| \(W(clt)\) |
Aggregated welfare |
UTILITY |
unitless |
| \(w_{t,n}\) |
Negishi weights |
w_negishi(t,n) |
unitless |
| \(C(t,n)\) |
Consumption |
Q(‘CC’,t,n) |
T$ |
| \(l(t,n)\) |
Population |
l(t,n) |
Million people |
| \(\beta\) |
Utility discount factor |
stpf(t) |
unitless |
| \(\eta\) |
Inverse of IES |
eta |
unitless |
| \(\rho\) |
Pure rate of time preference |
srtp(t) |
unitless |
| \(\gamma\) |
Degree or inequality aversion |
gamma |
unitless |
| \(C(t,n)\) |
Consumption |
Q(‘CC’,t,n) |
T$ |
| \(I_{FG}(t,n)\) |
Investment in final good |
I(‘FG’,t,n) |
T$ |
| \(I_j(t,n)\) |
Investment in energy technologies |
I_EN(jinv,t,n) |
T$ |
| \(I_{GRID}(t,n)\) |
Investment in electric grid |
I_EN_GRID(t,n) |
T$ |
| \(I_{OUT,f}(t,n)\) |
Investment in extraction |
I_OUT(f,t,n) |
T$ |
| \(I_{RD,j}(t,n)\) |
Investment in R&D |
I_RD(rd,t,n) |
T$ |
| \(I_{PRADA}(t,n)\) |
Investment in proactive adaptation |
I(‘PRADA’,t,n) |
T$ |
| \(I_{SCAP}(t,n)\) |
Investment in specific ad. capacity |
I(‘SCAP’,t,n) |
T$ |
| \(I_{RADA}(t,n)\) |
Investment in active adaptation |
I(‘RADA’,t,n) |
T$ |
| \(Y(t,n)\) |
Net Output |
Q(‘Y’,t,n) |
T$ |
| \(oem_j(t,n)\) |
O&M costs in energy technologies |
oem(j,t,n) |
$/TW |
| \(oem\_ex_f\) |
O&M coefficient in extraction |
oem_ex(f) |
$/TWh |
| \(K_j(t,n)\) |
Capital in energy tech. |
K_EN(j,t,n) |
TW |
| \(Q_{OUT,f}(t,n)\) |
Total extraction of fuel \(f\) |
Q_OUT(f,t,n) |
TWh |
| \(tfp0(n)\) |
Initial level of TFP |
tfp0(n) |
unitless |
| \(C_e(t,n)\) |
GHG emissions costs |
COST_EMI(j,t,n) |
T$ |
| \(C_f(t,n)\) |
Net cost of Primary Energy Supplies |
COST_PES(f,t,n) |
T$ |
| \(C_j(t,n)\) |
Energy technology penalty costs |
COST_EN(j,t,n) |
T$ |
| \(ES(t,n)\) |
Energy services |
Q(‘FEN’,t,n) |
T$ |
| \(K_{FG}(t,n)\) |
Capital in final good |
K(‘FG’,t,n) |
T$ |
| \(Q_E(ghg,t,n)\) |
Emissions |
Q_EMI(ghg,t,n) |
Gt-eqC |
| \(tfp_y(t,n)\) |
Total factor productivity |
tfpy(t,n) |
unitless |
| \(l(t,n)\) |
Population |
l(t,n) |
Million people |
| \(\delta_{FG}\) |
Yearly depreciation rate of capital |
delta(‘fg’,t,n) |
unitless |
| \(\Delta_{\text{t}}\) |
Time step duration |
tstep |
years |
| \(EN(t,n)\) |
Energy aggregate |
Q(‘en’,t,n) |
T$ |
| \(HE(t,n)\) |
R&D Capital in energy efficiency |
K_RD(‘en’,t,n) |
T$ |
| \(tfpn(t,n)\) |
Factor productivity of energy |
tfpn(t,n) |
unitless |
| \(EL(t,n)\) |
Energy aggregate from the electric sector |
Q(‘el’,t,n) |
T$ |
| \(NEL(t,n)\) |
