# HSC Model Notation

## Model Indices and Sets

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 power 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 power output in the inner time step of each year (or each representative period) |

$g \in \mathcal{G}$ | Index and set of all hydrogen generation resources (electrolysis, SMR plants and liquefiers and evaporators, if modeled) |

$k \in \mathcal{K}$ | Index and set of all gas-to-power resources (CCGT-H2, fuel cells) |

$s \in \mathcal{S}$ | Index and set of storage resources in hydrogen energy system representing hydrogen storage devices such as underground or above-ground storage |

$z \in \mathcal{Z}^{CO_2}_{p,mass}$ | we define a set of zones that can trade CO$_2$ allowance |

## Decision Variables

Notation | Description |
---|---|

$x_{z,t}^{\textrm{H,EMI}}$ | The amount of carbon dioxide emitted by the hydrogen supply chain at time $t$ in region $z$ |

$x_{g,z,t}^{\textrm{H,GEN}}$ | this term represents hydrogen injected into the grid by hydrogen generation resource $g$ in zone $z$ at time period $t$ |

$x_{g,z,t}^{\textrm{H,LIQ}}$ | this term represents liquefied hydrogen (gas to liquid) injected into the grid by hydrogen generation resource $g$ in zone $z$ at time period $t$ |

$x_{g,z,t}^{\textrm{H,EVAP}}$ | this term represents evaporated hydrogen (liquid to gas) injected into the grid by hydrogen generation resource $g$ in zone $z$ at time period $t$ |

$x_{s,z,t}^{\textrm{H,NSD}}$ | this term represents the total amount of hydrogen demand curtailed in demand segment $s$ at time period $t$ in zone $z$ |

$x_{s,z,t}^{\textrm{H,DIS}}$ | this term represents hydrogen injected into the grid by hydrogen storage resource $s$ in zone $z$ at time period $t$ |

$x_{s,z,t}^{\textrm{H,CHA}}$ | this term represents charged hydrogen into the storage device $s$ in zone $z$ at time period $t$ |

$x_{k,z,t}^{\textrm{H,G2P}}$ | representing energy injected into the grid by hydrogen to power resource $k$ in zone $z$ at time period $t$ |

$x_{z,t}^{\textrm{E,H-GEN}}$ | representing power consumed by electrolyzers in zone $z$ at time period $t$ |

$x_{i,z \rightarrow z^{\prime},t}^{\textrm{H,PIP}}$ | the hydrogen pipeline flow decision variable representing hydrogen flow via pipeline of type $i$ through path $z \rightarrow z^{\prime}$ at time period $t$ |

$y_{g,z}^{\textrm{H,GEN,existing}}$ | existing capacity of hydrogen generation resources in hydrogen sector |

$y_{g,z}^{\textrm{H,GEN,new}}$ | the newly invested capacity of hydrogen generation resources in hydrogen sector |

$y_{g,z}^{\textrm{H,GEN,retired}}$ | retired capacity of hydrogen generation resources in hydrogen sector |

$y_{k,z}^{\textrm{H,G2P}}$ | this term is the total installed capacity of hydrogen to power plants |

$y_{g}^{\textrm{H,G2P,total}}$ | existing capacity of hydrogen to power resources in hydrogen sector $y_{k,z}^{\textrm{H,G2P}} = y_{k,z}^{\textrm{H,G2P,total}}$ |

$y_{g}^{\textrm{H,G2P,existing}}$ | existing capacity of hydrogen to power resources in hydrogen sector |

$y_{g}^{\textrm{H,G2P,new}}$ | newly installed capacity of hydrogen to power resources in hydrogen sector |

$y_{g}^{\textrm{H,G2P,retired}}$ | retired capacity of hydrogen to power resources in hydrogen sector |

$y_{s,z}^{\textrm{H,STO,ENE}}$ | the installed energy storage capacity |

$y_{s,z}^{\textrm{H,STO,POW}}$ | the installed power capacity |

$y_{i,z \rightarrow z^{\prime}}^{\textrm{H,PIP}}$ | the hydrogen pipeline construction decision variable representing newly constructed hydrogen pipeline of type $i$ through path $z \rightarrow z^{\prime}$ |

$n_{k,z,t}^{\textrm{H,G2P}}$ | the commitment state variable of generator cluster $k$ in zone $z$ at time $t$ |

$n_{k,z,t}^{\textrm{H,G2P,UP}}$ | the number of startup decision variable of generator cluster $k$ in zone $z$ at time $t$ |

