operating with liquid heat tranfer medium. 4. In ae of heat exhanger oil, built in the torage tank, applying analytial olution I have determined the funtion whih deribe the oil outlet temperature varying in time. In the developed model the torage tank water temperature i the tate variable, the heat exhanger oil inlet temperature and the volumetri flow rate through the oil are the input variable. 5. Uing the individual blok-oriented model of the ubytem I have developed a linked model for the entire olar thermal ytem. I have elaborated the blok-oriented realization of the entire olar thermal ytem for the ae of internal and external heat exhanger of whih have an importane in the ontrution pratie. 20

21 6. I have developed different blok-oriented ontrol model in olar thermal ytem for the differential ontroller baed on the temperature differene and for the flow rate ontroller. One of the developed model i able to realize the ame on/off temperature differene band ontrol, while the other one i appropriate for differentiation in withing "on" and "off" tatue. The developed ma flow rate ontrol model i able to maintain the proe baed on an algorithm, a it i deigned along with a miroproeor ontrol. Baed on the ontrol model I have elaborated a ytem model of a ombined olar thermal ytem heating wimming pool water and dometi hot water. 21

22 5. CONCLUSIONS AND SUGGESTIONS The omparion of the imulation reult and the meaured data proved that the developed onentrated parameter mathematial model appropriate for deribing the time varying heat and ma tranfer proee in omponent of olar thermal ytem with liquid working medium. Baed on the developed model the blok-oriented realization i ompleted. The realized model are not only for ytem element imulation, but linking thoe one i good for thermal imulation of the entire ytem. Take advantage of the poibilitie of blok oriented imulation tehnique ombine the developed omponent model of olar thermal ytem, the entire ytem imulation an be exeuted. During the reearh the imulation of two different truture ytem had been done. One of the ytem had torage tank with built in heat exhanger oil, while the other one i ontruted with external heat exhanger. In ae of ytem with built in heat exhanger oil the alulated torage tank temperature fit fairly to the meaured one. Only two leer deviation wa oberved. Thee deviation were aued by two fator. One i when the torage tank heated up for night-time the alulated temperature remained on a ontant value, while the meaured one howed a mooth dereaing in time. Thi differene aued by the torage tank model whih doe not take into aount of the heat lo between the torage and the ambient. The other deviation between the meaured and alulated temperature ourred when the total water volume of torage tank had been diharged. Thi time, at the end of the diharging proe the meaured torage tank temperature wa higher than the alulated. Thi i generated by that the torage tank model alulate only with the heat apaity of water in the torage tank, while the torage tank itelf ha heat apaity a well, whih aue a o alled "reidual heat effet", when the remained heat i tranferred to the inlet old water in the torage tank. In the oure of the evaluation of meaured and imulated reult I have found that in the time period of inreaing and dereaing inolation intenity the ontroller are withing frequently between on and off tate. Thi phenomenon aue intability in the olletor loop, whih i diadvantageou in point of view of the ytem operation. To diolve the deribed ymptom and reover the olletor loop tability I have uggeted a minimal operation period for irulating pump whih i needed to et. For minimal pump operation period I have reommend at leat 3-5 minute. Saling thi behavior of the ytem intallation in the future, uh ontroller are needed to elet whih able to eliminate thi problem. Continuing the reearh it would be pratial to examine the effet of ontrol on the energy prodution of the ytem. In the future for development of ontrol algorithm apire to the optimization of energy prodution. 22

23 During the operation flat plate olletor behave like a dynami ytem. The heat and ma tranfer in time domain an be deribed a one variable ordinary differential equation independently from the pae oordinate. The equation from time-domain an be tranformed to "" domain with Laplae tranformation. Uing the time-domain equation parameter with phyial meaning the tranfer funtion an be determined in "" domain. Thu finding the tranfer funtion it give poibility to ue dynami ytem tet method developed in ontrol theory. In ae of flat plate olletor the effet of the tranient hange in the input variable a olar radiation, inlet heat tranfer medium temperature, ambient temperature and the initial value of the outlet temperature an be evaluated a the repone of the output variable, whih i the outlet olletor temperature. The time ontant an alo be determined whih i depend on the heat and ma torage harateriti of the olletor. Beyond the appliation poibility of dynami ytem tet method the tranfer funtion an be ued for imulation, parameter enitivity analyi and ontrol tak a well. 23

