2 Model

Pdf version of the model mathematical framework can be found here.

2.1 Sets

The model sets
Name	Alias	Description
comm	$c, c p, c e, c n$	commodity
region	$r, r p, r e, r n$	region
year	$y, y p, y e, y n$	year
slice	$s, s p, s e, s n$	time slices
sup	$s 1, s 1 p, s 1 e, s 1 n$	supply
dem	$d, d p, d e, d n$	demand
tech	$t, t p, t e, t n$	technology
stg	$s t 1, s t 1 p, s t 1 e, s t 1 n$	storage
trade	$t 1, t 1 p, t 1 e, t 1 n$	trade between regions
expp	$e, e p, e e, e n$	export to the rest of the world (ROW)
imp	$i, i p, i e, i n$	import from the ROW
group	$g, g p, g e, g n$	group of input or output commodities in technology
weather	$w t h 1, w t h 1 p, w t h 1 e, w t h 1 n$	weather

2.2 Parameters

The model parameters
Name	Alias	Description
pYearFraction(year)	$p Y e a r F r a c t i o n_{y}$	fraction of sum of sampled slices in year – experimental
pTechOlife(tech, region)	$p T e c h O l i f e_{t, r}$	Operational life of technologies
pTechCinp2ginp(tech, comm, region, year, slice)	$p T e c h C i n p 2 g i n p_{t, c, r, y, s}$	Commodity input to group input
pTechGinp2use(tech, group, region, year, slice)	$p T e c h G i n p 2 u s e_{t, g, r, y, s}$	Group input into use
pTechCinp2use(tech, comm, region, year, slice)	$p T e c h C i n p 2 u s e_{t, c, r, y, s}$	Commodity input to use
pTechUse2cact(tech, comm, region, year, slice)	$p T e c h U s e 2 c a c t_{t, c, r, y, s}$	Use to commodity activity
pTechCact2cout(tech, comm, region, year, slice)	$p T e c h C a c t 2 c o u t_{t, c, r, y, s}$	Commodity activity to commodity output
pTechEmisComm(tech, comm)	$p T e c h E m i s C o m m_{t, c}$	Combustion factor for input commodity (from 0 to 1)
pTechAct2AInp(tech, comm, region, year, slice)	$p T e c h A c t 2 A I n p_{t, c, r, y, s}$	Activity to aux-commodity input
pTechCap2AInp(tech, comm, region, year, slice)	$p T e c h C a p 2 A I n p_{t, c, r, y, s}$	Capacity to aux-commodity input
pTechNCap2AInp(tech, comm, region, year, slice)	$p T e c h N C a p 2 A I n p_{t, c, r, y, s}$	New capacity to aux-commodity input
pTechCinp2AInp(tech, comm, comm, region, year, slice)	$p T e c h C i n p 2 A I n p_{t, c, c, r, y, s}$	Commodity input to aux-commodity input
pTechCout2AInp(tech, comm, comm, region, year, slice)	$p T e c h C o u t 2 A I n p_{t, c, c, r, y, s}$	Commodity output to aux-commodity input
pTechAct2AOut(tech, comm, region, year, slice)	$p T e c h A c t 2 A O u t_{t, c, r, y, s}$	Activity to aux-commodity output
pTechCap2AOut(tech, comm, region, year, slice)	$p T e c h C a p 2 A O u t_{t, c, r, y, s}$	Capacity to aux-commodity output
pTechNCap2AOut(tech, comm, region, year, slice)	$p T e c h N C a p 2 A O u t_{t, c, r, y, s}$	New capacity to aux-commodity output
pTechCinp2AOut(tech, comm, comm, region, year, slice)	$p T e c h C i n p 2 A O u t_{t, c, c, r, y, s}$	Commodity to aux-commodity output
pTechCout2AOut(tech, comm, comm, region, year, slice)	$p T e c h C o u t 2 A O u t_{t, c, c, r, y, s}$	Commodity-output to aux-commodity input
pTechFixom(tech, region, year)	$p T e c h F i x o m_{t, r, y}$	Fixed Operating and maintenance (O\
pTechVarom(tech, region, year, slice)	$p T e c h V a r o m_{t, r, y, s}$	Variable O\
pTechInvcost(tech, region, year)	$p T e c h I n v c o s t_{t, r, y}$	Investment costs (per unit of capacity)
pTechEac(tech, region, year)	$p T e c h E a c_{t, r, y}$	Equivalent annual (investment) cost
pTechRetCost(tech, region, year)	$p T e c h R e t C o s t_{t, r, y}$	Early retirement costs
pTechShareLo(tech, comm, region, year, slice)	$p T e c h S h a r e L o_{t, c, r, y, s}$	Lower bound of the share of the commodity in total group input or output
pTechShareUp(tech, comm, region, year, slice)	$p T e c h S h a r e U p_{t, c, r, y, s}$	Upper bound of the share of the commodity in total group input or output
pTechAfLo(tech, region, year, slice)	$p T e c h A f L o_{t, r, y, s}$	Lower bound on availability factor by slices
pTechAfUp(tech, region, year, slice)	$p T e c h A f U p_{t, r, y, s}$	Upper bound on availability factor by slices
pTechRampUp(tech, region, year, slice)	$p T e c h R a m p U p_{t, r, y, s}$	Ramp Up on availability factor
pTechRampDown(tech, region, year, slice)	$p T e c h R a m p D o w n_{t, r, y, s}$	Ramp Down on availability
pTechAfsLo(tech, region, year, slice)	$p T e c h A f s L o_{t, r, y, s}$	Lower bound on availability factor by groups of slices
pTechAfsUp(tech, region, year, slice)	$p T e c h A f s U p_{t, r, y, s}$	Upper bound on availability factor by groups of slices
pTechAfcLo(tech, comm, region, year, slice)	$p T e c h A f c L o_{t, c, r, y, s}$	Lower bound for commodity output
pTechAfcUp(tech, comm, region, year, slice)	$p T e c h A f c U p_{t, c, r, y, s}$	Upper bound for commodity output
pTechStock(tech, region, year)	$p T e c h S t o c k_{t, r, y}$	Technology capacity stock
pTechCapUp(tech, region, year)	$p T e c h C a p U p_{t, r, y}$	Upper bound on technology capacity
pTechCapLo(tech, region, year)	$p T e c h C a p L o_{t, r, y}$	Lower bound on technology capacity
pTechNewCapUp(tech, region, year)	$p T e c h N e w C a p U p_{t, r, y}$	Upper bound on new technology capacity
pTechNewCapLo(tech, region, year)	$p T e c h N e w C a p L o_{t, r, y}$	Lower bound on new technology capacity
pTechRetUp(tech, region, year)	$p T e c h R e t U p_{t, r, y}$	Upper bound on early retirement
pTechRetLo(tech, region, year)	$p T e c h R e t L o_{t, r, y}$	Lower bound on early retirement
pTechCap2act(tech)	$p T e c h C a p 2 a c t_{t}$	Technology capacity units to activity units conversion factor
pTechCvarom(tech, comm, region, year, slice)	$p T e c h C v a r o m_{t, c, r, y, s}$	Commodity-specific variable costs (per unit of commodity input or output)
pTechAvarom(tech, comm, region, year, slice)	$p T e c h A v a r o m_{t, c, r, y, s}$	Auxilary Commodity-specific variable costs (per unit of commodity input or output)
pDiscount(region, year)	$p D i s c o u n t_{r, y}$	Discount rate (can be region and year specific)
pDiscountFactor(region, year)	$p D i s c o u n t F a c t o r_{r, y}$	Discount factor (cumulative)
pDiscountFactorMileStone(region, year)	$p D i s c o u n t F a c t o r M i l e S t o n e_{r, y}$	Discount factor (cumulative) sum for MileStone
pSupCost(sup, comm, region, year, slice)	$p S u p C o s t_{s 1, c, r, y, s}$	Costs of supply (price per unit)
pSupAvaUp(sup, comm, region, year, slice)	$p S u p A v a U p_{s 1, c, r, y, s}$	Upper bound for supply
pSupAvaLo(sup, comm, region, year, slice)	$p S u p A v a L o_{s 1, c, r, y, s}$	Lower bound for supply
pSupReserveUp(sup, comm, region)	$p S u p R e s e r v e U p_{s 1, c, r}$	Upper constraint on cumulative supply
pSupReserveLo(sup, comm, region)	$p S u p R e s e r v e L o_{s 1, c, r}$	Lower constraint on cumulative supply
pDemand(dem, comm, region, year, slice)	$p D e m a n d_{d, c, r, y, s}$	Exogenous demand
pEmissionFactor(comm, comm)	$p E m i s s i o n F a c t o r_{c, c}$	Emission factor
pDummyImportCost(comm, region, year, slice)	$p D u m m y I m p o r t C o s t_{c, r, y, s}$	Dummy costs parameters (for debugging)
pDummyExportCost(comm, region, year, slice)	$p D u m m y E x p o r t C o s t_{c, r, y, s}$	Dummy costs parameters (for debuging)
pTaxCostInp(comm, region, year, slice)	$p T a x C o s t I n p_{c, r, y, s}$	Commodity taxes for input
pTaxCostOut(comm, region, year, slice)	$p T a x C o s t O u t_{c, r, y, s}$	Commodity taxes for output
pTaxCostBal(comm, region, year, slice)	$p T a x C o s t B a l_{c, r, y, s}$	Commodity taxes for balance
pSubCostInp(comm, region, year, slice)	$p S u b C o s t I n p_{c, r, y, s}$	Commodity subsidies for input
pSubCostOut(comm, region, year, slice)	$p S u b C o s t O u t_{c, r, y, s}$	Commodity subsidies for output
pSubCostBal(comm, region, year, slice)	$p S u b C o s t B a l_{c, r, y, s}$	Commodity subsidies for balance
pAggregateFactor(comm, comm)	$p A g g r e g a t e F a c t o r_{c, c}$	Aggregation factor of commodities
pPeriodLen(year)	$p P e r i o d L e n_{y}$	Length of milestone-year-period
pSliceShare(slice)	$p S l i c e S h a r e_{s}$	Slice share in year
pSliceWeight(slice)	$p S l i c e W e i g h t_{s}$	Slice weight
ordYear(year)	$o r d Y e a r_{y}$	ord year (used in GLPK-MathProg)
cardYear(year)	$c a r d Y e a r_{y}$	card year (used in GLPK-MathProg)
pStorageInpEff(stg, comm, region, year, slice)	$p S t o r a g e I n p E f f_{s t 1, c, r, y, s}$	Storage input efficiency
pStorageOutEff(stg, comm, region, year, slice)	$p S t o r a g e O u t E f f_{s t 1, c, r, y, s}$	Storage output efficiency
pStorageStgEff(stg, comm, region, year, slice)	$p S t o r a g e S t g E f f_{s t 1, c, r, y, s}$	Storage time-efficiency (annual)
pStorageStock(stg, region, year)	$p S t o r a g e S t o c k_{s t 1, r, y}$	Storage capacity stock
pStorageCapUp(stg, region, year)	$p S t o r a g e C a p U p_{s t 1, r, y}$	Upper bound on storage capacity
pStorageCapLo(stg, region, year)	$p S t o r a g e C a p L o_{s t 1, r, y}$	Lower bound on storage capacity
pStorageNewCapUp(stg, region, year)	$p S t o r a g e N e w C a p U p_{s t 1, r, y}$	Upper bound on new storage capacity
pStorageNewCapLo(stg, region, year)	$p S t o r a g e N e w C a p L o_{s t 1, r, y}$	Lower bound on new storage capacity