Energy aggregate from the non-electric sector |
Q(‘nel’,t,n) |
T$ |
| \(I_j(t,n)\) |
Investment in energy tech. |
I_EN(jinv,t,n) |
T$ |
| \(K_j(t,n)\) |
Capital in energy tech. |
K_EN(j,t,n) |
TW |
| \(SC_j(t,n)\) |
Average investment cost |
MCOST_INV(j,t,n) |
T$/TW |
| \(\delta_j(t,n)\) |
depreciation rate |
delta(j,t,n) |
|
| \(EL(t,n)\) |
Electric sector aggregate |
Q(‘el’,t,n) |
T$ |
| \(EL2(t,n)\) |
Electric sector aggregate (w/o hydro) |
Q(‘el2’,t,n) |
T$ |
| \(EL_{coalwbio}(t,n)\) |
Coal & wood biomass power plant aggregate |
Q(‘coalwbio’,t,n) |
T$ |
| \(EL_{gas}(t,n)\) |
Gas power plant sector |
Q(‘gas’,t,n) |
T$ |
| \(EL_{hydro}(t,n)\) |
Hydroelectric sector |
Q(‘ces_elhydro’,t,n) |
T$ |
| \(EL_{intren}(t,n)\) |
Intermittent renewable aggregate |
Q(‘ces_elintren’,t,n) |
T$ |
| \(EL_{nucback}(t,n)\) |
Nuclear and backstop aggregate |
Q(‘ces_elnuclearback’,t,n) |
T$ |
| \(EL_{oil}(t,n)\) |
Oil power plant sector |
Q(‘oil’,t,n) |
T$ |
| \(ELFF(t,n)\) |
Fossil-fuel power plants aggregate |
Q(‘elff’,t,n) |
T$ |
| \(NEL(t,n)\) |
Non-electric sector aggregate |
Q(‘nel’,t,n) |
T$ |
| \(NEL_{coal}(t,n)\) |
Energy in Coal sector |
Q_EN(‘nelcoal’,t,n) |
TWh |
| \(NEL_{log}(t,n)\) |
Other non-electric sector aggregate |
Q(‘nelog’,t,n) |
T$ |
| \(NEL_{trbiomass}(t,n)\) |
Energy in traditional biomass sector |
Q_EN(‘neltrbiomass’,t,n) |
TWh |
| \(NEL_{oilback}(t,n)\) |
Energy in oil and backstop non-electric |
Q_EN(‘neloilback’,t,n) |
TWh |
| \(NEL_{gas}(t,n)\) |
Energy in gas sector |
Q_EN(‘nelgas’,t,n) |
TWh |
| \(NEL_{trbiofuel}(t,n)\) |
Energy in Traditional biofuel |
Q_EN(‘neltrbiofuel’,t,n) |
TWh |
| \(Q_f(t,n)\) |
Total amount of fuel consumed |
Q_PES(f,t,n) |
TWh |
| \(Q_{j,f}(t,n)\) |
Total amount of fuel consumed per sector |
Q_IN(f,jfed,t,n) |
TWh |
| \(Q_f(t,n)\) |
Total amount of fuel consumed |
Q_PES(f,t,n) |
TWh |
| \(X_f(t,n)\) |
Total amount of fuel extracted |
Q_OUT(f,t,n) |
TWh |
| \(C_f(t,n)\) |
Primary Energy Supplies cost |
COST_PES(f,t,n) |
T$ |
| \(MC_f(t,n)\) |
Average cost of Primary Energy Supplies |
MCOST_PES(f,t,n) |
T$/TWh |
| \(Q_f(t,n)\) |
Total amount of fuel consumed |
Q_PES(f,t,n) |
TWh |
| \(X_f(t,n)\) |
Total amount of fuel extracted |
Q_OUT(f,t,n) |
TWh |
| \(p_f(t,n)\) |
World market fuel prices |
FPRICE(f,t) |
T$/TWh |
| \(EL_j(t,n)\) |
Electric production capacity |
Q_EN(jel,t,n) |
TWh |
| \(KEL_j(t,n)\) |
Capital in electric production |
K_EN(jel,t,n) |
TW |
| \(\mu_j(t,n)\) |
