.. _nomenclature: Nomenclature ************ Indices and Index Sets ======================= .. tabularcolumns:: p{0.132\linewidth}p{0.434\linewidth}p{0.434\linewidth} .. list-table:: :header-rows: 1 * - Symbol - POMMES - Description * - :math:`a \in \mathcal{A}` - ``area`` - Areas * - :math:`i \in \mathcal{Y}^{inv}` - ``year_inv`` - Investment years * - :math:`y \in \mathcal{Y}^{op}` - ``year_op`` - Operation years * - :math:`d \in \mathcal{Y}^{dec}` - ``year_dec`` - Decommissioning years * - :math:`t \in \mathcal{T}` - ``hour`` - Operation snapshots * - :math:`r \in \mathcal{R}_{a}` - ``resource`` - Resources in area :math:`a` * - :math:`c \in \mathcal{C}^{tech}_{a, i}` - ``conversion_tech`` - Conversion technologies in area :math:`a` for year :math:`i` * - :math:`s \in \mathcal{S}^{tech}_{a, i}` - ``storage_tech`` - Storage technologies in area :math:`a` for year :math:`i` * - :math:`w \in \mathcal{W}^{tech}_{a, i}` - ``transport_tech`` - Transport technologies in area :math:`a` for year :math:`i` * - :math:`e \in \mathcal{E}^{tech}_{a, i}` - ``net_import_tech`` - Import/export technologies in area :math:`a` for year :math:`i` * - :math:`h \in \mathcal{H}^{type}` - ``hour_type`` - Hour type in TURPE * - :math:`j \in \mathcal{J}^{rep}` - ``retrofit_year`` - retrofit years General Parameters ================== .. tabularcolumns:: p{0.132\linewidth}p{0.434\linewidth}p{0.434\linewidth} .. list-table:: :header-rows: 1 * - Symbol - POMMES - Description * - :math:`d_{a, r, t, y}` - ``demand`` - Exogenous demand of :math:`r` in area :math:`a` in :math:`y` at :math:`t` [MWh] * - :math:`\lambda^{curt}_{a, r, y}` - ``load_shedding_cost`` - Energy curtailed cost [€/MWh] * - :math:`\lambda^{spill}_{a, r, y}` - ``spillage_cost`` - Resource spillage cost [€/MWh] * - :math:`g^{CO_2}_{a, y}` - ``carbon_goal`` - Maximum :math:`\mathrm{CO_2}` emissions in :math:`y` [kg :math:`\mathrm{CO_2}`] * - :math:`t^{CO_2}_{a, y}` - ``carbon_tax`` - Carbon tax value in :math:`y` [€/kg :math:`\mathrm{CO_2}`] * - :math:`\tau` - ``discount_rate`` - Discount rate [%] * - :math:`\alpha_{c}` - ``conversion_finance_rate`` - Conversion tech finance rate [%] * - :math:`\alpha_{c1, c2, j}` - ``retrofit_finance_rate`` - retrofit finance rate [%] * - :math:`\alpha_{s}` - ``storage_finance_rate`` - Storage tech finance rate [%] * - :math:`y_0` - ``year_ref`` - Reference year for actualisation * - :math:`\phi_1(\tau,y, y_0)` - ``discount_factor`` - Discount factor [%] * - :math:`\phi_2(\alpha, n)` - ``crf`` - Capital recovery factor [%] * - :math:`\Delta i = \Delta j = \Delta y` - ``planning_step`` - Time step for investment [year] * - :math:`(\Delta T)_{t}` - ``hour`` - Snapshot length [hour] Retrofit Parameters ===================== .. tabularcolumns:: p{0.132\linewidth}p{0.434\linewidth}p{0.434\linewidth} .. list-table:: :header-rows: 1 * - Symbol - POMMES - Description * - :math:`\beta^{rep}_{c_1,c,j}` - ``retrofit_invest_cost`` - Power capacity cost of retrofitting conversion technology :math:`c_1` to :math:`c` in year :math:`j` [€/MW] * - :math:`q^{rep}_{c_1,c}` - ``retrofit_factor`` - Retrofit factor from conversion technology :math:`c_1` to :math:`c` [%] * :math:`p^{c, min, rep}_{j,c}` - ``retrofit_power_capacity_investment_min`` - Minimum