pStorageRetUp(stg, region, year)	$p S t o r a g e R e t U p_{s t 1, r, y}$	Upper bound on early retirement
pStorageRetLo(stg, region, year)	$p S t o r a g e R e t L o_{s t 1, r, y}$	Lower bound on early retirement
pStorageOlife(stg, region)	$p S t o r a g e O l i f e_{s t 1, r}$	Storage operational life
pStorageCostStore(stg, region, year, slice)	$p S t o r a g e C o s t S t o r e_{s t 1, r, y, s}$	Storing costs per stored amount (annual)
pStorageCostInp(stg, region, year, slice)	$p S t o r a g e C o s t I n p_{s t 1, r, y, s}$	Storage input costs
pStorageCostOut(stg, region, year, slice)	$p S t o r a g e C o s t O u t_{s t 1, r, y, s}$	Storage output costs
pStorageFixom(stg, region, year)	$p S t o r a g e F i x o m_{s t 1, r, y}$	Storage fixed O\
pStorageInvcost(stg, region, year)	$p S t o r a g e I n v c o s t_{s t 1, r, y}$	Storage investment costs
pStorageEac(stg, region, year)	$p S t o r a g e E a c_{s t 1, r, y}$	Storage equivalent annual costs
pStorageRetCost(stg, region, year)	$p S t o r a g e R e t C o s t_{s t 1, r, y}$	Storage early retirement costs
pStorageCap2stg(stg)	$p S t o r a g e C a p 2 s t g_{s t 1}$	Storage (dis)charging capacity to accumulating capacity (to be renamed to duration)
pStorageAfLo(stg, region, year, slice)	$p S t o r a g e A f L o_{s t 1, r, y, s}$	Storage availability factor lower bound (minimum charging level)
pStorageAfUp(stg, region, year, slice)	$p S t o r a g e A f U p_{s t 1, r, y, s}$	Storage availability factor upper bound (maximum charging level)
pStorageCinpUp(stg, comm, region, year, slice)	$p S t o r a g e C i n p U p_{s t 1, c, r, y, s}$	Storage input upper bound
pStorageCinpLo(stg, comm, region, year, slice)	$p S t o r a g e C i n p L o_{s t 1, c, r, y, s}$	Storage input lower bound
pStorageCoutUp(stg, comm, region, year, slice)	$p S t o r a g e C o u t U p_{s t 1, c, r, y, s}$	Storage output upper bound
pStorageCoutLo(stg, comm, region, year, slice)	$p S t o r a g e C o u t L o_{s t 1, c, r, y, s}$	Storage output lower bound
pStorageNCap2Stg(stg, comm, region, year, slice)	$p S t o r a g e N C a p 2 S t g_{s t 1, c, r, y, s}$	Initial storage charge level for new investment
pStorageCharge(stg, comm, region, year, slice)	$p S t o r a g e C h a r g e_{s t 1, c, r, y, s}$	Initial storage charge level for stock
pStorageStg2AInp(stg, comm, region, year, slice)	$p S t o r a g e S t g 2 A I n p_{s t 1, c, r, y, s}$	Storage level to auxilary input
pStorageStg2AOut(stg, comm, region, year, slice)	$p S t o r a g e S t g 2 A O u t_{s t 1, c, r, y, s}$	Storage level output
pStorageCinp2AInp(stg, comm, region, year, slice)	$p S t o r a g e C i n p 2 A I n p_{s t 1, c, r, y, s}$	Storage input to auxilary input
pStorageCinp2AOut(stg, comm, region, year, slice)	$p S t o r a g e C i n p 2 A O u t_{s t 1, c, r, y, s}$	Storage input to auxilary output
pStorageCout2AInp(stg, comm, region, year, slice)	$p S t o r a g e C o u t 2 A I n p_{s t 1, c, r, y, s}$	Storage output to auxilary input
pStorageCout2AOut(stg, comm, region, year, slice)	$p S t o r a g e C o u t 2 A O u t_{s t 1, c, r, y, s}$	Storage output to auxilary output
pStorageCap2AInp(stg, comm, region, year, slice)	$p S t o r a g e C a p 2 A I n p_{s t 1, c, r, y, s}$	Storage capacity to auxilary input
pStorageCap2AOut(stg, comm, region, year, slice)	$p S t o r a g e C a p 2 A O u t_{s t 1, c, r, y, s}$	Storage capacity to auxilary output
pStorageNCap2AInp(stg, comm, region, year, slice)	$p S t o r a g e N C a p 2 A I n p_{s t 1, c, r, y, s}$	Storage new capacity to auxilary input
pStorageNCap2AOut(stg, comm, region, year, slice)	$p S t o r a g e N C a p 2 A O u t_{s t 1, c, r, y, s}$	Storage new capacity to auxilary output
pTradeIrEff(trade, region, region, year, slice)	$p T r a d e I r E f f_{t 1, r, r, y, s}$	Inter-regional trade efficiency
pTradeIrUp(trade, region, region, year, slice)	$p T r a d e I r U p_{t 1, r, r, y, s}$	Upper bound on trade flow
pTradeIrLo(trade, region, region, year, slice)	$p T r a d e I r L o_{t 1, r, r, y, s}$	Lower bound on trade flow
pTradeIrCost(trade, region, region, year, slice)	$p T r a d e I r C o s t_{t 1, r, r, y, s}$	Costs of trade flow
pTradeIrMarkup(trade, region, region, year, slice)	$p T r a d e I r M a r k u p_{t 1, r, r, y, s}$	Markup of trade flow
pTradeIrCsrc2Ainp(trade, comm, region, region, year, slice)	$p T r a d e I r C s r c 2 A i n p_{t 1, c, r, r, y, s}$	Auxiliary input commodity in source region
pTradeIrCsrc2Aout(trade, comm, region, region, year, slice)	$p T r a d e I r C s r c 2 A o u t_{t 1, c, r, r, y, s}$	Auxiliary output commodity in source region
pTradeIrCdst2Ainp(trade, comm, region, region, year, slice)	$p T r a d e I r C d s t 2 A i n p_{t 1, c, r, r, y, s}$	Auxiliary input commodity in destination region
pTradeIrCdst2Aout(trade, comm, region, region, year, slice)	$p T r a d e I r C d s t 2 A o u t_{t 1, c, r, r, y, s}$	Auxiliary output commodity in destination region
pExportRowRes(expp)	$p E x p o r t R o w R e s_{e}$	Upper bound on cumulative export to ROW
pExportRowUp(expp, region, year, slice)	$p E x p o r t R o w U p_{e, r, y, s}$	Upper bound on export to ROW
pExportRowLo(expp, region, year, slice)	$p E x p o r t R o w L o_{e, r, y, s}$	Lower bound on export to ROW
pExportRowPrice(expp, region, year, slice)	$p E x p o r t R o w P r i c e_{e, r, y, s}$	Export prices to ROW
pImportRowRes(imp)	$p I m p o r t R o w R e s_{i}$	Upper bound on cumulative import to ROW
pImportRowUp(imp, region, year, slice)	$p I m p o r t R o w U p_{i, r, y, s}$	Upper bount on import from ROW
pImportRowLo(imp, region, year, slice)	$p I m p o r t R o w L o_{i, r, y, s}$	Lower bound on import from ROW
pImportRowPrice(imp, region, year, slice)	$p I m p o r t R o w P r i c e_{i, r, y, s}$	Import prices from ROW
pTradeStock(trade, year)	$p T r a d e S t o c k_{t 1, y}$	Existing capacity
pTradeCapUp(trade, year)	$p T r a d e C a p U p_{t 1, y}$	Upper bound on trade capacity
pTradeCapLo(trade, year)	$p T r a d e C a p L o_{t 1, y}$	Lower bound on trade capacity
pTradeNewCapUp(trade, year)	$p T r a d e N e w C a p U p_{t 1, y}$	Upper bound on new trade capacity
pTradeNewCapLo(trade, year)	$p T r a d e N e w C a p L o_{t 1, y}$	Lower bound on new trade capacity
pTradeRetUp(trade, year)	$p T r a d e R e t U p_{t 1, y}$	Upper bound on early retirement
pTradeRetLo(trade, year)	$p T r a d e R e t L o_{t 1, y}$	Lower bound on early retirement
pTradeOlife(trade)	$p T r a d e O l i f e_{t 1}$	Operational life
pTradeInvcost(trade, region, year)	$p T r a d e I n v c o s t_{t 1, r, y}$	Overnight investment costs
pTradeEac(trade, region, year)	$p T r a d e E a c_{t 1, r, y}$	Equivalent annual costs
pTradeRetCost(trade, region, year)	$p T r a d e R e t C o s t_{t 1, r, y}$	Early retirement costs
pTradeFixom(trade, year)	$p T r a d e F i x o m_{t 1, y}$	Fixed O\
pTradeVarom(trade, region, region, year, slice)	$p T r a d e V a r o m_{t 1, r, r, y, s}$	Variable O\
pTradeCap2Act(trade)	$p T r a d e C a p 2 A c t_{t 1}$	Capacity to activity factor
pWeather(weather, region, year, slice)	$p W e a t h e r_{w t h 1, r, y, s}$	weather factors
pSupWeatherUp(weather, sup)	$p S u p W e a t h e r U p_{w t h 1, s 1}$	weather factor for supply upper value (ava.up)
pSupWeatherLo(weather, sup)	$p S u p W e a t h e r L o_{w t h 1, s 1}$	weather factor for supply lower value (ava.lo)
pTechWeatherAfLo(weather, tech)	$p T e c h W e a t h e r A f L o_{w t h 1, t}$	weather factor for technology availability lower value (af.lo)
pTechWeatherAfUp(weather, tech)	$p T e c h W e a t h e r A f U p_{w t h 1, t}$	weather factor for technology availability upper value (af.up)
pTechWeatherAfsLo(weather, tech)	$p T e c h W e a t h e r A f s L o_{w t h 1, t}$	weather factor for technology availability lower value (af.lo)
pTechWeatherAfsUp(weather, tech)	$p T e c h W e a t h e r A f s U p_{w t h 1, t}$	weather factor for technology availability upper value (afs.lo)
pTechWeatherAfcLo(weather, tech, comm)	$p T e c h W e a t h e r A f c L o_{w t h 1, t, c}$	weather factor for technology availability lower value (afs.lo)
pTechWeatherAfcUp(weather, tech, comm)	$p T e c h W e a t h e r A f c U p_{w t h 1, t, c}$	weather factor for commodity availability upper value (afc.lo)
pStorageWeatherAfLo(weather, stg)	$p S t o r a g e W e a t h e r A f L o_{w t h 1, s t 1}$	weather factor for storage availability lower value (af.lo)
pStorageWeatherAfUp(weather, stg)	$p S t o r a g e W e a t h e r A f U p_{w t h 1, s t 1}$	weather factor for storage availability upper value (af.up)
pStorageWeatherCinpUp(weather, stg)	$p S t o r a g e W e a t h e r C i n p U p_{w t h 1, s t 1}$	weather factor for storage commodity input upper value (cinp.up)
pStorageWeatherCinpLo(weather, stg)	$p S t o r a g e W e a t h e r C i n p L o_{w t h 1, s t 1}$	weather factor for storage commodity input lower value (cinp.lo)
pStorageWeatherCoutUp(weather, stg)	$p S t o r a g e W e a t h e r C o u t U p_{w t h 1, s t 1}$	weather factor for storage commodity output upper value (cout.up)
pStorageWeatherCoutLo(weather, stg)	$p S t o r a g e W e a t h e r C o u t L o_{w t h 1, s t 1}$	weather factor for storage commodity output lower value (cout.lo)
pLECLoACT(region)	$p L E C L o A C T_{r}$	levelized costs interim parameter