Capacity factor of maximum production |
mu(jel,t,n) |
TWh/TW |
| \(EL_{elback}(t,n)\) |
Electric backstop capacity |
Q_EN(‘elback’,t,n) |
TWh |
| \(KEL_j(t,n)\) |
Total electric capacity |
Q_EN(‘el’,t,n) |
TWh |
| \(Q_j(t,n)\) |
Production capacity |
Q_EN(jfed,t,n) |
TWh |
| \(Q_{j,f}(t,n)\) |
Amount of fuel consumed per sector |
Q_IN(f,jfed,t,n) |
TWh |
| \(\xi_{j,f}(t,n)\) |
Sector efficiency ratio |
csi(f,jfed,t,n) |
TWh/TWh |
| \(Q_j(t,n)\) |
Production capacity |
Q_EN(j,t,n) |
TWh |
| \(I_{PRADA}(t,n)\) |
Investment in proactive adaptation |
I(‘PRADA’,t,n) |
T$ |
| \(I_{SCAP}(t,n)\) |
Investment in specific ad. capacity |
I(‘SCAP’,t,n) |
T$ |
| \(I_{RADA}(t,n)\) |
Investment in active adaptation |
I(‘RADA’,t,n) |
T$ |
| \(NEL_{nelback}(t,n)\) |
Non-electric backstop capacity |
Q_PES(‘backnel’,t,n) |
TWh |
| \(Q_{CCS}(t,n)\) |
CCS emissions |
Q_EMI(‘ccs’,t,n) |
GtC-eq |
| \(M_{CCS}(k_{st},t,n)\) |
CCS cumulated emissions |
CUM_Q_STORED(k_storage,t,n) |
GtC-eq |
| \(C_{CCS}(n,t)\) |
CCS costs |
MCOST_EMI(‘ccs’,t,n) |
T$ |
| \(Q_E(\text{ghg},t,n)\) |
Regional emissions |
Q_EMI(ghg,t,n) |
GtC-eq |
| \(WE(\text{ghg},t)\) |
World emission |
W_EMI(ghg,t,n) |
GtC for CO2/Gt |
| \(M(\text{ghg},t)\) |
Concentrations |
WCUM_EMI(ghg,t,n) |
GtC for CO2/Gt |
| \(TRF(t)\) |
Total radiative forcing |
TRF(t,n) |
W/m2 |
| \(RF(\text{ghg},t)\) |
Gas radiative forcing |
RF(t,n) |
W/m2 |
| \(T(t)\) |
Global temperature increase |
TEMP(‘atm’,t,n) |
C |
| \(T^o(t)\) |
Ocean temperature increase |
TEMP(‘low’,t,n) |
C |
| \(Q_{CO2}(t,n)\) |
CO2 emissions |
Q_EMI(‘co2’,t,n) |
GtC-eq |
| \(Q_{CO2ind}(t,n)\) |
CO2 emissions from fossil-fuel |
Q_EMI(‘co2ind’,t,n) |
GtC-eq |
| \(Q_{CO2lu}(t,n)\) |
CO2 emissions from land-use change |
Q_EMI(‘co2lu’,t,n) |
GtC-eq |
| \(Q_{redd}(t,n)\) |
Avoided emissions from REDD |
Q_EMI(‘redd’,t,n) |
GtC-eq |
| \(Q_{CCS}(t,n)\) |
CCS emissions |
Q_EMI(‘ccs’,t,n) |
GtC-eq |
| \(EX_f(t,n)\) |
CO2 emissions from extraction |
Q_EMI_OUT(‘co2’,t,n) |
GtC-eq |
| \(Q_{oghg}(t,n)\) |
other ghg emissions |
Q_EMI(oghg,t,n) |
GtC-eq |
| \(ABAT(oghg,t,n)\) |
level of abatment |
ABAT(oghg,t,n) |
[0-1] |
| \(Q_{nip}(t,n)\) |
net import of carbon permits |
Q_EMI(‘nip’,t,n) |
GtC-eq |
| \(C_{CO2}(t,n)\) |
CO2 costs |
COST_EMI(‘co2’,t,n) |
T$ |
| \(Q_{nip}(t,n)\) |
net import of carbon permits |
Q_EMI(‘nip’,t,n) |
GtC-eq |
| \(p_{nip}(t,n)\) |
carbon permits price |
CPRICE(‘nip’,t,n) |
T$/GtC-eq |
| \(C_{e}(n,t)\) |
Non-CO2 emission costs |
