# HSC Model Notation

## Model Indices and Sets

NotationDescription
$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

NotationDescription
$x_{z,t}^{\textrm{H,EMI}}$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

NotationDescription
$\textrm{c}_{z}^{\textrm{H,EMI}}$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