$n_{k,z,t}^{\textrm{H,G2P,DN}}$ | the number of shutdown decision variable of generator cluster $k$ in zone $z$ at time $t$ |

$\tau_{k,z}^{\textrm{H,UP}}$ and $\tau_{k,z}^{\textrm{H,DN}}$ | is the minimum up or down time for units in generating cluster $k$ in zone $z$ |

$\epsilon_{z,p,load}^{maxCO_2}$ | denotes the emission limit in terms on tonne-CO$_2$/MWh |

$U_{s,z,t}^{\textrm{H,STO}}$ | this term represents initial hydrogen stored in the storage device $s$ in zone $z$ at all starting time period $t$ of modeled periods |

$\Delta U_{s,z,m}^{\textrm{H,STO}}$ | this term represents the change of storage hydrogen inventory level of the storage device $s$ in zone $z$ during each representative period $m$ |

$U_{i,z \rightarrow z^{\prime},t}^{\textrm{H,PIP}}$ | the hydrogen pipeline storage level decision variable representing hydrogen stored in pipeline of type $i$ through path $z \rightarrow z^{\prime}$ at time period $t$ |

$v_{CAP,j}^{\textrm{H,TRU}}$ | the total number of carbon capture of existing truck ??this may be is a error ,should let H truck replace CAP truck. |

$v_{RETCAP,j}^{\textrm{H,TRU}}$ | the total number of carbon capture of Truck retirements |

$v_{NEWCAP,j}^{\textrm{H,TRU}}$ | the total number of carbon capture of newly add Truck |

## Parameters

Notation | Description |
---|---|

$\textrm{c}_{z}^{\textrm{H,EMI}}$ | Cost of per ton carbon dioxide emitted in the hydrogen supply chain |

$\textrm{c}_{g}^{\textrm{H,INV}}$ | equipment investment cost per ton of hydrogen production capacity |

$\textrm{c}_{g}^{\textrm{H,FOM}}$ | fixed operation cost in hydrogen supply chain for hydrogen generationa nd storage devices |

$\textrm{c}^{\textrm{H,GEN,c}}$ | additional investment costs of hydrogen production |

$\textrm{n}_{s}^{\textrm{H,NSD}}$ | this term represents the marginal willingness to pay for hydrogen demand of this segment of demand |

$\textrm{D}_{z, t}^{\textrm{H}}$ | hydrogen demand in zone $z$ at time $t$ |

$\textrm{C}^{\textrm{H,GEN,o}}$ | total generation cost for per tonne of hydrogen from hydrogen generation plants |

$\textrm{c}_{g}^{\textrm{H,FUEL}}$ | fuel cost for hydrogen generation plants |

$\textrm{c}_{g}^{\textrm{H,VOM}}$ | variable cost for hydrogen generation plants |

$\overline{y}_{g}^{\textrm{\textrm{H,G2P}}}$ | upper bound of capacity is defined,then we impose constraints on maximum power capacity |

$\underline{y}_{g}^{\textrm{\textrm{H,G2P}}}$ | lower bound of capacity is defined,then we impose constraints on minimum power capacity |

$\eta_{s,z}^{\textrm{H,loss}}$ | the self discharge rate for the storage resource |

$\rho^{max}_{y,z,t}$ | the availability factor for Bounds on available demand flexibility |

$\Omega_{k,z}^{\textrm{H,G2P,size}}$ | is the unit size |

$\epsilon_{y,z}^{CO_2}$ | the parameter reflects the specific CO$_2$ emission intensity in tonne-CO$_2$/MWh associated with its operation |

$\rho_{y,z,t}^{max}$ | maximum deferrable demand as a fraction of available capacity in a particular time step $t$ |

$\tau_{y,z}^{advance/delay}$ | the maximum time this demand can be advanced and delayed, defined by parameters, $\tau_{y,z}^{advance}$ and $\tau_{y,z}^{delay}$,respectively |

$\eta_{y,z}^{dflex}$ | the energy losses associated with shifting demand |

$\overline{\textrm{R}}_{s,z}^{\textrm{H,CHA}}$ | For storage resources where upper bound is defined, then we impose constraints on minimum and maximum storage charge capacity |

$\underline{\textrm{R}}_{s,z}^{\textrm{H,CHA}}$ | For storage resources where lower bound is defined, then we impose constraints on minimum and maximum storage charge capacity |