COST_EMI(oghg,t,n) |
T$ |
| \(ref_e(n,t)\) |
Baseline emissions |
emi_baseline(oghg,t,n) |
GtC-eq |
| \(\overline{abat}_e(n,t)\) |
Maximum abatement |
emi_abat_max(oghg,t,n) |
[0,1] |
| \(ABAT_e(n,t)\) |
Non-CO2 emission abatment |
ABAT(t,n) |
[0,1] |
| \(C_{e}(n,t)\) |
Emission sink costs |
COST_EMI(e,t,n) |
T$ |
| \(Q_{e}(t,n)\) |
Emission sink |
Q_EMI(e,t,n) |
GtC-eq |
| \(M_{SAV}(t,n)\) |
Accumulated emission savings |
CUM_EMI(‘sav’,t,n) |
GtC-eq |
| \(Q_{SAV}(t,n)\) |
Emission savings |
Q_EMI(‘sav’,t,n) |
GtC-eq |
| \(\Omega(t,n)\) |
Damage coefficient |
OMEGA(t,n) |
unitless |
| \(\omega_{i,n}^-\) |
coefficients with negative impact |
comega_neg(n,i) |
unitless |
| \(\omega_{i,n}^+\) |
coefficients with positive impact |
comega_pos(n,i) |
unitless |
| \(T(t,n)\) |
atmospheric temperature increase from pre-industrial levels |
TEMP(‘atm’,t,n) |
C |
| \(Q(ADA,t,n)\) |
Adaptation factor |
Q(‘ADA’,t,n) |
|
| \(HE(n,t)\) |
R&D Capital in energy efficiency |
K_RD(‘en’,t,n) |
T$ |
| \(RD_{j}(n,t)\) |
R&D Capital in backstop technologies |
K_RD(rd,t,n) |
T$ |
| \(SPILL(n,t)\) |
Spillover knowledge |
SPILL(rd,t,n) |
T$ |
| \(wcum_{j}(t)\) |
Cumulated Installed Capacity |
wcum(jrd,t) |
T$ |
| \(\delta_{RD}\) |
Depreciation rate for R&D knowledge |
delta_RD(‘en’) |
|
| \(a\) |
Internal spillover |
crda(‘en’,t,n) |
|
| \(b\) |
Elasticity w.r.t. R&D Investment |
crdb(‘en’) |
|
| \(c\) |
Elasticity w.r.t. own past knowledge |
crdc(‘en’,t,n) |
|
| \(d\) |
Elasticity w.r.t. spillover knowledge |
crdd(‘en’) |
|
| \(lbrrate\) |
Learning by Searching Coefficient |
lbr_rate(‘jrd’) |
|
| \(lbdrate\) |
Learning by Doing Coefficient |
lbd_rate(‘jrd’) |
|
| \(kpat0\) |
knowledge stock in 2005 |
kpat0 |
|
| \(pat0\) |
annual flow of patents in 2005 |
pat0 |
|
| \(enintg0\) |
5 years decline in energy intensity (2005-2010) |
enintg0 |
|
| \(peng0\) |
5 years growth in energy price (2005-2010) |
peng0 |
|
| \(gdpg0\) |
5 years growth in gdp (2005-2010) |
gdpg0 |
|
| \(OIL_{cap}(t,n,g)\) |
Oil extraction capacity (by category) |
OILCAP(t,n,oilg) |
TWh |
| \(\Delta CAP(t,n,g)\) |
Additional oil capacity (by category) |
ADDOILCAP(t,n,oilg) |
TWh |
| \(I_{OILCAP}(t,n,g)\) |
Oil investment (by category) |
I_OIL(t,n,oilg) |
T$ |
| \(OIL_{capcost}(t,n,g)\) |
Oil Investment cost (by category) |
COST_OIL(t,n,oilg) |
T$/TWh |
| \(OIL_{prod}(t,n,g)\) |
Oil production (by category) |
OILPROD(t,n,oilg) |
TWh |
|
Cumulative production (by category) |
