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132 M.B. Blarke et al. / Energy and Buildings 50 (2012) 128–138 avoiding using electricity when net requirements are high (low wind/PV and/or peak demand periods). For individual options, extreme values are rarely achieved. But comparing options in terms of Rc allows maximizing the design and operational strategy of individual options towards supporting intermittent renewables in the energy system. 3.3. System-wide CO2 emissions COMPOSE applies a least-cost marginal dispatch energy sys- tem model for identifying marginal CO2 emissions for each hour of operation. The marginal electricity producer is identified by com- paring the short-term marginal cost of operation for dispatchable producers’ with the day-ahead spot market price. For each hour of operation, the marginal electricity producer is identified as the producer with the lowest marginal cost of operation that is higher than the day-ahead spot market price. Subsequently, the emissions M [kg] are found as stated in Eq. (2). where x is the specified set of variables. In actual model implemen- tation, the objective function includes proxy cost elements related to dumped thermal production, which is excluded here for the pur- pose of clarity. MCO2= wt t=1 CO2 ,t t (2) Phk,t + DumpPhk,t = F vk,t × COPhk,t Pck,t + DumpPck,t = F vk,t × COPck,t (5) K T f(x) = k=1 t=1 Fvk,t ×lk,t, wheret∈{1...24} (3) where sleh/slec is the heating/cooling storage loss when the storage is empty, and the differential heating/cooling loss sldh/sldc is the T f where the heat/cooling demand dh/dc [kWh] is equal to the heat/cooling production Ph/Pc minus net production to the thermal storage (storage in (ShIn/ScIn) minus storage out (ShOut/ScOut)). The heat/cooling production Ph/Pc is the product of the elec- tricity consumption Fv and the COPh/COPc. Furthermore, as the TB’s thermal production may not always be utilized, variables for dumped heating/cooling DumpPh/DumpPc are introduced as expressed in Eq. (5): where t is the hour of operation, w [kWh] is the electricity produc- tion, is the thermal efficiency of the identified marginal electricity producer, and f [kg/kWh] is the emission factor of the fuel used by the marginal electricity producer. 3.4. MathematicaleconomicdispatchmodelfortheTB The TB and the reference option are modeled according to least- cost principles. Thus, the objective function f(x) in the mathematical unit commitment model is to minimize the costs of operation. Let Fv be the electricity consumption [kWh], l the electricity price, and k the units (e.g. the resistance heater, but excluding storages), then f(x) is determined by Eq. (3): Dumped heating/cooling is assigned a very low cost and included in the objective function Eq. (3) to force for surplus thermal pro- duction to be stored rather than dumped. The balance of the thermal storages is obtained by Eq. (6): Sht = Sht−1 − Slht + ShInt − ShOutt Fig. 3. PG&E spot day-ahead market on July 19, 2011 (USD/MWh). The heating and cooling balance is given by Eq. (4): K dht = Phk,t − ShInt + ShOutt dct = Pck,t − ScInt + ScOutt k=1 K k=1 (4) Sct = Sct−1 − Slct + ScInt − ScOutt (6) where the heating/cooling storage content Sh/Sc [kWh] is equal to the storage content in the previous time interval minus the storage loss Slh/Slc plus net production to the storage. The heating/cooling storage loss Slh/Slc is given by Eq. (7): Slht = sleht + Sht × sldht sht Slct = slect + Sct × sldct sct (7)PDF Image | Thermal battery with CO2 compression heat pump
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