*3.2. Estimation of Income and Expenses*

The storable amount of energy in UPSH plants depends on the net head and the water mass moved. The maximum income from selling energy has been studied considering the amount of electricity generated in turbine mode considering the maximum prices in the day-ahead and ancillary services markets. Likewise, the downward tertiary regulation service and the day-ahead market have been analyzed to obtain the minimum price for purchasing energy. Figure 4a shows the maximum prices in the day-ahead and ancillary services and the minimum prices in the downward tertiary regulation service, considering DTCs between 4 and 10 h. The price spread between the day-ahead and the ancillary services markets for generation and consumption modes is shown in Figure 4b.

*Appl. Sci.* **2020**, *10*, x FOR PEER REVIEW 7 of 16

**Figure 4.** Analysis of electricity markets. (**a**) Maximum electricity prices in the day-ahead and ancillary services markets; minimum costs in the downward tertiary regulation service and annual generation cycles. (**b**) Price spread between the day-ahead and the ancillary services markets. **Figure 4.** Analysis of electricity markets. (**a**) Maximum electricity prices in the day-ahead and ancillary services markets; minimum costs in the downward tertiary regulation service and annual generation cycles. (**b**) Price spread between the day-ahead and the ancillary services markets.

Concerning Figure 4a, the number of annual generation cycles is calculated to obtain the amount of electricity generated in turbine mode. The electricity consumed in pumping mode is estimated assuming a round trip energy efficiency of about 0.77. The annual generation cycles decrease from 360 to 323 when the DTC increases from 4 to 10 h. The maximum price of electricity is 78.74 € MWh−<sup>1</sup> and is reached when participating in the ancillary services markets. That value, which corresponds to a DTC of 4 h, is progressively reduced by 7% when the DTC increases to 10 h. The minimum price in consumption mode is 22.13 € MWh−1. This cost for purchasing energy is increased by 22.81%, reaching 27.18 € MWh−1 when the DTC increases to 10 h. In Figure 4b, it is shown that the maximum price spread between the day-ahead and the ancillary service markets in generation mode is 24.92 € MWh−1. In consumption mode, the maximum price spread reaches −16.88 € MWh−1. The price spread decreases by 2.36 € MWh−1 in generation mode and 1.42 € MWh−1 in consumption mode when the DCT increases to 10 h. Concerning Figure 4a, the number of annual generation cycles is calculated to obtain the amount of electricity generated in turbine mode. The electricity consumed in pumping mode is estimated assuming a round trip energy efficiency of about 0.77. The annual generation cycles decrease from 360 to 323 when the DTC increases from 4 to 10 h. The maximum price of electricity is 78.74 € MWh−<sup>1</sup> and is reached when participating in the ancillary services markets. That value, which corresponds to a DTC of 4 h, is progressively reduced by 7% when the DTC increases to 10 h. The minimum price in consumption mode is 22.13 € MWh−<sup>1</sup> . This cost for purchasing energy is increased by 22.81%, reaching 27.18 € MWh−<sup>1</sup> when the DTC increases to 10 h. In Figure 4b, it is shown that the maximum price spread between the day-ahead and the ancillary service markets in generation mode is 24.92 € MWh−<sup>1</sup> . In consumption mode, the maximum price spread reaches <sup>−</sup>16.88 € MWh−<sup>1</sup> . The price spread decreases by 2.36 € MWh−<sup>1</sup> in generation mode and 1.42 € MWh−<sup>1</sup> in consumption mode when the DCT increases to 10 h.

For the purpose of analyzing the economic feasibility of the three HPSs considered in this study, the amount of energy generated and consumed and the maximum income from selling energy in generation mode (turbine) and minimum costs for purchasing energy in consumption mode (pumping) are shown in Figure 5 for the three HPSs. The maximum income decreases while the minimum expenses increase as the DTC increases from 4 to 10 h (see Figure 5d). For the purpose of analyzing the economic feasibility of the three HPSs considered in this study, the amount of energy generated and consumed and the maximum income from selling energy in generation mode (turbine) and minimum costs for purchasing energy in consumption mode (pumping) are shown in Figure 5 for the three HPSs. The maximum income decreases while the minimum expenses increase as the DTC increases from 4 to 10 h (see Figure 5d).

