Most frequently the inquiry of the optimal value of thedecision variable is done numerically, taking intoconsideration the discrete character of cost functions andvariables.We discretize the possible value aggregation of theactual status variable – for example Z M – , and for eachexact value we search for the U M (Z M ) value of decisionvariable, resulting in optimal minimal value O(Z M ), whichwe store.Figure 1. White box model of serial decision system [7]With the appropriate choice of U M decision variable inthe function of Z M decision variable we have the optimumof the partial system containing M, M+1,…, N-1 stages,that is the optimal cost of U M,opt, U M+1,opt , …U N-1,optoptimal decisions. This optimization is called dynamic,backward recursive optimization.In the first phase of optimization we define the O N-1((U N-1 , Z N-1 ), Z N ) function as followsOON1 ( ZN1) min fN1ZN1,ZN,UAs a second stepN2N 1UN1( ZN2) min fN2ZN2,UN2 ON1(ZN1)UN 2. (4), (5)but it is observable thatZ N1 gN1( UN2,ZN1), (6)thereforeON2( ZN2 fN2ZN2,UN2 ) min UN 2ON1(gN1(UN2,ZN1)). (7)By this optimization of the decision variable O N-2 (Z N-2 )for U N-2 we can define optimal value of U N-2 , which thenwe substitute to the function O N-2 (Z M-2 , U N-2 ). Hence, weget to know the optimal (maximal or minimal) costs of thestudied stages in the function of Z N-2 inputs.III. DECISION SYSTEM THEORY MODEL OF OPERATINGHEAT PUMP SYSTEMS WITH U-TUBE CONSTALLATIONWhen describing to the optimization of an operatingsystem, we refer to the search of those operatingparameters of an installed and operating system –considering heat demand of the consumer - , by which theoperating costs of the system are minimal. For this wehave to know precisely the type and size of the elementsin the system and the demand of the consumer. Wedemonstrate the system theory scheme of an operatingsystem in “Fig. 2”.Decision variables determining the operation duringoptimization of an operating system: By U-tube heat source: mass flow of primer liquid( mp), temperature of primer liquid (forward flow)upcoming from U-tube (T pe ); By evaporator: mass flow ( mh) of refrigerant appliedat cycle; By compressor: condensation temperature (T c ) andevaporation temperature (T o ); By consumer: mass flow of heating water ( ms),temperature of the forward heating water (T se );Objective function of the decision system of heatpumps, demonstrated in “Fig 2” is as follows:K(Q Kconsumercompressor) min K Küevaporator min( K KU tubeconsumer) Kcondensator. (8)A. Optimal function by the consumer’s stageThe consumer’s heat demand is given, which is theknown output of the decision stage. The input of the stageis the circulated heating mass flow, which we consider asparameter. We link the optimal function of the stage tothis parameter, which is the electric power cost of theheating water’s circulation. Mass flow msof thecirculated heating water is parameter and at the same timedecision variable.O m3 s1ms ke Rs s e11 , (9)Whereby R s is the coefficient of hydraulic resistance ofthe known pipe system with given geometric parameters,k e is the unit cost of electric power, is the pumpefficiency and is the electric motor efficiency.mThe function expresses the utilized electric powerefficiency for satisfying consumer’s demand with a givenme92
parameter of pump in the function of the parameter, likeFigure 2. Decision system theory model of an operating heat pumpsystemthe mass flow of the circulated heating water on thesecondary side. Provided that we set particular exactvalues of msparameter, then correspondingly, we cancalculate the secondary forward going and returning watertemperature with the help of formulas (10) and (11).QconsumerQconsumerTsv Tse Tb ms cskrad AradQconsumer ,(10) m c2s sTse TQsvconsumer2mscsQmc.consumerss TbQkradconsumer Arad(11)B. The optimal function for the partial system with acondensatorWhile in operation, new operating costs do not emergeby the decision stage of the condensator. Therefore,O Tc O m211 s. (12)In case of an operating system mass flow of theoperating system on the secondary side by the stage of thecondensator remains as parameter. Optimum of the stageequals with the optimum of the previous level. We do notperform optimization. Condensation temperature isdetermined. It is known from former stages that QconsumerQcondT cTb, (13) krad Aradkcond Acondby whichO TcQ21 consumer O1ms. (14)For the production of O m1 s we search for the lowestallowed (lower than nominal) circulate able heating massflow m .sC. The optimal function for the partial systemsupplemented by compressor stageA new cost element enters, namely the electric powerutilization of the compressor. In the optimization functionwe place this electric power utilization of the compressornext to the O m21 staken from the previous decisionstage. To the optimal function of the newly supplemented321 system we involve the evaporation temperature asparameter, given that electric power use and COP value ofthe compressor is determined by condensation andevaporation temperature.ETo,Tc( Qconsumer)O321 To O T . (15)c( Q21 consumerHereby E T T c Q 0,consumeris the electric powerutilization of the compressor, and its cost. TheT c ( Q ) and T o determines the value of COP and thevalue ofconsumerQ evapQThe values ofas well, wherebyQevap PrealCOP .Prealare calculated by equations (16) and(17), while Prealcan be calculated by equation (18).equals with heat quantity extractable by U-tube.evap mpcpevap evap mpcpT T 1e, (16)QpeokA93
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4 4 th IEEE International Symposium
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EXPRES 20124 th International Sympo
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Application of Thermopile Technolog
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Design of a Solar Hybrid System....
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environmental protection and global
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But can we use the human body sweat
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IX. REFERENCES[1] Todorovic B. Cvje
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QQ⎛ Λt⎞=⎜⎟⎝ Λ ⎠Nt Nwh
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Analysis of the Energy-Optimum of H
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V. OBJECTIVE FUNCTIONThe objective
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The Set-Up Geometry of Sun Collecto
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continuous east-west sun collector
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continuously measure the thermal ch
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CEvaluation of measurement resultsA
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Application of Thermopile Technolog
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Temperature of the components [C]90
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nighttime, to weather or to the cha
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η uη u0.50.40.30.20.1T 1 - 400K0.
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Figure 10. . SPS Concept illustrati
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[16] Zoya B. Popović: Wireless Pow
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