Nomenclature
Indices and Index Sets
Symbol |
POMMES |
Description |
|---|---|---|
\(a \in \mathcal{A}\) |
|
Areas |
\(i \in \mathcal{Y}^{inv}\) |
|
Investment years |
\(y \in \mathcal{Y}^{op}\) |
|
Operation years |
\(d \in \mathcal{Y}^{dec}\) |
|
Decommissioning years |
\(t \in \mathcal{T}\) |
|
Operation snapshots |
\(r \in \mathcal{R}_{a}\) |
|
Resources in area \(a\) |
\(c \in \mathcal{C}^{tech}_{a, i}\) |
|
Conversion technologies in area \(a\) for year \(i\) |
\(s \in \mathcal{S}^{tech}_{a, i}\) |
|
Storage technologies in area \(a\) for year \(i\) |
\(w \in \mathcal{W}^{tech}_{a, i}\) |
|
Transport technologies in area \(a\) for year \(i\) |
\(e \in \mathcal{E}^{tech}_{a, i}\) |
|
Import/export technologies in area \(a\) for year \(i\) |
\(h \in \mathcal{H}^{type}\) |
|
Hour type in TURPE |
\(j \in \mathcal{J}^{rep}\) |
|
retrofit years |
General Parameters
Symbol |
POMMES |
Description |
|---|---|---|
\(d_{a, r, t, y}\) |
|
Exogenous demand of \(r\) in area \(a\) in \(y\) at \(t\) [MWh] |
\(\lambda^{curt}_{a, r, y}\) |
|
Energy curtailed cost [€/MWh] |
\(\lambda^{spill}_{a, r, y}\) |
|
Resource spillage cost [€/MWh] |
\(g^{CO_2}_{a, y}\) |
|
Maximum \(\mathrm{CO_2}\) emissions in \(y\) [kg \(\mathrm{CO_2}\)] |
\(t^{CO_2}_{a, y}\) |
|
Carbon tax value in \(y\) [€/kg \(\mathrm{CO_2}\)] |
\(\tau\) |
|
Discount rate [%] |
\(\alpha_{c}\) |
|
Conversion tech finance rate [%] |
\(\alpha_{c1, c2, j}\) |
|
retrofit finance rate [%] |
\(\alpha_{s}\) |
|
Storage tech finance rate [%] |
\(y_0\) |
|
Reference year for actualisation |
\(\phi_1(\tau,y, y_0)\) |
|
Discount factor [%] |
\(\phi_2(\alpha, n)\) |
|
Capital recovery factor [%] |
\(\Delta i = \Delta j = \Delta y\) |
|
Time step for investment [year] |
\((\Delta T)_{t}\) |
|
Snapshot length [hour] |
Retrofit Parameters
Conversion Parameters
Symbol |
POMMES |
Description |
|---|---|---|
\(\beta_{c}\) |
|
Specific overnight cost of \(c\) [€/MW] |
\(\omega_{c}\) |
|
Fixed OPEX of \(c\) [€/MW/yr] |
\(\lambda_{c}\) |
|
Variable OPEX of \(c\) [€/MWh] |
\(a_{y, t, c, i}\) |
|
Availability of \(c\) [\(0, 1\)] |
\(k_{c, i, r}\) |
|
Conversion factor for \(c\) [%] |
\(\varepsilon^{CO_2}_{c}\) |
|
\(\mathrm{CO_2}\) emission rate for \(c\) [kg \(\mathrm{CO_2}/\text{MWh}\)] |
\(l_{c}\) |
|
Life length of \(c\) [year] |
\(p^{c, min}_{c}\) |
|
Minimum capacity of \(c\) [MW] |
\(p^{c, max}_{c}\) |
|
Maximum capacity of \(c\) [MW] |
Storage Parameters
Symbol |
POMMES |
Description |
|---|---|---|
\(\beta_{a, i, s}\) |
|
Power capacity cost of \(s\) [€/MW] |
\(\sigma_{a, i, s}\) |
|
Energy capacity cost of \(s\) [€/MWh] |
\(\omega_{a, i, s}\) |