**Figure 5.** Maximum income from selling energy and minimum cost for purchasing energy, considering DTCs between 4 and 10 h: (**a**) HPS 1; (**b**) HPS 2; (**c**) HPS 3. (**d**) Amount of energy generated **Figure 5.** Maximum income from selling energy and minimum cost for purchasing energy, considering DTCs between 4 and 10 h: (**a**) HPS 1; (**b**) HPS 2; (**c**) HPS 3. (**d**) Amount of energy generated and consumed for HPS 1, HPS 2 and HPS 3.

and consumed for HPS 1, HPS 2 and HPS 3.

respectively, when the DTC increases from 4 to 10 h day−1.

The design of the DTC influences the annual number of production cycles and therefore the amount of electricity generated. The electricity generated is reduced from 226.46 to 203.00 GWh year−<sup>1</sup> in HPS 1, from 391.19 to 350.16 GWh year−1 in HPS 2 and from 789.73 to 701.32 GWh year−1 in HPS 3 when the DTC increases from 4 to 10 h. The maximum theoretical income reaches 49.06 M€ year−<sup>1</sup> and is obtained in HPS 3 when the DTC is 4 h. The maximum income is reduced by 16.70% and the minimum costs are increased by 8.56% in HPS 3 when the DTC is increased to 10 h. Consequently, the spread between the income from selling electricity and the cost for purchasing electricity is also reduced from 31.59 to 21.91 M€ year−1 in HPS 3 when the DTC increases to 10 h. The maximum The design of the DTC influences the annual number of production cycles and therefore the amount of electricity generated. The electricity generated is reduced from 226.46 to 203.00 GWh year−<sup>1</sup> in HPS 1, from 391.19 to 350.16 GWh year−<sup>1</sup> in HPS 2 and from 789.73 to 701.32 GWh year−<sup>1</sup> in HPS 3 when the DTC increases from 4 to 10 h. The maximum theoretical income reaches 49.06 M€ year−<sup>1</sup> and is obtained in HPS 3 when the DTC is 4 h. The maximum income is reduced by 16.70% and the minimum costs are increased by 8.56% in HPS 3 when the DTC is increased to 10 h. Consequently, the spread between the income from selling electricity and the cost for purchasing electricity is also reduced from 31.59 to 21.91 M€ year−<sup>1</sup> in HPS 3 when the DTC increases to 10 h. The maximum incomes reach 13.91 and 24.41 M€ year−<sup>1</sup> in HPS 1 and HPS 2 when the DTC is 4 h. In addition,

incomes reach 13.91 and 24.41 M€ year−1 in HPS 1 and HPS 2 when the DTC is 4 h. In addition, the spreads between the income and expenses are reduced by 45.86% and 31.12% in HPS 1 and HPS 2, the spreads between the income and expenses are reduced by 45.86% and 31.12% in HPS 1 and HPS 2, respectively, when the DTC increases from 4 to 10 h day−<sup>1</sup> .

As a presumable guideline, Table 2 shows the maximum theoretical income and the expenses of the three HPSs when considering a DTC of 8 h. In this scenario, the maximum output powers (turbine mode) for HPS 1, HPS 2 and HPS 3 are 62, 109 and 219 MW, respectively, while the maximum input powers (pumping mode) are 53, 92 and 185 MW for HPS 1, HPS 2 and HPS 3, respectively. The maximum income and the minimum cost for purchasing energy are obtained participating in the day-ahead and the ancillary services markets. The costs for purchasing energy represent 84%, 85% and 87% of the total costs in HPS 1, HPS 2 and HPS 3, respectively. In addition, O&M costs, start-up costs, grid access tariff and hydraulic cannon have been considered. As established in Spanish electrical regulation, a cost of 0.5 € MWh−<sup>1</sup> has been considered as grid access tariff. O&M costs include personnel, insurance, spare parts and external service costs. Finally, the operating margins (income from selling electricity minus the cost for purchasing electricity and operation costs) have been estimated, reaching 6.07, 10.99 and 22.71 M€ year−<sup>1</sup> in HPS 1, HPS 2 and HPS 3, respectively. Repeating all these considerations when a DTC of 4 h is designed, the operating margins increase to 7.83, 14.11 and 28.81 M€ year−<sup>1</sup> in HPS 1, HPS 2 and HPS 3, respectively.


