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3.3.2. Variable energy tariff In figure 7(a) the total energy cost is given for several storage sizes for both the stratified and mixed model. In the case of variable energy prices, the optimal storage size using the stratified model remains 1.1 times the total energy demand as in the case of the day-night tariff. The minimum relative energy cost rises to 0.88. The mixed model however shows a local minimal cost at 0.7 times the energy demand. The minimal cost is however still obtained with the largest storage size and has a value of 0.98. This increase in cost relative to the day-night pricing scheme is caused by the smaller variation of the energy prices. Although both control profiles (figure 8(a)) look very similar the mixed model uses more energy and thus has a higher cost. 1.05 1.25 1 1.2 Stratified Mixed Stratified Mixed 0.95 0.9 0.85 1.15 1.1 1.05 0.8 0 0.5 1 1.5 0 0.5 1 1.5 1 (a) Energy cost Figure 7: Relative total energy cost assuming the variable energy price tariff for several storage sizes. The optimized energy flow to the storage tank and the energy content of the storage assuming the variable energy price tariff for the optimal storage size is presented in figure 8. As the energy tariff has a distinct minimum the optimization attempts to concentrate the charging around this minimum. The reduction in maximum heater power observed under the day-night tariff assumption for the mixed storage model is thereby eliminated. 7 1.5 E∗ max E∗ max (b) Total supplied energy 6 5 4 3 2 1 1 0.5 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 8: Optimized energy flow profile and storage energy content assuming a variable 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 In both the stratified and mixed tank optimizations the load peaks present in the situation without energy storage will be shifted to other periods but will not diminish in size. When the 8 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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