24 6. SUMMARY In the oure of the reearh a related literature urvey wa arried out onerning to the Hungarian olar radiation energy ditribution and the ubvention poliy influening the intallation of olar thermal ytem. The literature dealing with the main omponent of olar dometi hot water ytem had been proeed. A review wa made on the tandard onneted with the tet proedure of olar thermal ytem. Information wa olleted on different imulation oftware for modeling of olar thermal ytem. In the hapter of material and method baed on the literature a detailed introdution wa given on the phyially baed modeling of flat plate olar olletor operating with fluid working medium and mot frequently ued in olar thermal ytem. A phyially baed model wa developed whih deribe the heat tranfer proee in the olletor. The tranfer funtion onerning to the outlet heat tranfer fluid temperature of the flat plate olar olletor wa determined for different input variable of the olletor a olar radiation intenity, inlet working medium temperature, ambient temperature and the initial repone of the outlet heat tranfer fluid temperature. Model were developed for the olar torage tank a another main omponent of the olar thermal ytem. The different model verion an be ued to deribe divided torage tank, torage tank with built in heat exhanger oil and torage tank without heat exhanger. For the one of the motly ued ontrution of the olar thermal ytem a model with external heat exhanger wa elaborated allowing to alulate the heat tranfer between the olletor loop and the torage loop. To arry out of ytem imulation different blok-oriented ontrol model were developed. The ontrol model an be parameterized on different way and they are operated on the temperature differene between the olletor outlet temperature and the torage tank temperature, a well. A imulation wa arried out uing the blok-oriented imulation tehnique with the integration of the developed ubytem model for different olar thermal ontrution. In the oure of the tudy the mot frequently ued two ontrution were taken into aount. One type of the ytem i intalled a torage tank with built in heat exhanger oil, while the other one built with external heat exhanger. For the latter type, the imulation wa arried out for two different ize of olar thermal ytem. Monitoring tak of a olar thermal wimming pool heating ytem wa arried out and the utilized energy ratio between wimming pool water heating and hot water heating wa alo determined. 24

25 7. PUBLICATIONS RELATED TO THE RESEARCH Referred artile in Englih: 1. Buzá,J., Farka,I., Biró,A., Németh,R. (1998): Modelling and imulation apet of a olar hot water ytem, Mathemati and Computer in Simulation, Vol. 48, No. 1, p Citation: - Zahár A., Azódi A. (2001): Napkollektoro melegvíz-tároló hőmérékleti rétegződée, Magyar Energetika, IX. évf., 2001/5. z., o. - Zahár A. (2003): Termiku rétegződé haználati melegvíztárolókban, Doktori értekezé, Szent Itván Egyetem, Gödöllő, p El Mahad, H.M., Van Loon, W.K.P., Zeeman, G., Bot, G.P.A., Letinga, G. (2004): Deign of a olar thermophili anaerobi reator for mall farm, Bioytem Engineering, 87 (3), p Hegyi K. (2007): Folyadéko napkollektor modellezée a hőhordozó közeg paramétereinek alapján, MTA Agrár-Műzaki Bizottág, XXXI. Kutatái é Fejleztéi Tanákozá, Gödöllő, jan. 23, 3. kötet, o. - Petrah, J., Steinfeld, A. (2007): Dynami of a olar thermohemial reator for team-reforming of methane, Chemial Engineering Siene, 62 (16) p Gézyné V. P. (2007): Napkollektoro rendzerek modellezée neuráli hálóval, Doktori értekezé, Szent Itván Egyetem, Gödöllő, p Chao Shen, Ya-Ling He, Ying-Wen Liu, Wen-Quan Tao (2008): Modelling and imulation of olar radiation data proeing with Simulink, Simulation Modelling Pratie and Theory, 16 (7) p Petrah, J., Oh, P., Steinfeld, A. (2009): Dynami and ontrol of olar thermohemial reator, Chemial Engineering Journal, 145 (3) p Referred artile in Hungarian: 1. Farka I., Biró A., Buzá J., Hegyi K., Lágymányoi A., Sere I., Sere E.E., Szű M. (1998): Oktatái é demontráió élú napenergia haznoító berendezéek, Magyar Energetika, VI. évf. 3. zám, júniu, p

