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both models is explained by increasing heat losses with storage size, this also explains the rise in energy cost seen in the stratified storage model. 1.05 1.35 Stratified Mixed 1 0.95 1.3 1.25 1.2 0.9 1.15 1.1 1.05 0.8 0 0.5 1 1.5 0 0.5 1 1.5 0.85 1 (a) Energy cost Figure 5: Relative total energy cost assuming the day-night tariff for several storage sizes. The optimal energy flow profile to the storage tank and the energy content of the storage for the optimal storage sizes is shown in figure 6. The sizes shown are 1.1 times the energy demand for the stratified storage tank and 1.5 times the energy demand for the mixed storage tank. In figure 6(a) the load shift away from the high price period towards the low price period is clearly seen. As in this figure the storage is large enough the entire production of energy is shifted to the low price period. However, in figure 6(b) can be seen that the maximum amount of stored energy is almost equal for both models. A mixed storage will thus have to be larger than a stratified storage in order to be able to receive an equal amount of energy due to limited capacity flow rates. Due to heat losses it is most efficient to add the energy to the storage as close to the time of discharge as possible. Due to the rising inlet temperature of the heater and the constrained mass flow in the mixed model, the deliverable power decreases as the storage charges. The energy will thus be added at earlier times which deteriorates the cost reduction. 7 6 5 4 3 2 1 1.2 1 0.8 0.6 0.4 0.2 E∗ max E∗ max Stratified Mixed (b) Total supplied energy 00 0 5 10 15 20 t (h) (a) Storage energy flow 0 5 10 15 20 t (h) (b) Storage energy content Stratified Mixed Figure 6: Optimized energy flow profile and storage energy content assuming day-night energy price tariff for the optimal storage size, 1.1 times the energy demand for the stratified storage tank and 1.5 times the energy demand for the mixed storage tank 7 Stratified Mixed Q ̇ ∗sup J∗ E∗ E∗ supPDF Image | Energy cost reduction by optimal control of ideal sensible thermal energy storage
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