CUM_OIL(t,n,oilg) |
TWh |
|
Total Oil investment (all categories) |
I_OUT(t,n) |
T$ |
|
Total oil production (all categories) |
Q_OUT(oil,t,n) |
TWh |
|
Emissions from oil extraction (all categories) |
Q_EMI_OUT(t,n) |
GtC-eq |
| \(\lambda(g)\) |
Fixed floor cost component (by categories) |
data_oilcost(n,oilg) |
T$/TWh |
| \(\zeta(n,g)\) |
Annual Expansion threshold |
esp_cap(n,oilg) |
TWh |
| \(\mu(g)\) |
Fixed floor cost difference (among categories) |
cum_param_oil(n,oilg) |
T$/TWh |
| \(OIL_{res}(t,n,g)\) |
Oil resources |
resmax_oil(n,oilg) |
TWh |
|
Stoichiometric coefficient for oil extraction |
emi_st_oil(n,oilg) |
GtC/TWh |
| \(K_{EN}(jel,t,n)\) |
Electric capacity |
K_EN(jel,t,n) |
TW |
| \(Q_{EN}(jel,t,n)\) |
Electric energy generation |
Q_EN(jel,t,n) |
TWh |
| \(K_{EN}(jel_{solar},t,n)\) |
Electric capacity |
K_EN(jel_solar,t,n) |
TW |
| \(dens(jel_{solar},n)\) |
Installation density |
inst_density(n,jel_solar) |
MW/km^2 |
| \(area(solar_{distance},n)\) |
Competition area |
inst_area(n,solar_distance) |
km^2 |
| \(SHARE_{EL}(jel,t,n)\) |
Share in the electricity mix |
SHARE_EL(jel,t,n) |
unitless |
| \(c(n)\) |
Peak load fraction |
firm_coeff(n) |
unitless |
| \(cf(jel,t,n)\) |
Capacity factor |
cap_factor(jel,t,n) |
unitless |
| \(cv(SHARE_{EL})\) |
Capacity value |
cap_value(jel,t,n) |
unitless |
| \(f(jel)\) |
Flexibility coefficient |
flex_coeff(jel) |
unitless |
| \(K_{EN\_GRID}(t,n)\) |
Capital of the electrical grid |
K_EN_GRID(t,n) |
TW |
| \(I_{EN\_GRID}(t,n)\) |
Investments in the electrical grid |
I_EN_GRID(t,n) |
T$ |
| \(delta\_grid(t,n)\) |
Grid depreciation rate |
grid_delta(t,n) |
unitless |
| \(grid\_cost\) |
Grid specific investment cost |
grid_cost |
T$/TW |
| \(transm\_cost(jel,distance)\) |
Distance-dependant transmission cost |
transm_cost(jel,distance) |
T$/TW |
| \(tfpy(t,n)\) |
Total factor productivity |
tfpy(t,n) |
unitless |
| \(tfpn(t,n)\) |
Factor Productivity of energy |
tfpn(t,n) |
unitless |
| \(Y_{kali}(n,t)\) |
Calibration GDP |
ykali(t,n) |
T$ |
| \(TPES_{kali}(n,t)\) |
Calibration Energy demand |
tpes_kali(t,n) |
EJ |
| \(\varepsilon_{Y,E}(n,t)\) |
Investment in extraction |
income_ela(t,n) |
unitless |
| \(r\) |
Relationship between traditional biomass consumption and GDP |
trbio_ctr |
unitless |
| \(\phi_{n}\) |
Share of traditional biomass on TPES |
trbio_ctr(‘phi’,n) |
percentage |
| \(Q_{trbiomass,t,n}\) |
Quantity of primary energy of traditional biomass |
