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constant at Theater,out. The fluid entering the heater is at a temperature Theater,in. The storage tank receives heat Q ̇ sup = C ̇sup(Theater,out − Theater,in) from the heater. The temperature of the fluid entering the emission system is Temission,in while the temperature of the fluid exiting the system is Temission,out. The emission system is modelled as having a uniform temperature Tem towhichaheatflowQ ̇em =C ̇em(Temission,in−Temission,out)isaddedfromthestoragetank. The variation of state of the storage system can now be written as: dE =Q ̇sup −Q ̇em −Q ̇hl (1) dt With E the energy in the storage tank and Q ̇ hl the heat lost from the storage to the ambient air through heat transfer which can be calculated as: Q ̇ =UA (T ̄ −T ) (2) dt Theater,out Q ̇ sup 2.3. Boundary conditions Temission,in Q ̇ em hl sto sto amb Here the storage is assumed to be outside of the heated volume, transferring heat losses directly to the ambient temperature (Tamb). To provide for the temperatures exiting the storage, the storage model must be further specified. The simplest choices are the assumptions of known and constant temperature at the top (Th) and at the bottom of the tank (Tc) or the assumption of a uniform, but variable, temperature throughout the tank. The former represents an ideally stratified storage tank while the latter represents an ideally mixed storage tank. The values for Th and Tc are determined from the heating system and the emission system. Th will be equal to the heater outlet temperature while Tc is equal to the average emission system return temperature. For the ideally stratified model the state equation turns into: dE =C ̇sup(Th −Tc)−Q ̇em −Q ̇hl (3) dt While for the ideally mixed model the state equation becomes: dE =C ̇sup(Th −T)−Q ̇em −Q ̇hl (4) E Q ̇ hl Figure 2: Model of a thermal energy storage tank Theater,in Tem Temission,out The emission system provides the interaction between heating system and building. To obtain a certain level of thermal comfort the heating system needs to supply, at any time, a certain amount of heat to the emission system (Q ̇ em) which needs to be at a certain temperature (Tem) to be able to transfer the energy to the entire building. These two values can thus be used to 3PDF Image | Energy cost reduction by optimal control of ideal sensible thermal energy storage
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