retrofitted capacity into :math:`c` [MW] * :math:`p^{c, max, rep}_{j,c}` - ``retrofit_power_capacity_investment_max`` - Maximum retrofitted capacity into :math:`c` [MW] Conversion Parameters ===================== .. tabularcolumns:: p{0.132\linewidth}p{0.434\linewidth}p{0.434\linewidth} .. list-table:: :header-rows: 1 * - Symbol - POMMES - Description * - :math:`\beta_{c}` - ``conversion_invest_cost`` - Specific overnight cost of :math:`c` [€/MW] * - :math:`\omega_{c}` - ``conversion_fixed_cost`` - Fixed OPEX of :math:`c` [€/MW/yr] * - :math:`\lambda_{c}` - ``conversion_variable_cost`` - Variable OPEX of :math:`c` [€/MWh] * - :math:`a_{y, t, c, i}` - ``conversion_availability`` - Availability of :math:`c` [:math:`0, 1`] * - :math:`k_{c, i, r}` - ``conversion_factor`` - Conversion factor for :math:`c` [%] * - :math:`\varepsilon^{CO_2}_{c}` - ``conversion_emission_factor`` - :math:`\mathrm{CO_2}` emission rate for :math:`c` [kg :math:`\mathrm{CO_2}/\text{MWh}`] * - :math:`l_{c}` - ``conversion_life_span`` - Life length of :math:`c` [year] * - :math:`p^{c, min}_{c}` - ``conversion_power_capacity_investment_min`` - Minimum capacity of :math:`c` [MW] * - :math:`p^{c, max}_{c}` - ``conversion_power_capacity_investment_max`` - Maximum capacity of :math:`c` [MW] Storage Parameters ================== .. tabularcolumns:: p{0.132\linewidth}p{0.434\linewidth}p{0.434\linewidth} .. list-table:: :header-rows: 1 * - Symbol - POMMES - Description * - :math:`\beta_{a, i, s}` - ``storage_invest_cost_power`` - Power capacity cost of :math:`s` [€/MW] * - :math:`\sigma_{a, i, s}` - ``storage_invest_cost_energy`` - Energy capacity cost of :math:`s` [€/MWh] * - :math:`\omega_{a, i, s}` - ``storage_fixed_cost_power`` - Fixed OPEX of :math:`s` [€/MW/yr] * - :math:`\eta_{a, i, s}` - ``storage_dissipation`` - Dissipation losses over 1 hour [%] * - :math:`k^{in}_{s, i, r}` - ``storage_factor_in`` - Charging factor for :math:`s` [%] * - :math:`k^{keep}_{s, i, r}` - ``storage_factor_keep`` - Consumption factor to keep 1 MWh in :math:`s` [:math:`\text{h}^{-1}`] * - :math:`k^{out}_{s, i, r}` - ``storage_factor_out`` - Discharging factor for :math:`s` [%] * - :math:`res_{s}` - ``storage_main_resource`` - Main resource stored by :math:`s` * - :math:`l_{a, i, s}` - ``storage_life_span`` - Life length of :math:`s` [year] * - :math:`p^{s, min}_{a, i, s}` - ``storage_power_capacity_investment_min`` - Minimum storage power capacity [MW] * - :math:`p^{s, max}_{a, i, s}` - ``storage_power_capacity_investment_max`` - Maximum storage power capacity [MW] * - :math:`s^{s, min}_{a, i, s}` - ``storage_energy_capacity_investment_min`` - Minimum storage energy capacity [MWh] * - :math:`s^{s, max}_{a, i, s}` - ``storage_energy_capacity_investment_max`` - Maximum storage energy capacity [MWh] Transport Parameters ==================== .. tabularcolumns:: p{0.132\linewidth}p{0.434\linewidth}p{0.434\linewidth} .. list-table:: :header-rows: 1 * - Symbol - POMMES - Description * - :math:`\gamma_{y, r, t}` - ``TODO`` - Importation cost of :math:`r` in :math:`y` at :math:`t` from ROW [€/MWh] Networks Parameters ==================== .. tabularcolumns:: p{0.132\linewidth}p{0.434\linewidth}p{0.434\linewidth} .. list-table:: :header-rows: 1 * - Symbol - POMMES - Description * - :math:`\gamma^{imp}_{y, r, t}` - ``net_import_import_cost`` - Importation cost of :math:`r` in :math:`y` at :math:`t` from ROW [€/MWh] * - :math:`\gamma^{exp}_{y, r, t}` - ``net_import_export_cost`` - Exportation price of :math:`r` in :math:`y` at :math:`t` to ROW [€/MWh] * - :math:`\varepsilon^{CO_2}_{y, r, t}` - ``net_import_emission_factor`` - Importation emission rate of :math:`r` in :math:`y` at :math:`t` from ROW [kg :math:`\mathrm{CO_2}`/MWh] * - :math:`\pi^{max, imp}_{y, r, t}` - ``net_import_max_yearly_energy_import`` - Max yearly importation volume of :math:`r` in :math:`y` from ROW [MWh] * - :math:`\pi^{max, exp}_{y, r, t}` - ``net_import_max_yearly_energy_export`` - Max yearly exportation volume of :math:`r` in :math:`y` to ROW [MWh] * - :math:`\varphi(t)` - ``turpe_calendar`` - Matching key between operation hour and TURPE hour type :math:`h` * - :math:`\psi_{y, h}` - ``turpe_fixed_cost`` - Fixed cost of withdrawal component of TURPE for :math:`h` [€/MW] * - :math:`\theta_{y, h}` - ``turpe_variable_cost`` - Variable cost of withdrawal component of TURPE for :math:`h` [€/MWh] Investment Variables ===================== .. tabularcolumns:: p{0.132\linewidth}p{0.434\linewidth}p{0.434\linewidth} .. list-table:: :header-rows: 1 * - Symbol - POMMES - Description * - :math:`\mathbf{P}^{c, inv}_{c, i, d}` - ``planning_conversion_power_capacity`` - Capacity of :math:`c` invested for year :math:`i` decommissioned for year :math:`d` [MW] * - :math:`\mathbf{P}^{s, inv}_{s, i, d}` - ``Planning_storage_power_capacity`` - Storage power capacity of :math:`s` invested for year :math:`i` decommissioned for year :math:`d` [MW] * - :math:`\mathbf{S}^{inv}_{s, i, d}` - ``Planning_storage_energy_capacity`` - Storage energy capacity of :math:`s` invested for year :math:`i` decommissioned for year :math:`d` [MWh] * - :math:`\mathbf{P}^{rep}_{c_1, i_1, j, c, d}` - ``planning_retrofit_power_capacity`` - Total retrofit power capacity from conversion technology :math:`c_1` invested in :math:`i_1` to conversion technology :math:`c` in retrofit year :math:`j` and operation in year :math:`y` [MW] * - :math:`\bar{P}^{c}_{y, c, i}` - ``operation_conversion_power_capacity`` - Total capacity of :math:`c` invested for :math:`i` in operation in year :math:`y` [MW] * - :math:`\bar{P}^{s}_{y, s, i}` - ``operation_storage_power_capacity`` - Total storage power capacity of :math:`s` invested for :math:`i` in operation in year :math:`y` [MW] * - :math:`\bar{S}_{y, s, i}` - ``operation_storage_energy_capacity`` - Total storage energy capacity of :math:`s` invested for :math:`i` in operation in year :math:`y` [MWh] Operation Variables ==================== .. tabularcolumns:: p{0.132\linewidth}p{0.434\linewidth}p{0.434\linewidth} .. list-table:: :header-rows: 1 * - Symbol - POMMES - Description * - :math:`\mathbf{P}^{c}_{y, t, c, i}` - ``operation_conversion_power`` - Power of :math:`(c, i)` in :math:`y` at :math:`t` [MW] * - :math:`U^{net, c}_{y, t, r}` - ``operation_conversion_net_generation`` - Resource :math:`r` net generation from conversion technologies in :math:`y` at :math:`t` [MWh] * - :math:`\mathbf{P}^{s, in}_{y, t, s, i}` - ``operation_storage_power_in`` - Storage charging power of :math:`(s, i)` in :math:`y` at :math:`t` [MW] * - :math:`\mathbf{P}^{s, out}_{y, t, s, i}` - ``operation_storage_power_out`` - Storage discharging power of :math:`(s, i)` in :math:`y` at :math:`t` [MW] * - :math:`\mathbf{S}_{y, t, s, i}` - ``operation_storage_level`` - Amount of energy in :math:`(s, i)` in :math:`y` at :math:`t` [MWh] * - :math:`U^{net, s}_{y, t, r}` - ``operation_storage_net_generation`` - Resource :math:`r` net generation from storage technologies in :math:`y` at :math:`t` [MWh] * - :math:`\mathbf{U}^{curt}_{y, t, r}` - ``operation_load_shedding`` - Curtailed energy for resource :math:`r` in :math:`y` at :math:`t` [MWh] * - :math:`U^{spill}_{y, t, r}` - ``operation_spillage`` - Resource spillage for :math:`r` in :math:`y` at :math:`t` [MWh] * - :math:`\mathbf{I}_{y, t, r}` - ``operation_net_import_import`` - Importation of :math:`r` in :math:`y` at :math:`t` from ROW [MWh] * - :math:`\mathbf{E}_{y, t, r}` - ``operation_net_import_export`` - Exportation of :math:`r` in :math:`y` at :math:`t` to ROW [MWh] * - :math:`I^{net}_{y, t, r}` - ``operation_net_import_net_generation`` - Net imports from ROW [MWh] * - :math:`R_{y, t, r}` - ``operation_net_import_abs`` - Absolute exchanges from and to ROW [MWh] * - :math:`\mathbf{CP}^{w}_{y, h}` - ``turpe_TODO !!`` - Withdrawal contract power for electricity imports from ROW for :math:`h` [MW] * - :math:`E^{CO_2}_{y, t}` - ``operation_carbon_emissions`` - :math:`\mathrm{CO_2}` emission at :math:`t` [kg :math:`\mathrm{CO_2}`] Cost Variables =============== .. tabularcolumns:: p{0.132\linewidth}p{0.434\linewidth}p{0.434\linewidth} .. list-table:: :header-rows: 1 * - Symbol - POMMES - Description * - :math:`\mathcal{CAP}_{a, y}` - ``annualised_totex`` - Annualised cost of capital of the system in :math:`y` * - :math:`\mathcal{FIX}_{a, y}` - included in operation costs - Fixed operation costs of the system in :math:`y` * - :math:`\mathcal{VAR}_{a, y}` - included operation _costs - Variable (proportional) operation costs of the system in :math:`y` * - :math:`\mathcal{A}^{var}_{a, y}` - sum of ``operation_load_shedding_costs`` and ``operation_spillage_costs`` - Adequacy (curtailment and spillage) costs in :math:`y` * - :math:`\mathcal{C}^{cap}_{a, y}` - ``planning_conversion_costs`` - Conversion annualised capital cost in :math:`y` * - :math:`\mathcal{C}^{fix}_{a, y}` - included in ``operation_conversion_costs`` - Conversion fixed operation cost in :math:`y` * - :math:`\mathcal{C}^{var}_{a, y}` - included in ``operation_conversion_costs`` - Conversion variable operation cost in :math:`y` * - :math:`\mathcal{S}^{cap}_{a, y}` - ``planning_storage_costs`` - Storage annualised capital cost in :math:`y` * - :math:`\mathcal{S}^{fix}_{a, y}` - included in ``operation_storage_costs`` - Storage fixed operation cost in :math:`y` * - :math:`\mathcal{I}^{net, var}_{a, y}` - ``operation_net_import_costs`` - Net imports from ROW variable costs in :math:`y` * - :math:`\mathcal{R}^{rep}_{a, y}` - ``planning_retrofit_costs`` - Retrofit annualised capital cost in :math:`y` * - :math:`\mathcal{T}^{w, fix}_{a, y}` - ``TODO`` - Electricity withdrawal contract power related tax (TURPE) in :math:`y` * - :math:`\mathcal{T}^{w, var}_{a, y}` - ``TODO`` - Electricity withdrawal proportional tax (TURPE) in :math:`y`