|
Fixed OPEX of \(s\) [€/MW/yr] |
\(\eta_{a, i, s}\) |
|
Dissipation losses over 1 hour [%] |
\(k^{in}_{s, i, r}\) |
|
Charging factor for \(s\) [%] |
\(k^{keep}_{s, i, r}\) |
|
Consumption factor to keep 1 MWh in \(s\) [\(\text{h}^{-1}\)] |
\(k^{out}_{s, i, r}\) |
|
Discharging factor for \(s\) [%] |
\(res_{s}\) |
|
Main resource stored by \(s\) |
\(l_{a, i, s}\) |
|
Life length of \(s\) [year] |
\(p^{s, min}_{a, i, s}\) |
|
Minimum storage power capacity [MW] |
\(p^{s, max}_{a, i, s}\) |
|
Maximum storage power capacity [MW] |
\(s^{s, min}_{a, i, s}\) |
|
Minimum storage energy capacity [MWh] |
\(s^{s, max}_{a, i, s}\) |
|
Maximum storage energy capacity [MWh] |
Transport Parameters
Symbol |
POMMES |
Description |
|---|---|---|
\(\gamma_{y, r, t}\) |
|
Importation cost of \(r\) in \(y\) at \(t\) from ROW [€/MWh] |
Networks Parameters
Symbol |
POMMES |
Description |
|---|---|---|
\(\gamma^{imp}_{y, r, t}\) |
|
Importation cost of \(r\) in \(y\) at \(t\) from ROW [€/MWh] |
\(\gamma^{exp}_{y, r, t}\) |
|
Exportation price of \(r\) in \(y\) at \(t\) to ROW [€/MWh] |
\(\varepsilon^{CO_2}_{y, r, t}\) |
|
Importation emission rate of \(r\) in \(y\) at \(t\) from ROW [kg \(\mathrm{CO_2}\)/MWh] |
\(\pi^{max, imp}_{y, r, t}\) |
|
Max yearly importation volume of \(r\) in \(y\) from ROW [MWh] |
\(\pi^{max, exp}_{y, r, t}\) |
|
Max yearly exportation volume of \(r\) in \(y\) to ROW [MWh] |
\(\varphi(t)\) |
|
Matching key between operation hour and TURPE hour type \(h\) |
\(\psi_{y, h}\) |
|
Fixed cost of withdrawal component of TURPE for \(h\) [€/MW] |
\(\theta_{y, h}\) |
|
Variable cost of withdrawal component of TURPE for \(h\) [€/MWh] |
Investment Variables
Symbol |
POMMES |
Description |
|---|---|---|
\(\mathbf{P}^{c, inv}_{c, i, d}\) |
|
Capacity of \(c\) invested for year \(i\) decommissioned for year \(d\) [MW] |
\(\mathbf{P}^{s, inv}_{s, i, d}\) |
|
Storage power capacity of \(s\) invested for year \(i\) decommissioned for year \(d\) [MW] |
\(\mathbf{S}^{inv}_{s, i, d}\) |
|
Storage energy capacity of \(s\) invested for year \(i\) decommissioned for year \(d\) [MWh] |
\(\mathbf{P}^{rep}_{c_1, i_1, j, c, d}\) |
|
Total retrofit power capacity from conversion technology \(c_1\) invested in \(i_1\) to conversion technology \(c\) in retrofit year \(j\) and operation in year \(y\) [MW] |
\(\bar{P}^{c}_{y, c, i}\) |
|
Total capacity of \(c\) invested for \(i\) in operation in year \(y\) [MW] |
\(\bar{P}^{s}_{y, s, i}\) |
|
Total storage power capacity of \(s\) invested for \(i\) in operation in year \(y\) [MW] |
\(\bar{S}_{y, s, i}\) |
|
