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Energy Systems and Technologies for the Coming Century ...

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. .WcFWcTeFTeFrostCompressorsCompressorsLTPCPC.QeF.QeMTTCEvaporatorsTCCondensor.QcTcrFFrost roomTambHeat loadTcrCold roomTaSurroundingsFig. 2.Schematic layout of basic refrigeration system.which puts <strong>the</strong> heat load on <strong>the</strong> refrigeration system. The states <strong>and</strong> control variables of <strong>the</strong>system are limited by <strong>the</strong> following constraints:T cr,min ≤ T cr ≤ T cr,max0≤T cr − T e ≤ ∞0≤ ˙Q e ≤(UA) cr−e,max·(T cr − T e )The work done by <strong>the</strong> compressor dominates <strong>the</strong> power consumption in <strong>the</strong> system <strong>and</strong> canbe expressed by <strong>the</strong> mass flow of refrigerant (m re f ) <strong>and</strong> <strong>the</strong> change in energy content of <strong>the</strong>refrigerant. <strong>Energy</strong> content is described by enthalpy of <strong>the</strong> refrigerant at <strong>the</strong> inlet <strong>and</strong> at <strong>the</strong>outlet of <strong>the</strong> compressor (h ic <strong>and</strong> h oc respectively). Hereby <strong>the</strong> expression in Eq. (3) is given.Ẇ c = m re f ·(h oc (T e ,P c )−h ic (T e ))η is (P c /P e )where <strong>the</strong> enthalpies depend on <strong>the</strong> evaporation temperature <strong>and</strong> <strong>the</strong> condensing pressure asstated. The mass flow can be determined as <strong>the</strong> ratio between cooling capacity <strong>and</strong> changeof enthalpy over <strong>the</strong> evaporator:m re f =˙Q eh oe (T e )−h ie (P c )All <strong>the</strong> enthalpies given here as functions of (T e , P c ) or both are non-linear refrigerantdependent functions which can be calculated e.g. by <strong>the</strong> software package ”RefEqns” [20].For <strong>the</strong> studies in section 4.1 we have assumed that <strong>the</strong> work done in <strong>the</strong> compressor isdirectly proportional with <strong>the</strong> delivered cooling capacity while we in section 4.3 use <strong>the</strong> realnon-linear description of Ẇ c described in [21] where polynomials are fitted <strong>for</strong> <strong>the</strong> enthalpydifferences. For <strong>the</strong> latter we have fur<strong>the</strong>rmore collected data from several supermarkets inreal operation in Denmark. From <strong>the</strong>se data typical parameters such as time constants, heatloads, temperature ranges <strong>and</strong> capacities in both individual display cases <strong>and</strong> <strong>for</strong> <strong>the</strong> overallsystem have been estimated. The running compressor capacity have been monitored <strong>and</strong> from<strong>the</strong> data sheets <strong>the</strong> relation to energy consumption has been found.3.2 Building with Heat PumpHeat dynamics of a buildingIn this section, we develop a model of <strong>the</strong> heat dynamics of a house floor heating systemconnected to a geo<strong>the</strong>rmal heat pump. The system is illustrated in Fig. 3. The model isbased on <strong>the</strong> energy balances <strong>for</strong> <strong>the</strong> air in <strong>the</strong> room, <strong>the</strong> floor <strong>and</strong> <strong>the</strong> water in <strong>the</strong> floorheating pipes <strong>and</strong> condenser water tank. The house is considered to be one big room with <strong>the</strong>following simplifying assumptions: 1) One uni<strong>for</strong>m air temperature, 2) no ventilation, 3) noinfluence from humidity of <strong>the</strong> air, 4) no influence from <strong>the</strong> heat released from people in <strong>the</strong>room, 5) no influence from wind. In our model two heat accumulating media are included(2a)(2b)(2c)(3)(4)Risø International <strong>Energy</strong> Conference 2011 Proceedings Page 167

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