| Notation | Description |
|---|
| $z \in \mathcal{Z}$ | $z$ denotes a zone and $\mathcal{Z}$ is the set of zones in the network |
| $t \in \mathcal{T}$ | $t$ denotes an time step and $\mathcal{T}$ is the set of time steps |
| $t \in \mathcal{T}^{start}$ | This set of time-coupling constraints wrap around to ensure the output in the first time step of each year (or each representative period) |
| $t \in \mathcal{T}^{interior}$ | This set of time-coupling constraints wrap around to ensure the output in the inner time step of each year (or each representative period) |
| $f \in \mathcal{F}$ | Index and set of all synthetic fuels resources |
| $b \in \mathcal{B}$ | Index and set of all synthetic fuels process byproducts |
| Notation | Description |
|---|
| $x_{f,t}^{\textrm{C,Syn}}$ | this term represents CO2 input by synthetic fuels resource $f$ at time period $t$ |
| $x_{f,b,t}^{\textrm{By,Syn}}$ | this term represents the byproducts $b$ produced by synthetic fuels resource $f$ at time period $t$ |
| $y_{f,t}^{\textrm{C,Syn}}$ | capacity of synthetic fuels resources in the liquid fuels supply chain |
| $x_{z,t}^{\textrm{Gasoline,Conv}}$ | this term represents conventional gasoline purchased by zone $z$ at time period $t$ |
| $x_{z,t}^{\textrm{Jetfuel,Conv}}$ | this term represents conventional jetfuel purchased by zone $z$ at time period $t$ |
| $x_{z,t}^{\textrm{Diesel,Conv}}$ | this term represents conventional diesel purchased by zone $z$ at time period $t$ |
| Notation | Description |
|---|
| $\textrm{c}_{f}^{\textrm{Syn,INV}}$ | investment cost per tonne CO2 input of synthetic fuels resource |
| $\textrm{c}_{f}^{\textrm{Syn,FOM}}$ | fixed operation cost per tonne CO2 input of synthetic fuels resource |
| $\textrm{c}_{f}^{\textrm{Syn,VOM}}$ | variable operation cost per tonne of CO2 input by synthetic fuels resource |
| $\textrm{c}_{g}^{\textrm{Syn,FUEL}}$ | fuel cost per tonne of CO2 input by synthetic fuels resource |
| $\textrm{c}_{b}^{\textrm{By,Syn}}$ | selling price per mmbtu of byproduct by synthetic fuels resource (if any) |
| $\textrm{c}_{z}^{\textrm{Gasoline,Conv}}$ | purchase cost per mmbtu of conventional gasoline |
| $\textrm{c}_{z}^{\textrm{Jetfuel,Conv}}$ | purchase cost per mmbtu of conventional jetfuel |
| $\textrm{c}_{z}^{\textrm{Diesel,Conv}}$ | purchase cost per mmbtu of conventional diesel |
| $\overline{y}_{f}^{\textrm{\textrm{C,Syn}}}$ | upper bound of capacity is defined,then we impose constraints on maximum CO2 input capacity of synthetic fuels resource |
| $\underline{y}_{f}^{\textrm{\textrm{C,Syn}}}$ | lower bound of capacity is defined,then we impose constraints on minimum CO2 input capacity of synthetic fuels resource |