2.3 Variables

The model variables $[- I n f, + I n f]$
Name	Alias	Description
vTechInv(tech, region, year)	${v T e c h I n v}_{t, r, y}$	Overnight investment costs
vTechEac(tech, region, year)	${v T e c h E a c}_{t, r, y}$	Annualized investment costs
vTechOMCost(tech, region, year)	${v T e c h O M C o s t}_{t, r, y}$	Sum of all operational costs is equal vTechFixom + vTechVarom (AVarom + CVarom + ActVarom)
vSupCost(sup, region, year)	${v S u p C o s t}_{s 1, r, y}$	Supply costs (weighted)
vEmsFuelTot(comm, region, year, slice)	${v E m s F u e l T o t}_{c, r, y, s}$	Total emissions from fuels combustion (technologies) (weighted)
vBalance(comm, region, year, slice)	${v B a l a n c e}_{c, r, y, s}$	Net commodity balance (all sources) (weighted)
vTotalCost(region, year)	${v T o t a l C o s t}_{r, y}$	Regional annual total costs (weighted)
vObjective	$v O b j e c t i v e$	Objective costs
vTaxCost(comm, region, year)	${v T a x C o s t}_{c, r, y}$	Total tax levies (tax costs)
vSubsCost(comm, region, year)	${v S u b s C o s t}_{c, r, y}$	Total subsidies (substracted from costs)
vAggOutTot(comm, region, year, slice)	${v A g g O u t T o t}_{c, r, y, s}$	Aggregated commodity output (weighted)
vStorageOMCost(stg, region, year)	${v S t o r a g e O M C o s t}_{s t 1, r, y}$	Storage O\
vTradeCost(region, year)	${v T r a d e C o s t}_{r, y}$	Total trade costs (weighted)
vTradeRowCost(region, year)	${v T r a d e R o w C o s t}_{r, y}$	Trade with ROW costs (weighted)
vTradeIrCost(region, year)	${v T r a d e I r C o s t}_{r, y}$	Interregional trade costs (weighted)

The model positive variables $[0, + I n f]$
Name	Alias	Description
vTechNewCap(tech, region, year)	${v T e c h N e w C a p}_{t, r, y}$	New capacity
vTechRetiredStockCum(tech, region, year)	${v T e c h R e t i r e d S t o c k C u m}_{t, r, y}$	Early retired stock
vTechRetiredStock(tech, region, year)	${v T e c h R e t i r e d S t o c k}_{t, r, y}$	Early retired stock
vTechRetiredNewCap(tech, region, year, year)	${v T e c h R e t i r e d N e w C a p}_{t, r, y, y}$	Early retired new capacity
vTechCap(tech, region, year)	${v T e c h C a p}_{t, r, y}$	Total capacity of the technology
vTechAct(tech, region, year, slice)	${v T e c h A c t}_{t, r, y, s}$	Activity level of technology
vTechInp(tech, comm, region, year, slice)	${v T e c h I n p}_{t, c, r, y, s}$	Input level
vTechOut(tech, comm, region, year, slice)	${v T e c h O u t}_{t, c, r, y, s}$	Commodity output from technology - tech timeframe
vTechAInp(tech, comm, region, year, slice)	${v T e c h A I n p}_{t, c, r, y, s}$	Auxiliary commodity input
vTechAOut(tech, comm, region, year, slice)	${v T e c h A O u t}_{t, c, r, y, s}$	Auxiliary commodity output
vSupOut(sup, comm, region, year, slice)	${v S u p O u t}_{s 1, c, r, y, s}$	Output of supply
vSupReserve(sup, comm, region)	${v S u p R e s e r v e}_{s 1, c, r}$	Cumulative supply (weighted)
vDemInp(comm, region, year, slice)	${v D e m I n p}_{c, r, y, s}$	Input to demand
vOutTot(comm, region, year, slice)	${v O u t T o t}_{c, r, y, s}$	Total commodity output (all processes) (weighted)
vInpTot(comm, region, year, slice)	${v I n p T o t}_{c, r, y, s}$	Total commodity input (all processes) (weighted)
vInp2Lo(comm, region, year, slice, slice)	${v I n p 2 L o}_{c, r, y, s, s}$	Desagregation of slices for input parent to (grand)child
vOut2Lo(comm, region, year, slice, slice)	${v O u t 2 L o}_{c, r, y, s, s}$	Desagregation of slices for output parent to (grand)child
vSupOutTot(comm, region, year, slice)	${v S u p O u t T o t}_{c, r, y, s}$	Total commodity supply (weighted)
vTechInpTot(comm, region, year, slice)	${v T e c h I n p T o t}_{c, r, y, s}$	Total commodity (main \
vTechOutTot(comm, region, year, slice)	${v T e c h O u t T o t}_{c, r, y, s}$	Total commodity (main \
vStorageInpTot(comm, region, year, slice)	${v S t o r a g e I n p T o t}_{c, r, y, s}$	Total commodity (main \
vStorageOutTot(comm, region, year, slice)	${v S t o r a g e O u t T o t}_{c, r, y, s}$	Total commodity (main \
vStorageAInp(stg, comm, region, year, slice)	${v S t o r a g e A I n p}_{s t 1, c, r, y, s}$	Aux-commodity input to storage
vStorageAOut(stg, comm, region, year, slice)	${v S t o r a g e A O u t}_{s t 1, c, r, y, s}$	Aux-commodity input from storage
vDummyImport(comm, region, year, slice)	${v D u m m y I m p o r t}_{c, r, y, s}$	Dummy import (for debugging)
vDummyExport(comm, region, year, slice)	${v D u m m y E x p o r t}_{c, r, y, s}$	Dummy export (for debugging)
vStorageInp(stg, comm, region, year, slice)	${v S t o r a g e I n p}_{s t 1, c, r, y, s}$	Storage input
vStorageOut(stg, comm, region, year, slice)	${v S t o r a g e O u t}_{s t 1, c, r, y, s}$	Storage output
vStorageStore(stg, comm, region, year, slice)	${v S t o r a g e S t o r e}_{s t 1, c, r, y, s}$	Storage level
vStorageInv(stg, region, year)	${v S t o r a g e I n v}_{s t 1, r, y}$	Storage investments
vStorageEac(stg, region, year)	${v S t o r a g e E a c}_{s t 1, r, y}$	Storage EAC investments
vStorageCap(stg, region, year)	${v S t o r a g e C a p}_{s t 1, r, y}$	Storage capacity
vStorageNewCap(stg, region, year)	${v S t o r a g e N e w C a p}_{s t 1, r, y}$	Storage new capacity
vImportTot(comm, region, year, slice)	${v I m p o r t T o t}_{c, r, y, s}$	Total regional import (Ir + ROW) (weighted)
vExportTot(comm, region, year, slice)	${v E x p o r t T o t}_{c, r, y, s}$	Total regional export (Ir + ROW) (weighted)
vTradeIr(trade, comm, region, region, year, slice)	${v T r a d e I r}_{t 1, c, r, r, y, s}$	Total physical trade flows between regions
vTradeIrAInp(trade, comm, region, year, slice)	${v T r a d e I r A I n p}_{t 1, c, r, y, s}$	Trade auxilari input
vTradeIrAInpTot(comm, region, year, slice)	${v T r a d e I r A I n p T o t}_{c, r, y, s}$	Trade total auxilari input (weighted)
vTradeIrAOut(trade, comm, region, year, slice)	${v T r a d e I r A O u t}_{t 1, c, r, y, s}$	Trade auxilari output
vTradeIrAOutTot(comm, region, year, slice)	${v T r a d e I r A O u t T o t}_{c, r, y, s}$	Trade auxilari output total (weighted)
vExportRowCum(expp, comm)	${v E x p o r t R o w C u m}_{e, c}$	Cumulative export to ROW
vExportRow(expp, comm, region, year, slice)	${v E x p o r t R o w}_{e, c, r, y, s}$	Export to ROW
vImportRowCum(imp, comm)	${v I m p o r t R o w C u m}_{i, c}$	Cumulative import from ROW
vImportRow(imp, comm, region, year, slice)	${v I m p o r t R o w}_{i, c, r, y, s}$	Import from ROW
vTradeCap(trade, year)	${v T r a d e C a p}_{t 1, y}$	Trade capacity
vTradeInv(trade, region, year)	${v T r a d e I n v}_{t 1, r, y}$	Investment in trade capacity (overnight)
vTradeEac(trade, region, year)	${v T r a d e E a c}_{t 1, r, y}$	Investment in trade capacity (EAC)
vTradeNewCap(trade, year)	${v T r a d e N e w C a p}_{t 1, y}$	New trade capacity
vTotalUserCosts(region, year)	${v T o t a l U s e r C o s t s}_{r, y}$	Total additional costs (set by user)