26 Citation: - Rik K. (1999): Szolári zárítóban kialakuló termézete konvekió mérée, Gödöllői Agrártudományi Egyetem, Fizika é Folyamatirányítái Tanzék, Report No. 12, január, o. - Gézyné V. P. (2007): Napkollektoro rendzerek modellezée neuráli hálóval, Doktori értekezé, Szent Itván Egyetem, Gödöllő, p Farka I., Biró A., Buzá J. (1999): Napenergia növényházi haznoítáa, Energiagazdálkodá, 40. évf., 1. zám, január, p Farka I., Buzá J., Lágymányoi A., Kalmár I. (2001): Napenergiá uzodai vízmelegítő rendzer, Magyar Energetika, IX. évf. 3. zám, júniu, p Citation: - Gézyné V. P. (2007): Napkollektoro rendzerek modellezée neuráli hálóval, Doktori értekezé, Szent Itván Egyetem, Gödöllő, p Farka I., Lágymányoi A. Buzá J. (2001): Tetőbe integrált napkollektoro rendzer aládi ház melegvíz-ellátáára, Magyar Energetika, IX. évf. 4. zám, auguztu, p Farka I., Lágymányoi A., Buzá J. (2002): Caládi ház tetőbe integrált napkollektoro vízmelegítő rendzerének monitorozái eredményei, Energiagazdálkodá, 43. évf., 2002, 2. z., o. 6. Buzá J., Farka I., Lágymányoi A., Tóth M. (2002): Úzómedene napenergiá vízmelegítő rendzerének monitorozái eredményei, Energiagazdálkodá, 43. évf., 2002, 3. z., o. Citation: - Zebik, A. (2002): Motivationen und Grenzen der Verwendung erneuerbarer Energie in Ungarn, Berliner Energietage, VIK Verband der Indutriellen Energie- und Kraftwirthaft e.v., Berlin, 15. Mai, Hegyi K. (2003): Szolárfolyadék anyagi paramétereinek vizgálata fizikai módzerekkel, MTA Agrár-Műzaki Bizottág, XXVII. Kutatái é Fejleztéi Tanákozá, Gödöllő, jan , 3. kötet, o. - Hegyi K. (2004): Szolárfolyadék termodinamikai paramétereinek vizgálata, MTA Agrár-Műzaki Bizottág, XXVIII. Kutatái é Fejleztéi Tanákozá, Gödöllő, jan , 4. kötet, o. 26

