## 3 Applications
### Development of DRSFO-EES Model
\(\widetilde{B}_{kt}(B_{kt}{}^{1},B_{kt}{}^{2},B_{kt}{}^{3})\) denote the variable cost of capacity expansion. \(Z_{kth}\) denotes the continuous variable of the capacity expansion amount. (10) Generation costs for primary energy resources. This cost is calculated in terms of the unit-price of primary energy (i.e., coal, natural gas, and crude oil) and the amount of primary generation. \[ \begin{array}{l}\widetilde{f}_{10}=\sum\limits_{i=1}^{3}\sum\limits_{t=1}^{3 }0.25(EPP_{lt}{}^{1}+2\cdot EPP_{lt}{}^{2}+EPP_{lt}{}^{3})\cdot EPA_{it}\\ +\lambda_{1}\cdot\sum\limits_{i=1}^{3}\sum\limits_{t=1}^{3}[EPP_{lt}{}^{3}-0.25 \cdot(EPP_{lt}{}^{1}+2\cdot EPP_{lt}{}^{2}+EPP_{lt}{}^{3})]\cdot EPA_{it}\\ +\lambda_{2}\cdot\sum\limits_{i=1}^{3}\sum\limits_{t=1}^{3}[0.25\cdot(EPP_{lt}{}^{1 }+2\cdot EPP_{lt}{}^{2}+EPP_{lt}{}^{3})-EPP_{lt}{}^{1}]\cdot EPA_{it}\end{array}  \tag{32}\]  
where \(E\widetilde{P}P_{it}(EPP_{lt}{}^{1},EPP_{lt}{}^{2},EPP_{lt}{}^{3})\) is the production cost per unit of energy resource; and \(EPA_{it}\) is the production amount. (11) Subsidy for solar power. The government provides a subsidy for units of electricity generated by solar power, and it is calculated in terms of the unit-subsidy of solar power and the amount of electricity generation amount of solar power. \[ \begin{array}{l}\widetilde{f}_{11}=\sum\limits_{t=1}^{3}\left[0.25(SP_{t}{}^{ 1}{+}2 SP_{t}{}^{2}+SP_{t}{}^{3})\cdot(W_{3t}{}^{-}+rr_{3t}{\cdot}\Delta W_{3t}) \right.\\ \left.+\sum\limits_{t=1}^{3}\left[SP_{t}{}^{3}-0.25(SP_{t}{}^{1}{+}2 SP_{t}{}^{ 2}+SP_{t}{}^{3})\right]\right.(W_{3t}{}^{-}+rr_{3t}{\cdot}\Delta W_{3t})\\ \left.+\sum\limits_{t=1}^{3}\left[0.25(SP_{t}{}^{1}{+}2 SP_{t}{}^{2}+SP_{t}{}^{ 3})\right.\right.-SP_{t}{}^{1})\left.(W_{3t}{}^{-}+rr_{3t}{\cdot}\Delta W_{3t}) \right.\end{array}  \tag{33}\]  
where \(S\widetilde{P}_{t}(SP_{t}{}^{1},SP_{t}{}^{2},SP_{t}{}^{3})\) is the solar subsidy provided by government for unit of electricity generated by solar power. (12) Subsidy for wind power. The government provides a subsidy for units of electricity generated by wind power, and it is calculated in terms of the unit-subsidy of wind power and the amount of electricity generation amount of wind power. \[ \begin{array}{l}\widetilde{f}_{12}=\sum\limits_{t=1}^{3}\left[0.25(WP_{t}{}^ {1}{+}2 WP_{t}{}^{2}+WP_{t}{}^{3})\cdot(W_{4t}{}^{-}+rr_{4t}{\cdot}\Delta W_{4t })\right.\\ \left.+\sum\limits_{t=1}^{3}\left[WP_{t}{}^{3}-0.25(WP_{t}{}^{1}{+}2 WP_{t}{}^ {2}+WP_{t}{}^{3})\right]\right.(W_{4t}{}^{-}+rr_{4t}{\cdot}\Delta W_{4t})\\ \left.+\sum\limits_{t=1}^{3}\left[0.25(WP_{t}{}^{1}{+}2 WP_{t}{}^{2}+WP_{t}{}^ {3})\right.\right.-WP_{t}{}^{1})\left.(W_{4t}{}^{-}+rr_{4t}{\cdot}\Delta W_{4t })\right.\end{array}  \tag{34}\]  
where \(WP_{t}{}^{1},WP_{t}{}^{2},WP_{t}{}^{3})\) is the wind subsidy provided by government for unit of electricity generated by wind power. (13) Costs for battery charging piles. It is calculated in terms of the average charging pile amount for unit of electric vehicle, the EVs population, as well as the investment cost per EV charging pile. \[f_{13}=\sum\limits_{t=1}^{3}EVA_{t}REC_{t}FCD_{t} \tag{35}\]  
where \(EVA_{t}\) is the EVs population; \(REC_{t}\) is the average charging pile amount for unit of electric vehicle; \(FCD_{t}\) is the investment cost per EV charging pile. (14) Costs for battery changing station. It is calculated in terms of the average changing station amount for unit of electric vehicle, the EVs population, as well as the investment cost per EV changing station. \[f_{14}=\sum\limits_{t=1}^{3}EVA_{t}REV_{t}FVD_{t} \tag{36}\]  
where \(REV_{t}\) is the average changing station amount for unit of electric vehicles; \(FVD_{t}\) is the investment cost per \(EV\) changing station. (15) Costs for pollutant reduction. These costs include reduction costs for three pollutants, i.e., SO\({}_{2}\), NO\({}_{X}\), and PM emissions.