2.4 Equations

2.4.0.1 `eqTechSng2Sng`: Technology input to output


${v T e c h I n p}_{t, c, r, y, s} * p T e c h C i n p 2 u s e_{t, c, r, y, s} = \frac{{v T e c h O u t}_{t, c p, r, y, s}}{p T e c h U s e 2 c a c t_{t, c p, r, y, s} * p T e c h C a c t 2 c o u t_{t, c p, r, y, s}}$

2.4.0.2 `eqTechGrp2Sng`: Technology group input to output


$p T e c h G i n p 2 u s e_{t, g, r, y, s} * \sum_{c} ({v T e c h I n p}_{t, c, r, y, s} * p T e c h C i n p 2 g i n p_{t, c, r, y, s}) = \frac{{v T e c h O u t}_{t, c p, r, y, s}}{p T e c h U s e 2 c a c t_{t, c p, r, y, s} * p T e c h C a c t 2 c o u t_{t, c p, r, y, s}}$

2.4.0.3 `eqTechSng2Grp`: Technology input to group output


${v T e c h I n p}_{t, c, r, y, s} * p T e c h C i n p 2 u s e_{t, c, r, y, s} = \sum_{c p} (\frac{{v T e c h O u t}_{t, c p, r, y, s}}{p T e c h U s e 2 c a c t_{t, c p, r, y, s} * p T e c h C a c t 2 c o u t_{t, c p, r, y, s}})$

2.4.0.4 `eqTechGrp2Grp`: Technology group input to group output


$p T e c h G i n p 2 u s e_{t, g, r, y, s} * \sum_{c} ({v T e c h I n p}_{t, c, r, y, s} * p T e c h C i n p 2 g i n p_{t, c, r, y, s}) = \sum_{c p} (\frac{{v T e c h O u t}_{t, c p, r, y, s}}{p T e c h U s e 2 c a c t_{t, c p, r, y, s} * p T e c h C a c t 2 c o u t_{t, c p, r, y, s}})$


${v T e c h I n p}_{t, c, r, y, s} \geq p T e c h S h a r e L o_{t, c, r, y, s} * \sum_{c p} ({v T e c h I n p}_{t, c p, r, y, s})$


${v T e c h I n p}_{t, c, r, y, s} \leq p T e c h S h a r e U p_{t, c, r, y, s} * \sum_{c p} ({v T e c h I n p}_{t, c p, r, y, s})$


${v T e c h O u t}_{t, c, r, y, s} \geq p T e c h S h a r e L o_{t, c, r, y, s} * \sum_{c p} ({v T e c h O u t}_{t, c p, r, y, s})$


${v T e c h O u t}_{t, c, r, y, s} \leq p T e c h S h a r e U p_{t, c, r, y, s} * \sum_{c p} ({v T e c h O u t}_{t, c p, r, y, s})$

2.4.0.9 `eqTechAInp`: Technology auxiliary commodity input


${v T e c h A I n p}_{t, c, r, y, s} = ({v T e c h A c t}_{t, r, y, s} * p T e c h A c t 2 A I n p_{t, c, r, y, s}) + (\frac{{v T e c h C a p}_{t, r, y} * p T e c h C a p 2 A I n p_{t, c, r, y, s}}{p T e c h C a p 2 a c t_{t}}) + ({v T e c h N e w C a p}_{t, r, y} * p T e c h N C a p 2 A I n p_{t, c, r, y, s}) + \sum_{c p} (p T e c h C i n p 2 A I n p_{t, c, c p, r, y, s} * {v T e c h I n p}_{t, c p, r, y, s}) + \sum_{c p} (p T e c h C o u t 2 A I n p_{t, c, c p, r, y, s} * {v T e c h O u t}_{t, c p, r, y, s})$

{v T e c h A I n p}_{t, c, r, y, s} = ({v T e c h A c t}_{t, r, y, s} * p T e c h A c t 2 A I n p_{t, c, r, y, s}) + (\frac{{v T e c h C a p}_{t, r, y} * p T e c h C a p 2 A I n p_{t, c, r, y, s}}{p T e c h C a p 2 a c t_{t}}) + ({v T e c h N e w C a p}_{t, r, y} * p T e c h N C a p 2 A I n p_{t, c, r, y, s}) + \sum_{c p} (p T e c h C i n p 2 A I n p_{t, c, c p, r, y, s} * {v T e c h I n p}_{t, c p, r, y, s}) + \sum_{c p} (p T e c h C o u t 2 A I n p_{t, c, c p, r, y, s} * {v T e c h O u t}_{t, c p, r, y, s})

2.4.0.10 `eqTechAOut`: Technology auxiliary commodity output


${v T e c h A O u t}_{t, c, r, y, s} = ({v T e c h A c t}_{t, r, y, s} * p T e c h A c t 2 A O u t_{t, c, r, y, s}) + (\frac{{v T e c h C a p}_{t, r, y} * p T e c h C a p 2 A O u t_{t, c, r, y, s}}{p T e c h C a p 2 a c t_{t}}) + ({v T e c h N e w C a p}_{t, r, y} * p T e c h N C a p 2 A O u t_{t, c, r, y, s}) + \sum_{c p} (p T e c h C i n p 2 A O u t_{t, c, c p, r, y, s} * {v T e c h I n p}_{t, c p, r, y, s}) + \sum_{c p} (p T e c h C o u t 2 A O u t_{t, c, c p, r, y, s} * {v T e c h O u t}_{t, c p, r, y, s})$

{v T e c h A O u t}_{t, c, r, y, s} = ({v T e c h A c t}_{t, r, y, s} * p T e c h A c t 2 A O u t_{t, c, r, y, s}) + (\frac{{v T e c h C a p}_{t, r, y} * p T e c h C a p 2 A O u t_{t, c, r, y, s}}{p T e c h C a p 2 a c t_{t}}) + ({v T e c h N e w C a p}_{t, r, y} * p T e c h N C a p 2 A O u t_{t, c, r, y, s}) + \sum_{c p} (p T e c h C i n p 2 A O u t_{t, c, c p, r, y, s} * {v T e c h I n p}_{t, c p, r, y, s}) + \sum_{c p} (p T e c h C o u t 2 A O u t_{t, c, c p, r, y, s} * {v T e c h O u t}_{t, c p, r, y, s})

2.4.0.11 `eqTechAfLo`: Technology availability factor lower bound


$p T e c h A f L o_{t, r, y, s} * p T e c h C a p 2 a c t_{t} * {v T e c h C a p}_{t, r, y} * p S l i c e S h a r e_{s} * \prod_{w t h 1} (p T e c h W e a t h e r A f L o_{w t h 1, t} * p W e a t h e r_{w t h 1, r, y, s}) \leq {v T e c h A c t}_{t, r, y, s}$

2.4.0.12 `eqTechAfUp`: Technology availability factor upper bound


${v T e c h A c t}_{t, r, y, s} \leq p T e c h A f U p_{t, r, y, s} * p T e c h C a p 2 a c t_{t} * {v T e c h C a p}_{t, r, y} * p S l i c e S h a r e_{s} * \prod_{w t h 1} (p T e c h W e a t h e r A f U p_{w t h 1, t} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.13 `eqTechAfsLo`: Technology availability factor for sum of slices lower bound


$p T e c h A f s L o_{t, r, y, s} * p T e c h C a p 2 a c t_{t} * {v T e c h C a p}_{t, r, y} * p S l i c e S h a r e_{s} * \prod_{w t h 1} (p T e c h W e a t h e r A f s L o_{w t h 1, t} * p W e a t h e r_{w t h 1, r, y, s}) \leq \sum_{s p} ({v T e c h A c t}_{t, r, y, s p})$

2.4.0.14 `eqTechAfsUp`: Technology availability factor for sum of slices upper bound


$\sum_{s p} ({v T e c h A c t}_{t, r, y, s p}) \leq p T e c h A f s U p_{t, r, y, s} * p T e c h C a p 2 a c t_{t} * {v T e c h C a p}_{t, r, y} * p S l i c e S h a r e_{s} * \prod_{w t h 1} (p T e c h W e a t h e r A f s U p_{w t h 1, t} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.15 `eqTechRampUp`: Technology ramp up


$\frac{{v T e c h A c t}_{t, r, y, s}}{p S l i c e S h a r e_{s}} - \frac{{v T e c h A c t}_{t, r, y, s p}}{p S l i c e S h a r e_{s p}} \leq \frac{p S l i c e S h a r e_{s} * p T e c h C a p 2 a c t_{t} * p T e c h C a p 2 a c t_{t} * {v T e c h C a p}_{t, r, y}}{p T e c h R a m p U p_{t, r, y, s}}$