27 - Hegyi K. (2005): Folyadéko napkollektorok hőhordozó közegének é áramlái jellemzőinek vizgálata, MTA Agrár-Műzaki Bizottág, XXIX. Kutatái é Fejleztéi Tanákozá, Gödöllő, jan , 3. kötet, o. - Hegyi K. (2006): A hőhordozó közeg anyagi paramétereinek hatáa a folyadéko napkollektorok működéére, MTA Agrár-Műzaki Bizottág, XXX. Kutatái é Fejleztéi Tanákozá, Gödöllő, jan. 24, 3. kötet, o. International onferene proeeding: 1. Matrawy,K.K., Farka,I., Buzá,J. (1996): Optimum eletion for the apet ratio of olar torage tank, EuroSun 96, Proeeding, Vol. 1, Freiburg, September 16-19, p Farka,I., Matrawy,K.K., Buzá,J. (1996): Theoretial and experimental tudy of olar olletor under tranient ondition, Energy and Environment Congre, Vol. I. /ed by B. Frankovi/, Croatian Solar Energy Aoiation, Opatija, Otober 23-25, p Buzá,J., Farka,I., Biró,A., Németh,R. (1997): Modelling and imulation of a olar thermal ytem, Proeeding of IMACS/IFAC Seond International Sympoium on Mathematial Modelling and Simulation in Agriultural and Bio-Indutrie, May 7-9, 1997, Budapet, Hungary, p Sere,E.E., Farka,I., Biró,A., Buzá,J., Lágymányoi,A. (1997): Data logging and monitoring tool ued for imulation and modelling of a olar ytem, Proeeding of IMACS/IFAC Seond International Sympoium on Mathematial Modelling and Simulation in Agriultural and Bio-Indutrie, May 7-9, 1997, Budapet, Hungary, p Sere,E.E., Farka,I., Biró,A., Buzá,J., Lágymányoi,A. (1997): Data logging and monitoring of an integrated rural energy ytem, Preprint of the 3rd Workhop on Mathematial and Control Appliation in Agriulture & Hortiulture, September 28 - Otober 2, 1997, /ed by A. Munah and H.-J. Tantau/, Pergamon, Hannover, Germany, p Buzá,J., Farka,I., Jedriko,C. (1999): Simulation of a olar dometi hot water ytem, Proeeding of the Conferene on Energy and Agriulture toward the Third Millennium, AgEnergy'99, Athen, Greee, 2-5 June 1999, Volume 1, p Buzá,J., Farka,I. (2000): Solar dometi hot water ytem imulation uing blok-oriented oftware, The 3 rd ISES-Europe Solar Congre (EuroSun 2000), Copenhagen, Denmark, June 19-22, 2000, CD-ROM Proeeding, pp

28 Citation: - Kiiny, R. (2008): Performane modelling of ombined olar heating ytem with ordinary- and with an energetially-baed ontrol, Energy and Environment in pratie, Proeeding of the Seminar of Dotorate Student from Jutu Liebig Univerity and Szent Itván Univerity, 19-21, Augut 2008, p Farka,I., Buzá,J., Lágymányoi,A., Kalmár,I., Kaboldy,E., Nagy,L. (2000): A ombined olar hot water ytem for the ue of wimming pool and kindergarten operation, Energy and the Environment 2000, Vol. I. /ed by B. Frankovi/, Croatian Solar Energy Aoiation, Opatija, Otober 25-27, 2000, p Buzá,J., Farka,I. (2001): Monitoring of a olar heated wimming pool, Reearh and Teahing at Department of Phyi in the Context of Univerity Eduation, Proeeding of the International Sientifi Conferene, Nitra, Slovak Republi, January 26, 2001, p Farka,I., Buzá,J., Lágymányoi,A., Tóth,M. (2001): Experiene with the ue of a olar olletor ytem integrated in to the roof truture of a family houe, CD-ROM Proeeding of North Sun 2001, Leiden, The Netherland, 6-8 May 2001, pp Farka,I., Buzá,J. (2001): Experiene with a ombined olar ytem for heating wimming pool and produing dometi hot water, CD-ROM Proeeding of ISES World Congre, Adelaide, Autralia, November 25-30, 2001, p Buzá,J., Farka,I., Tóth,M. (2002): Performane evaluation of a olar heated wimming pool, The 4th ISES-Europe Solar Congre (EuroSun 2002), Bologna, Italy, June 23-26, 2002, CD-ROM Proeeding, pp Tóth,L., Shrempfl,N., Buzá,J., Fogarai,L. (2005): Solar-energy utilization ytem wellne hotel, Proeeding 9th International Congre on Mehanization and Energy in Agriulture & 27th International Conferene of CIGR Setion IV (The Effiient Ue of Eletriity and Renewable Energy Soure) September 27-29, 2005, Ízmir, Turkey, p Hungarian onferene proeeding: 1. Benik T., Buzá J. (1996): Napenergia alkalmazá lehetőégeinek elemzée a haználati melegvíz zolgáltatában, MTA Agrár-Műzaki Bizottág, Kutatái é Fejleztéi Tanákozá, Gödöllő, január

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