Q_PES(‘trbiomass’,t,n) |
EJ |
| \(ldv\_total(t,n)\) |
Total number of ldvs |
ldv_total(t,n) |
million vehicles |
| \(ldv\_pthc (t,n)\) |
Number of ldvs per thousand capita |
ldv_pthc(t,n) |
vehicles per thousand capita |
| \(stfr\_total(t,n)\) |
Total number of trucks |
ldv_total(t,n) |
million vehicles |
| \(K_{EN}(jveh,t,n)\) |
Number of ldvs per type |
K_EN(jveh,t,n) |
million vehicles |
| \(Q_{EN}(jveh,t,n)\) |
Energy used by ldvs |
Q_EN(jveh,t,n) |
TWh |
| \(fuel\_cons(jveh,t,n)\) |
Fuel consumption per ldv |
fuel_cons(jveh,t,n) |
MWh/km |
| \(fueleff\_rate(t,n)\) |
Fuel efficiency improvement rate |
fueleff_rate(t,n) |
unitless |
| \(travel\_intensity\_ldv(t,n)\) |
Travel Intensity LDV |
travel_intensity_ldv(t,n) |
km/$ |
| \(km\_d\_ldv(t,n)\) |
Kilometre demand per LDV |
km_d_ldv(t,n) |
km/veh |
| \(km\_d\_ldv\_tot(t,n)\) |
Total kilometre demand LDV |
km_d_ldv_tot(t,n) |
million km |
| \(km\_d\_stfr(t,n)\) |
Kilometre demand per truck |
km_d_stfr(t,n) |
km/veh |
| \(km\_d\_stfr\_tot(t,n)\) |
Total kilometre demand freight |
km_d_stfr_tot(t,n) |
million km |
| \(load\_factor\_ldv(t,n)\) |
Load factor LDV |
load_factor_ldv(t,n) |
persons/vehicle |
| \(load\_factor\_stfr(t,n)\) |
Load factor freight |
load_factor_stfr(t,n) |
tons/vehicle |
| \(s\_d\_ldv(t,n)\) |
Service demand per LDV |
s_d_ldv(t,n) |
pkm/veh |
| \(s\_d\_ldv\_tot(t,n)\) |
Total service demand LDV |
s_d_ldv_tot(t,n) |
million pkm |
| \(s\_d\_stfr(t,n)\) |
Service demand per truck |
s_d_stfr(t,n) |
tkm/veh |
| \(s\_d\_stfr\_tot(t,n)\) |
Total service demand freight |
s_d_stfr_tot(t,n) |
million tkm |
| \(veh\_cost(jveh,t,n)\) |
Vehicle cost |
MCOST_INV(jveh,t,n) |
T$/million vehicles |
| \(inv\_cost\_trad\_cars\) |
Capital cost of traditional cars |
inv_cost_veh(‘trad_cars’) |
T$/million vehicles |
| \(size\_battery(jveh)\) |
Battery size |
size_battery(jveh) |
kWh/veh |
| \(Q_{st}(k_{st},t,n)\) |
Quantity of CO2 stored |
Q_STORED(k_storage,t,n) |
GtCO2/yr |
| \(Q_{CO2lk}(t,n)\) |
Quantity of CO2 leaked from storage |
Q_EMI(co2leak,t,n) |
GtCO2/yr |
| \(c'_{tr}\) |
Specific CO2 transport cost |
transp_coeff |
$/(tCO2*km) |
| \(\lambda_{st}\) |
Leakage rate |
leak_factor |
%/yr |
| \(l_{tr}(k_{st},n)\) |
Average distance from CO2 storage |
avg_stor_dist(n,k_storage) |
km |
| \(c_{st}(k_{st})\) |
Specific cost of CO2 storage |
cost_storage(k_storage) |
T$/GtonCO2 |
| \(ccs\_capture\_rate(j)\) |
Carbon capture rate ratio |
ccs_capture_eff(jccs) |
unitless |