2.4.0.16 `eqTechRampDown`: Technology ramp down


$\frac{{v T e c h A c t}_{t, r, y, s p}}{p S l i c e S h a r e_{s p}} - \frac{{v T e c h A c t}_{t, r, y, s}}{p S l i c e S h a r e_{s}} \leq \frac{p S l i c e S h a r e_{s} * p T e c h C a p 2 a c t_{t} * p T e c h C a p 2 a c t_{t} * {v T e c h C a p}_{t, r, y}}{p T e c h R a m p D o w n_{t, r, y, s}}$

2.4.0.17 `eqTechActSng`: Technology activity to commodity output


${v T e c h A c t}_{t, r, y, s} = \frac{{v T e c h O u t}_{t, c, r, y, s}}{p T e c h C a c t 2 c o u t_{t, c, r, y, s}}$

2.4.0.18 `eqTechActGrp`: Technology activity to group output


${v T e c h A c t}_{t, r, y, s} = \sum_{c} (\frac{{v T e c h O u t}_{t, c, r, y, s}}{p T e c h C a c t 2 c o u t_{t, c, r, y, s}})$

2.4.0.19 `eqTechAfcOutLo`: Technology commodity availability factor lower bound


$p T e c h C a c t 2 c o u t_{t, c, r, y, s} * p T e c h A f c L o_{t, c, r, y, s} * p T e c h C a p 2 a c t_{t} * {v T e c h C a p}_{t, r, y} * p S l i c e S h a r e_{s} * \prod_{w t h 1} (p T e c h W e a t h e r A f c L o_{w t h 1, t, c} * p W e a t h e r_{w t h 1, r, y, s}) \leq {v T e c h O u t}_{t, c, r, y, s}$

2.4.0.20 `eqTechAfcOutUp`: Technology commodity availability factor upper bound


${v T e c h O u t}_{t, c, r, y, s} \leq p T e c h C a c t 2 c o u t_{t, c, r, y, s} * p T e c h A f c U p_{t, c, r, y, s} * p T e c h C a p 2 a c t_{t} * {v T e c h C a p}_{t, r, y} * \prod_{w t h 1} (p T e c h W e a t h e r A f c U p_{w t h 1, t, c} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.21 `eqTechAfcInpLo`: Technology commodity availability factor lower bound


$p T e c h A f c L o_{t, c, r, y, s} * p T e c h C a p 2 a c t_{t} * {v T e c h C a p}_{t, r, y} * p S l i c e S h a r e_{s} * \prod_{w t h 1} (p T e c h W e a t h e r A f c L o_{w t h 1, t, c} * p W e a t h e r_{w t h 1, r, y, s}) \leq {v T e c h I n p}_{t, c, r, y, s}$

2.4.0.22 `eqTechAfcInpUp`: Technology commodity availability factor upper bound


${v T e c h I n p}_{t, c, r, y, s} \leq p T e c h A f c U p_{t, c, r, y, s} * p T e c h C a p 2 a c t_{t} * {v T e c h C a p}_{t, r, y} * p S l i c e S h a r e_{s} * \prod_{w t h 1} (p T e c h W e a t h e r A f c U p_{w t h 1, t, c} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.23 `eqTechCap`: Technology capacity


${v T e c h C a p}_{t, r, y} = p T e c h S t o c k_{t, r, y} - {v T e c h R e t i r e d S t o c k C u m}_{t, r, y} + \sum_{y p} (p P e r i o d L e n_{y p} * ({v T e c h N e w C a p}_{t, r, y p} - \sum_{y e} ({v T e c h R e t i r e d N e w C a p}_{t, r, y p, y e})))$

2.4.0.24 `eqTechCapLo`: Technology capacity lower bound


${v T e c h C a p}_{t, r, y} \geq p T e c h C a p L o_{t, r, y}$

2.4.0.25 `eqTechCapUp`: Technology capacity upper bound


${v T e c h C a p}_{t, r, y} \leq p T e c h C a p U p_{t, r, y}$

2.4.0.26 `eqTechNewCapLo`: __


${v T e c h N e w C a p}_{t, r, y} \geq p T e c h N e w C a p L o_{t, r, y}$

2.4.0.27 `eqTechNewCapUp`: __


${v T e c h N e w C a p}_{t, r, y} \leq p T e c h N e w C a p U p_{t, r, y}$

2.4.0.28 `eqTechRetiredNewCap`: Retirement of new capacity


$\sum_{y p} ({v T e c h R e t i r e d N e w C a p}_{t, r, y, y p}) \leq {v T e c h N e w C a p}_{t, r, y}$

2.4.0.29 `eqTechRetiredStockCum`: Retirement of stock cumulative


${v T e c h R e t i r e d S t o c k C u m}_{t, r, y} \leq p T e c h S t o c k_{t, r, y}$

2.4.0.30 `eqTechRetiredStock`: Retirement of stock


${v T e c h R e t i r e d S t o c k}_{t, r, y} = {v T e c h R e t i r e d S t o c k C u m}_{t, r, y} - \sum_{y p} ({v T e c h R e t i r e d S t o c k C u m}_{t, r, y p})$

2.4.0.31 `eqTechEac`: Technology Equivalent Annual Cost (EAC)


${v T e c h E a c}_{t, r, y} = \sum_{y p} (p T e c h E a c_{t, r, y p} * p P e r i o d L e n_{y p} * ({v T e c h N e w C a p}_{t, r, y p} - \sum_{y e} ({v T e c h R e t i r e d N e w C a p}_{t, r, y p, y e})))$

2.4.0.32 `eqTechInv`: Technology overnight investment costs


${v T e c h I n v}_{t, r, y} = p T e c h I n v c o s t_{t, r, y} * {v T e c h N e w C a p}_{t, r, y}$

2.4.0.33 `eqTechOMCost`: Technology O&M costs (weighted)


${v T e c h O M C o s t}_{t, r, y} = p T e c h F i x o m_{t, r, y} * {v T e c h C a p}_{t, r, y} + \sum_{s} (p T e c h V a r o m_{t, r, y, s} * p S l i c e W e i g h t_{s} * {v T e c h A c t}_{t, r, y, s}) + \sum_{s} (\sum_{c} (p T e c h C v a r o m_{t, c, r, y, s} * p S l i c e W e i g h t_{s} * {v T e c h I n p}_{t, c, r, y, s})) + \sum_{s} (\sum_{c} (p T e c h C v a r o m_{t, c, r, y, s} * p S l i c e W e i g h t_{s} * {v T e c h O u t}_{t, c, r, y, s})) + \sum_{s} (\sum_{c} (p T e c h A v a r o m_{t, c, r, y, s} * p S l i c e W e i g h t_{s} * {v T e c h A O u t}_{t, c, r, y, s})) + \sum_{s} (\sum_{c} (p T e c h A v a r o m_{t, c, r, y, s} * p S l i c e W e i g h t_{s} * {v T e c h A I n p}_{t, c, r, y, s}))$

{v T e c h O M C o s t}_{t, r, y} = p T e c h F i x o m_{t, r, y} * {v T e c h C a p}_{t, r, y} + \sum_{s} (p T e c h V a r o m_{t, r, y, s} * p S l i c e W e i g h t_{s} * {v T e c h A c t}_{t, r, y, s}) + \sum_{s} (\sum_{c} (p T e c h C v a r o m_{t, c, r, y, s} * p S l i c e W e i g h t_{s} * {v T e c h I n p}_{t, c, r, y, s})) + \sum_{s} (\sum_{c} (p T e c h C v a r o m_{t, c, r, y, s} * p S l i c e W e i g h t_{s} * {v T e c h O u t}_{t, c, r, y, s})) + \sum_{s} (\sum_{c} (p T e c h A v a r o m_{t, c, r, y, s} * p S l i c e W e i g h t_{s} * {v T e c h A O u t}_{t, c, r, y, s})) + \sum_{s} (\sum_{c} (p T e c h A v a r o m_{t, c, r, y, s} * p S l i c e W e i g h t_{s} * {v T e c h A I n p}_{t, c, r, y, s}))

2.4.0.34 `eqSupAvaUp`: Supply availability upper bound


${v S u p O u t}_{s 1, c, r, y, s} \leq p S u p A v a U p_{s 1, c, r, y, s} * \prod_{w t h 1} (p S u p W e a t h e r U p_{w t h 1, s 1} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.35 `eqSupAvaLo`: Supply availability lower bound


${v S u p O u t}_{s 1, c, r, y, s} \geq p S u p A v a L o_{s 1, c, r, y, s} * \prod_{w t h 1} (p S u p W e a t h e r L o_{w t h 1, s 1} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.36 `eqSupReserve`: Cumulative supply (use of reserve)


${v S u p R e s e r v e}_{s 1, c, r} = \sum_{y, s} (p P e r i o d L e n_{y} * p S l i c e W e i g h t_{s} * {v S u p O u t}_{s 1, c, r, y, s})$

2.4.0.37 `eqSupReserveUp`: Cumulative supply upper constraint


${v S u p R e s e r v e}_{s 1, c, r} \leq p S u p R e s e r v e U p_{s 1, c, r}$

2.4.0.38 `eqSupReserveLo`: Cumulative supply lower constraint


${v S u p R e s e r v e}_{s 1, c, r} \geq p S u p R e s e r v e L o_{s 1, c, r}$

2.4.0.39 `eqSupCost`: Supply costs


${v S u p C o s t}_{s 1, r, y} = \sum_{c, s} (p S u p C o s t_{s 1, c, r, y, s} * p S l i c e W e i g h t_{s} * {v S u p O u t}_{s 1, c, r, y, s})$

2.4.0.40 `eqDemInp`: Demand equation


${v D e m I n p}_{c, r, y, s} = \sum_{d} (p D e m a n d_{d, c, r, y, s})$

2.4.0.41 `eqAggOutTot`: Aggregating-commodity output (weighted)


${v A g g O u t T o t}_{c, r, y, s} = \sum_{c p} (p A g g r e g a t e F a c t o r_{c, c p} * \sum_{s p} ({v O u t T o t}_{c p, r, y, s p}))$

2.4.0.42 `eqEmsFuelTot`: Total emissions from commodity consumption (weighted)