Total storage energy capacity of \(s\) invested for \(i\) in operation in year \(y\) [MWh] |
Operation Variables
Symbol |
POMMES |
Description |
|---|---|---|
\(\mathbf{P}^{c}_{y, t, c, i}\) |
|
Power of \((c, i)\) in \(y\) at \(t\) [MW] |
\(U^{net, c}_{y, t, r}\) |
|
Resource \(r\) net generation from conversion technologies in \(y\) at \(t\) [MWh] |
\(\mathbf{P}^{s, in}_{y, t, s, i}\) |
|
Storage charging power of \((s, i)\) in \(y\) at \(t\) [MW] |
\(\mathbf{P}^{s, out}_{y, t, s, i}\) |
|
Storage discharging power of \((s, i)\) in \(y\) at \(t\) [MW] |
\(\mathbf{S}_{y, t, s, i}\) |
|
Amount of energy in \((s, i)\) in \(y\) at \(t\) [MWh] |
\(U^{net, s}_{y, t, r}\) |
|
Resource \(r\) net generation from storage technologies in \(y\) at \(t\) [MWh] |
\(\mathbf{U}^{curt}_{y, t, r}\) |
|
Curtailed energy for resource \(r\) in \(y\) at \(t\) [MWh] |
\(U^{spill}_{y, t, r}\) |
|
Resource spillage for \(r\) in \(y\) at \(t\) [MWh] |
\(\mathbf{I}_{y, t, r}\) |
|
Importation of \(r\) in \(y\) at \(t\) from ROW [MWh] |
\(\mathbf{E}_{y, t, r}\) |
|
Exportation of \(r\) in \(y\) at \(t\) to ROW [MWh] |
\(I^{net}_{y, t, r}\) |
|
Net imports from ROW [MWh] |
\(R_{y, t, r}\) |
|
Absolute exchanges from and to ROW [MWh] |
\(\mathbf{CP}^{w}_{y, h}\) |
|
Withdrawal contract power for electricity imports from ROW for \(h\) [MW] |
\(E^{CO_2}_{y, t}\) |
|
\(\mathrm{CO_2}\) emission at \(t\) [kg \(\mathrm{CO_2}\)] |
Cost Variables
Symbol |
POMMES |
Description |
|---|---|---|
\(\mathcal{CAP}_{a, y}\) |
|
Annualised cost of capital of the system in \(y\) |
\(\mathcal{FIX}_{a, y}\) |
included in operation costs |
Fixed operation costs of the system in \(y\) |
\(\mathcal{VAR}_{a, y}\) |
included operation _costs |
Variable (proportional) operation costs of the system in \(y\) |
\(\mathcal{A}^{var}_{a, y}\) |
sum of |
Adequacy (curtailment and spillage) costs in \(y\) |
\(\mathcal{C}^{cap}_{a, y}\) |
|
Conversion annualised capital cost in \(y\) |
\(\mathcal{C}^{fix}_{a, y}\) |
included in |
Conversion fixed operation cost in \(y\) |
\(\mathcal{C}^{var}_{a, y}\) |
included in |
Conversion variable operation cost in \(y\) |
\(\mathcal{S}^{cap}_{a, y}\) |
|
Storage annualised capital cost in \(y\) |
\(\mathcal{S}^{fix}_{a, y}\) |
included in |
Storage fixed operation cost in \(y\) |
\(\mathcal{I}^{net, var}_{a, y}\) |
|
Net imports from ROW variable costs in \(y\) |
\(\mathcal{R}^{rep}_{a, y}\) |
|
Retrofit annualised capital cost in \(y\) |
\(\mathcal{T}^{w, fix}_{a, y}\) |
|
Electricity withdrawal contract power related tax (TURPE) in \(y\) |
\(\mathcal{T}^{w, var}_{a, y}\) |
|
Electricity withdrawal proportional tax (TURPE) in \(y\) |