${v E m s F u e l T o t}_{c, r, y, s} = \sum_{c p} (p E m i s s i o n F a c t o r_{c, c p} * \sum_{t} (p T e c h E m i s C o m m_{t, c p} * \sum_{s p} ({v T e c h I n p}_{t, c p, r, y, s p}))) * p S l i c e W e i g h t_{s}$

2.4.0.43 `eqStorageAInp`: Storage level


${v S t o r a g e A I n p}_{s t 1, c, r, y, s} = \sum_{c p} (p S t o r a g e S t g 2 A I n p_{s t 1, c, r, y, s} * {v S t o r a g e S t o r e}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C i n p 2 A I n p_{s t 1, c, r, y, s} * {v S t o r a g e I n p}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C o u t 2 A I n p_{s t 1, c, r, y, s} * {v S t o r a g e O u t}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C a p 2 A I n p_{s t 1, c, r, y, s} * {v S t o r a g e C a p}_{s t 1, r, y}) + \sum_{c p} (p S t o r a g e N C a p 2 A I n p_{s t 1, c, r, y, s} * {v S t o r a g e N e w C a p}_{s t 1, r, y})$

{v S t o r a g e A I n p}_{s t 1, c, r, y, s} = \sum_{c p} (p S t o r a g e S t g 2 A I n p_{s t 1, c, r, y, s} * {v S t o r a g e S t o r e}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C i n p 2 A I n p_{s t 1, c, r, y, s} * {v S t o r a g e I n p}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C o u t 2 A I n p_{s t 1, c, r, y, s} * {v S t o r a g e O u t}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C a p 2 A I n p_{s t 1, c, r, y, s} * {v S t o r a g e C a p}_{s t 1, r, y}) + \sum_{c p} (p S t o r a g e N C a p 2 A I n p_{s t 1, c, r, y, s} * {v S t o r a g e N e w C a p}_{s t 1, r, y})

2.4.0.44 `eqStorageAOut`: Storage availability factor lower


${v S t o r a g e A O u t}_{s t 1, c, r, y, s} = \sum_{c p} (p S t o r a g e S t g 2 A O u t_{s t 1, c, r, y, s} * {v S t o r a g e S t o r e}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C i n p 2 A O u t_{s t 1, c, r, y, s} * {v S t o r a g e I n p}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C o u t 2 A O u t_{s t 1, c, r, y, s} * {v S t o r a g e O u t}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C a p 2 A O u t_{s t 1, c, r, y, s} * {v S t o r a g e C a p}_{s t 1, r, y}) + \sum_{c p} (p S t o r a g e N C a p 2 A O u t_{s t 1, c, r, y, s} * {v S t o r a g e N e w C a p}_{s t 1, r, y})$

{v S t o r a g e A O u t}_{s t 1, c, r, y, s} = \sum_{c p} (p S t o r a g e S t g 2 A O u t_{s t 1, c, r, y, s} * {v S t o r a g e S t o r e}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C i n p 2 A O u t_{s t 1, c, r, y, s} * {v S t o r a g e I n p}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C o u t 2 A O u t_{s t 1, c, r, y, s} * {v S t o r a g e O u t}_{s t 1, c p, r, y, s}) + \sum_{c p} (p S t o r a g e C a p 2 A O u t_{s t 1, c, r, y, s} * {v S t o r a g e C a p}_{s t 1, r, y}) + \sum_{c p} (p S t o r a g e N C a p 2 A O u t_{s t 1, c, r, y, s} * {v S t o r a g e N e w C a p}_{s t 1, r, y})

2.4.0.45 `eqStorageStore`: Storage availability factor upper


${v S t o r a g e S t o r e}_{s t 1, c, r, y, s} = p S t o r a g e C h a r g e_{s t 1, c, r, y, s} + (p S t o r a g e N C a p 2 S t g_{s t 1, c, r, y, s} * {v S t o r a g e N e w C a p}_{s t 1, r, y}) + p S t o r a g e I n p E f f_{s t 1, c, r, y, s p} * {v S t o r a g e I n p}_{s t 1, c, r, y, s p} + ({p S t o r a g e S t g E f f_{s t 1, c, r, y, s}}^{p S l i c e S h a r e_{s}}) * {v S t o r a g e S t o r e}_{s t 1, c, r, y, s p} - \frac{{v S t o r a g e O u t}_{s t 1, c, r, y, s p}}{p S t o r a g e O u t E f f_{s t 1, c, r, y, s p}}$

{v S t o r a g e S t o r e}_{s t 1, c, r, y, s} = p S t o r a g e C h a r g e_{s t 1, c, r, y, s} + (p S t o r a g e N C a p 2 S t g_{s t 1, c, r, y, s} * {v S t o r a g e N e w C a p}_{s t 1, r, y}) + p S t o r a g e I n p E f f_{s t 1, c, r, y, s p} * {v S t o r a g e I n p}_{s t 1, c, r, y, s p} + ({p S t o r a g e S t g E f f_{s t 1, c, r, y, s}}^{p S l i c e S h a r e_{s}}) * {v S t o r a g e S t o r e}_{s t 1, c, r, y, s p} - \frac{{v S t o r a g e O u t}_{s t 1, c, r, y, s p}}{p S t o r a g e O u t E f f_{s t 1, c, r, y, s p}}

2.4.0.46 `eqStorageAfLo`: Storage output vs level


${v S t o r a g e S t o r e}_{s t 1, c, r, y, s} \geq p S t o r a g e A f L o_{s t 1, r, y, s} * p S t o r a g e C a p 2 s t g_{s t 1} * {v S t o r a g e C a p}_{s t 1, r, y} * \prod_{w t h 1} (p S t o r a g e W e a t h e r A f L o_{w t h 1, s t 1} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.47 `eqStorageAfUp`: Storage aux-commodity input


${v S t o r a g e S t o r e}_{s t 1, c, r, y, s} \leq p S t o r a g e A f U p_{s t 1, r, y, s} * p S t o r a g e C a p 2 s t g_{s t 1} * {v S t o r a g e C a p}_{s t 1, r, y} * \prod_{w t h 1} (p S t o r a g e W e a t h e r A f U p_{w t h 1, s t 1} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.48 `eqStorageClear`: Storage aux-commodity output


$\frac{{v S t o r a g e O u t}_{s t 1, c, r, y, s}}{p S t o r a g e O u t E f f_{s t 1, c, r, y, s}} \leq {v S t o r a g e S t o r e}_{s t 1, c, r, y, s}$

2.4.0.49 `eqStorageInpUp`: Storage input upper constraint


${v S t o r a g e I n p}_{s t 1, c, r, y, s} \leq {v S t o r a g e C a p}_{s t 1, r, y} * p S t o r a g e C i n p U p_{s t 1, c, r, y, s} * \prod_{w t h 1} (p S t o r a g e W e a t h e r C i n p U p_{w t h 1, s t 1} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.50 `eqStorageInpLo`: Storage input lower constraint


${v S t o r a g e I n p}_{s t 1, c, r, y, s} \geq {v S t o r a g e C a p}_{s t 1, r, y} * p S t o r a g e C i n p L o_{s t 1, c, r, y, s} * \prod_{w t h 1} (p S t o r a g e W e a t h e r C i n p L o_{w t h 1, s t 1} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.51 `eqStorageOutUp`: Storage output upper constraint


${v S t o r a g e O u t}_{s t 1, c, r, y, s} \leq {v S t o r a g e C a p}_{s t 1, r, y} * p S t o r a g e C o u t U p_{s t 1, c, r, y, s} * \prod_{w t h 1} (p S t o r a g e W e a t h e r C o u t U p_{w t h 1, s t 1} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.52 `eqStorageOutLo`: Storage output lower constraint


${v S t o r a g e O u t}_{s t 1, c, r, y, s} \geq {v S t o r a g e C a p}_{s t 1, r, y} * p S t o r a g e C o u t L o_{s t 1, c, r, y, s} * \prod_{w t h 1} (p S t o r a g e W e a t h e r C o u t L o_{w t h 1, s t 1} * p W e a t h e r_{w t h 1, r, y, s})$

2.4.0.53 `eqStorageCap`: Storage capacity


${v S t o r a g e C a p}_{s t 1, r, y} = p S t o r a g e S t o c k_{s t 1, r, y} + \sum_{y p} (p P e r i o d L e n_{y p} * {v S t o r a g e N e w C a p}_{s t 1, r, y p})$

2.4.0.54 `eqStorageCapLo`: Storage capacity lower bound


${v S t o r a g e C a p}_{s t 1, r, y} \geq p S t o r a g e C a p L o_{s t 1, r, y}$

2.4.0.55 `eqStorageCapUp`: Storage capacity upper bound


${v S t o r a g e C a p}_{s t 1, r, y} \leq p S t o r a g e C a p U p_{s t 1, r, y}$

2.4.0.56 `eqStorageNewCapLo`: Storage new capacity lower bound


${v S t o r a g e N e w C a p}_{s t 1, r, y} \geq p S t o r a g e N e w C a p L o_{s t 1, r, y}$

2.4.0.57 `eqStorageNewCapUp`: Storage new capacity upper bound


${v S t o r a g e N e w C a p}_{s t 1, r, y} \leq p S t o r a g e N e w C a p U p_{s t 1, r, y}$

2.4.0.58 `eqStorageInv`: Storage overnight investment costs


${v S t o r a g e I n v}_{s t 1, r, y} = p S t o r a g e I n v c o s t_{s t 1, r, y} * {v S t o r a g e N e w C a p}_{s t 1, r, y}$

2.4.0.59 `eqStorageEac`: Storage equivalent annual cost


${v S t o r a g e E a c}_{s t 1, r, y} = \sum_{y p} (p S t o r a g e E a c_{s t 1, r, y p} * p P e r i o d L e n_{y p} * {v S t o r a g e N e w C a p}_{s t 1, r, y p})$

2.4.0.60 `eqStorageCost`: Storage total costs

{v S t o r a g e O M C o s t}_{s t 1, r, y} = p S t o r a g e F i x o m_{s t 1, r, y} * {v S t o r a g e C a p}_{s t 1, r, y} + \sum_{c} (\sum_{s} (p S t o r a g e C o s t I n p_{s t 1, r, y, s} * p S l i c e W e i g h t_{s} * {v S t o r a g e I n p}_{s t 1, c, r, y, s}) + \sum_{s} (p S t o r a g e C o s t O u t_{s t 1, r, y, s} * p S l i c e W e i g h t_{s} * {v S t o r a g e O u t}_{s t 1, c, r, y, s}) + \sum_{s} (p S t o r a g e C o s t S t o r e_{s t 1, r, y, s} * p S l i c e W e i g h t_{s} * {v S t o r a g e S t o r e}_{s t 1, c, r, y, s}))

2.4.0.61 `eqImportTot`: Import equation (Ir & ROW)


${v I m p o r t T o t}_{c, d s t, y, s} = \sum_{t 1} (\sum_{s r c} (p T r a d e I r E f f_{t 1, s r c, d s t, y, s} * {v T r a d e I r}_{t 1, c, s r c, d s t, y, s})) * p S l i c e W e i g h t_{s} + \sum_{i} ({v I m p o r t R o w}_{i, c, d s t, y, s}) * p S l i c e W e i g h t_{s}$

2.4.0.62 `eqExportTot`: Export equation (Ir & ROW)


${v E x p o r t T o t}_{c, s r c, y, s} = \sum_{t 1} (\sum_{d s t} ({v T r a d e I r}_{t 1, c, s r c, d s t, y, s})) * p S l i c e W e i g h t_{s} + \sum_{e} ({v E x p o r t R o w}_{e, c, s r c, y, s}) * p S l i c e W e i g h t_{s}$

2.4.0.63 `eqTradeFlowUp`: Trade upper bound


${v T r a d e I r}_{t 1, c, s r c, d s t, y, s} \leq p T r a d e I r U p_{t 1, s r c, d s t, y, s}$

2.4.0.64 `eqTradeFlowLo`: Trade lower bound


${v T r a d e I r}_{t 1, c, s r c, d s t, y, s} \geq p T r a d e I r L o_{t 1, s r c, d s t, y, s}$

2.4.0.65 `eqCostTrade`: Total trade costs


${v T r a d e C o s t}_{r, y} = {v T r a d e R o w C o s t}_{r, y} + {v T r a d e I r C o s t}_{r, y}$

2.4.0.66 `eqCostRowTrade`: Costs of trade with the Rest of the World (ROW)


${v T r a d e R o w C o s t}_{r, y} = \sum_{i, c, s} (p I m p o r t R o w P r i c e_{i, r, y, s} * p S l i c e W e i g h t_{s} * {v I m p o r t R o w}_{i, c, r, y, s}) - \sum_{e, c, s} (p E x p o r t R o w P r i c e_{e, r, y, s} * p S l i c e W e i g h t_{s} * {v E x p o r t R o w}_{e, c, r, y, s})$

2.4.0.67 `eqCostIrTrade`: Costs of import

{v T r a d e I r C o s t}_{r, y} = \sum_{t 1} (p T r a d e F i x o m_{t 1, y} * p T r a d e S t o c k_{t 1, y}) + \sum_{t 1} (p T r a d e F i x o m_{t 1, y} * ({v T r a d e C a p}_{t 1, y} - p T r a d e S t o c k_{t 1, y})) + \sum_{t 1} ({v T r a d e E a c}_{t 1, r, y}) + \sum_{t 1, s r c} (\sum_{c} (\sum_{s} ((p T r a d e I r C o s t_{t 1, s r c, r, y, s} + p T r a d e I r M a r k u p_{t 1, s r c, r, y, s}) * {v T r a d e I r}_{t 1, c, s r c, r, y, s} * p S l i c e W e i g h t_{s}))) - \sum_{t 1, d s t} (\sum_{c} (\sum_{s} ((p T r a d e I r C o s t_{t 1, r, d s t, y, s} + p T r a d e I r M a r k u p_{t 1, r, d s t, y, s}) * {v T r a d e I r}_{t 1, c, r, d s t, y, s} * p S l i c e W e i g h t_{s})))

2.4.0.68 `eqExportRowUp`: Export to ROW upper constraint


${v E x p o r t R o w}_{e, c, r, y, s} \leq p E x p o r t R o w U p_{e, r, y, s}$

2.4.0.69 `eqExportRowLo`: Export to ROW lower constraint


${v E x p o r t R o w}_{e, c, r, y, s} \geq p E x p o r t R o w L o_{e, r, y, s}$

2.4.0.70 `eqExportRowCum`: Cumulative export to ROW


${v E x p o r t R o w C u m}_{e, c} = \sum_{r, y, s} (p P e r i o d L e n_{y} * p S l i c e W e i g h t_{s} * {v E x p o r t R o w}_{e, c, r, y, s})$

2.4.0.71 `eqExportRowResUp`: Cumulative export to ROW upper constraint


${v E x p o r t R o w C u m}_{e, c} \leq p E x p o r t R o w R e s_{e}$

2.4.0.72 `eqImportRowUp`: Import from ROW upper constraint


${v I m p o r t R o w}_{i, c, r, y, s} \leq p I m p o r t R o w U p_{i, r, y, s}$

2.4.0.73 `eqImportRowLo`: Import of ROW lower constraint


${v I m p o r t R o w}_{i, c, r, y, s} \geq p I m p o r t R o w L o_{i, r, y, s}$

2.4.0.74 `eqImportRowCum`: Cumulative import from ROW


${v I m p o r t R o w C u m}_{i, c} = \sum_{r, y, s} (p P e r i o d L e n_{y} * p S l i c e W e i g h t_{s} * {v I m p o r t R o w}_{i, c, r, y, s})$

2.4.0.75 `eqImportRowResUp`: Cumulative import from ROW upper constraint


${v I m p o r t R o w C u m}_{i, c} \leq p I m p o r t R o w R e s_{i}$

2.4.0.76 `eqTradeCapFlow`: Trade capacity


$p S l i c e S h a r e_{s} * p T r a d e C a p 2 A c t_{t 1} * {v T r a d e C a p}_{t 1, y} \geq \sum_{s r c, d s t} ({v T r a d e I r}_{t 1, c, s r c, d s t, y, s})$

2.4.0.77 `eqTradeCap`: Trade capacity lower bound


${v T r a d e C a p}_{t 1, y} = p T r a d e S t o c k_{t 1, y} + \sum_{y p} (p P e r i o d L e n_{y p} * {v T r a d e N e w C a p}_{t 1, y p})$

2.4.0.78 `eqTradeCapLo`: Trade capacity upper bound


${v T r a d e C a p}_{t 1, y} \geq p T r a d e C a p L o_{t 1, y}$

2.4.0.79 `eqTradeCapUp`: Trade new capacity lower bound


${v T r a d e C a p}_{t 1, y} \leq p T r a d e C a p U p_{t 1, y}$

2.4.0.80 `eqTradeNewCapLo`: Trade new capacity upper bound


${v T r a d e N e w C a p}_{t 1, y} \geq p T r a d e N e w C a p L o_{t 1, y}$

2.4.0.81 `eqTradeNewCapUp`: Trade overnight investment costs


${v T r a d e N e w C a p}_{t 1, y} \leq p T r a d e N e w C a p U p_{t 1, y}$

2.4.0.82 `eqTradeInv`: Trade equivalent annual costs


${v T r a d e I n v}_{t 1, r, y} = p T r a d e I n v c o s t_{t 1, r, y} * {v T r a d e N e w C a p}_{t 1, y}$

2.4.0.83 `eqTradeEac`: Trade capacity to activity


${v T r a d e E a c}_{t 1, r, y} = \sum_{y p} (p T r a d e E a c_{t 1, r, y p} * p P e r i o d L e n_{y p} * {v T r a d e N e w C a p}_{t 1, y p})$

2.4.0.84 `eqTradeIrAInp`: Trade auxiliary commodity input


${v T r a d e I r A I n p}_{t 1, c, r, y, s} = \sum_{d s t} (p T r a d e I r C s r c 2 A i n p_{t 1, c, r, d s t, y, s} * \sum_{c p} ({v T r a d e I r}_{t 1, c p, r, d s t, y, s})) + \sum_{s r c} (p T r a d e I r C d s t 2 A i n p_{t 1, c, s r c, r, y, s} * \sum_{c p} ({v T r a d e I r}_{t 1, c p, s r c, r, y, s}))$

2.4.0.85 `eqTradeIrAOut`: Trade auxiliary commodity output


${v T r a d e I r A O u t}_{t 1, c, r, y, s} = \sum_{d s t} (p T r a d e I r C s r c 2 A o u t_{t 1, c, r, d s t, y, s} * \sum_{c p} ({v T r a d e I r}_{t 1, c p, r, d s t, y, s})) + \sum_{s r c} (p T r a d e I r C d s t 2 A o u t_{t 1, c, s r c, r, y, s} * \sum_{c p} ({v T r a d e I r}_{t 1, c p, s r c, r, y, s}))$

2.4.0.86 `eqTradeIrAInpTot`: Trade auxiliary commodity input


${v T r a d e I r A I n p T o t}_{c, r, y, s} = p S l i c e W e i g h t_{s} * \sum_{t 1, s p} ({v T r a d e I r A I n p}_{t 1, c, r, y, s p})$

2.4.0.87 `eqTradeIrAOutTot`: Trade auxiliary commodity output


${v T r a d e I r A O u t T o t}_{c, r, y, s} = p S l i c e W e i g h t_{s} * \sum_{t 1, s p} ({v T r a d e I r A O u t}_{t 1, c, r, y, s p})$

2.4.0.88 `eqBalLo`: commodity balance <= 0 (e.g. upper limit - deficit is allowed)


${v B a l a n c e}_{c, r, y, s} \geq 0$

2.4.0.89 `eqBalUp`: commodity balance >= 0 (e.g. lower limit - excess is allower)


${v B a l a n c e}_{c, r, y, s} \leq 0$

2.4.0.90 `eqBalFx`: commodity balance >= 0 (no excess nor deficit is allowed)


${v B a l a n c e}_{c, r, y, s} = 0$

2.4.0.91 `eqBal`: Commodity balance definition


${v B a l a n c e}_{c, r, y, s} = {v O u t T o t}_{c, r, y, s} - {v I n p T o t}_{c, r, y, s}$

2.4.0.92 `eqOutTot`: Total commodity output

{v O u t T o t}_{c, r, y, s} = p S l i c e W e i g h t_{s} * {v D u m m y I m p o r t}_{c, r, y, s} + {v S u p O u t T o t}_{c, r, y, s} + {v E m s F u e l T o t}_{c, r, y, s} + {v A g g O u t T o t}_{c, r, y, s} + {v T e c h O u t T o t}_{c, r, y, s} + {v S t o r a g e O u t T o t}_{c, r, y, s} + {v I m p o r t T o t}_{c, r, y, s} + {v T r a d e I r A O u t T o t}_{c, r, y, s} + p S l i c e W e i g h t_{s} * \sum_{s p} ({v O u t 2 L o}_{c, r, y, s p, s})

2.4.0.93 `eqOut2Lo`: Total commodity input


$\sum_{s p} ({v O u t 2 L o}_{c, r, y, s, s p}) = {v S u p O u t T o t}_{c, r, y, s} + {v E m s F u e l T o t}_{c, r, y, s} + {v A g g O u t T o t}_{c, r, y, s} + {v T e c h O u t T o t}_{c, r, y, s} + {v S t o r a g e O u t T o t}_{c, r, y, s} + {v I m p o r t T o t}_{c, r, y, s} + {v T r a d e I r A O u t T o t}_{c, r, y, s}$

2.4.0.94 `eqInpTot`: From commodity slice to lo level

{v I n p T o t}_{c, r, y, s} = p S l i c e W e i g h t_{s} * {v D e m I n p}_{c, r, y, s} + p S l i c e W e i g h t_{s} * {v D u m m y E x p o r t}_{c, r, y, s} + {v T e c h I n p T o t}_{c, r, y, s} + {v S t o r a g e I n p T o t}_{c, r, y, s} + {v E x p o r t T o t}_{c, r, y, s} + {v T r a d e I r A I n p T o t}_{c, r, y, s} + p S l i c e W e i g h t_{s} * \sum_{s p} ({v I n p 2 L o}_{c, r, y, s p, s})

2.4.0.95 `eqInp2Lo`: From commodity slice to lo level


$\sum_{s p} ({v I n p 2 L o}_{c, r, y, s, s p}) = {v T e c h I n p T o t}_{c, r, y, s} + {v S t o r a g e I n p T o t}_{c, r, y, s} + {v E x p o r t T o t}_{c, r, y, s} + {v T r a d e I r A I n p T o t}_{c, r, y, s}$

2.4.0.96 `eqSupOutTot`: Supply total output


${v S u p O u t T o t}_{c, r, y, s} = p S l i c e W e i g h t_{s} * \sum_{s 1} ({v S u p O u t}_{s 1, c, r, y, s})$

2.4.0.97 `eqTechInpTot`: Technology total input


${v T e c h I n p T o t}_{c, r, y, s} = p S l i c e W e i g h t_{s} * \sum_{t} ({v T e c h I n p}_{t, c, r, y, s}) + p S l i c e W e i g h t_{s} * \sum_{t} (\sum_{s p} ({v T e c h I n p}_{t, c, r, y, s p})) + p S l i c e W e i g h t_{s} * \sum_{t} ({v T e c h A I n p}_{t, c, r, y, s}) + p S l i c e W e i g h t_{s} * \sum_{t} (\sum_{s p} ({v T e c h A I n p}_{t, c, r, y, s p}))$

2.4.0.98 `eqTechOutTot`: Technology total output


${v T e c h O u t T o t}_{c, r, y, s} = p S l i c e W e i g h t_{s} * \sum_{t} ({v T e c h O u t}_{t, c, r, y, s}) + p S l i c e W e i g h t_{s} * \sum_{t} (\sum_{s p} ({v T e c h O u t}_{t, c, r, y, s p})) + p S l i c e W e i g h t_{s} * \sum_{t} ({v T e c h A O u t}_{t, c, r, y, s}) + p S l i c e W e i g h t_{s} * \sum_{t} (\sum_{s p} ({v T e c h A O u t}_{t, c, r, y, s p}))$

2.4.0.99 `eqStorageInpTot`: Storage total input


${v S t o r a g e I n p T o t}_{c, r, y, s} = p S l i c e W e i g h t_{s} * \sum_{s t 1} ({v S t o r a g e I n p}_{s t 1, c, r, y, s}) + p S l i c e W e i g h t_{s} * \sum_{s t 1} ({v S t o r a g e A I n p}_{s t 1, c, r, y, s})$

2.4.0.100 `eqStorageOutTot`: Storage total output


${v S t o r a g e O u t T o t}_{c, r, y, s} = p S l i c e W e i g h t_{s} * \sum_{s t 1} ({v S t o r a g e O u t}_{s t 1, c, r, y, s}) + p S l i c e W e i g h t_{s} * \sum_{s t 1} ({v S t o r a g e A O u t}_{s t 1, c, r, y, s})$

2.4.0.101 `eqCost`: Total costs (weighted)

{v T o t a l C o s t}_{r, y} = \sum_{t} ({v T e c h E a c}_{t, r, y}) + \sum_{t} (p T e c h R e t C o s t_{t, r, y} * ({v T e c h R e t i r e d S t o c k}_{t, r, y} + \sum_{y p} ({v T e c h R e t i r e d N e w C a p}_{t, r, y p, y}))) + \sum_{t, y p} (p T e c h R e t C o s t_{t, r, y} * {v T e c h R e t i r e d N e w C a p}_{t, r, y p, y}) + \sum_{t} ({v T e c h O M C o s t}_{t, r, y}) + \sum_{s 1} ({v S u p C o s t}_{s 1, r, y}) + \sum_{c, s} (p D u m m y I m p o r t C o s t_{c, r, y, s} * p S l i c e W e i g h t_{s} * {v D u m m y I m p o r t}_{c, r, y, s}) + \sum_{c, s} (p D u m m y E x p o r t C o s t_{c, r, y, s} * p S l i c e W e i g h t_{s} * {v D u m m y E x p o r t}_{c, r, y, s}) + \sum_{c} ({v T a x C o s t}_{c, r, y}) - \sum_{c} ({v S u b s C o s t}_{c, r, y}) + \sum_{s t 1} ({v S t o r a g e O M C o s t}_{s t 1, r, y}) + \sum_{s t 1} ({v S t o r a g e E a c}_{s t 1, r, y}) + {v T r a d e C o s t}_{r, y} + {v T o t a l U s e r C o s t s}_{r, y}

2.4.0.102 `eqTaxCost`: Commodity taxes (weighted)


${v T a x C o s t}_{c, r, y} = \sum_{s} (p T a x C o s t O u t_{c, r, y, s} * {v O u t T o t}_{c, r, y, s}) + \sum_{s} (p T a x C o s t I n p_{c, r, y, s} * {v I n p T o t}_{c, r, y, s}) + \sum_{s} (p T a x C o s t B a l_{c, r, y, s} * {v B a l a n c e}_{c, r, y, s})$

2.4.0.103 `eqSubsCost`: Commodity subsidy (weighted)


${v S u b s C o s t}_{c, r, y} = \sum_{s} (p S u b C o s t O u t_{c, r, y, s} * {v O u t T o t}_{c, r, y, s}) + \sum_{s} (p S u b C o s t I n p_{c, r, y, s} * {v I n p T o t}_{c, r, y, s}) + \sum_{s} (p S u b C o s t B a l_{c, r, y, s} * {v B a l a n c e}_{c, r, y, s})$

2.4.0.104 `eqObjective`: Objective equation NPV of total costs


$v O b j e c t i v e = \sum_{r, y} (p D i s c o u n t F a c t o r M i l e S t o n e_{r, y} * {v T o t a l C o s t}_{r, y})$

2.4.0.105 `eqLECActivity`: levelized costs (auxiliary equation)


$\sum_{s} ({v T e c h A c t}_{t, r, y, s}) \geq p L E C L o A C T_{r}$

2.1 Sets

2.2 Parameters

2.3 Variables

2.4 Equations

2.4.0.1 eqTechSng2Sng: Technology input to output

2.4.0.2 eqTechGrp2Sng: Technology group input to output

2.4.0.3 eqTechSng2Grp: Technology input to group output

2.4.0.4 eqTechGrp2Grp: Technology group input to group output

2.4.0.5 eqTechShareInpLo: Technology lower bound on input share

2.4.0.6 eqTechShareInpUp: Technology upper bound on input share

2.4.0.7 eqTechShareOutLo: Technology lower bound on output share

2.4.0.8 eqTechShareOutUp: Technology upper bound on output share

2.4.0.9 eqTechAInp: Technology auxiliary commodity input

2.4.0.10 eqTechAOut: Technology auxiliary commodity output

2.4.0.11 eqTechAfLo: Technology availability factor lower bound

2.4.0.12 eqTechAfUp: Technology availability factor upper bound

2.4.0.13 eqTechAfsLo: Technology availability factor for sum of slices lower bound

2.4.0.14 eqTechAfsUp: Technology availability factor for sum of slices upper bound

2.4.0.15 eqTechRampUp: Technology ramp up

2.4.0.16 eqTechRampDown: Technology ramp down

2.4.0.17 eqTechActSng: Technology activity to commodity output

2.4.0.18 eqTechActGrp: Technology activity to group output

2.4.0.19 eqTechAfcOutLo: Technology commodity availability factor lower bound

2.4.0.20 eqTechAfcOutUp: Technology commodity availability factor upper bound

2.4.0.21 eqTechAfcInpLo: Technology commodity availability factor lower bound

2.4.0.22 eqTechAfcInpUp: Technology commodity availability factor upper bound

2.4.0.23 eqTechCap: Technology capacity

2.4.0.24 eqTechCapLo: Technology capacity lower bound

2.4.0.25 eqTechCapUp: Technology capacity upper bound

2.4.0.26 eqTechNewCapLo: __

2.4.0.27 eqTechNewCapUp: __

2.4.0.28 eqTechRetiredNewCap: Retirement of new capacity

2.4.0.29 eqTechRetiredStockCum: Retirement of stock cumulative

2.4.0.30 eqTechRetiredStock: Retirement of stock

2.4.0.31 eqTechEac: Technology Equivalent Annual Cost (EAC)

2.4.0.32 eqTechInv: Technology overnight investment costs

2.4.0.33 eqTechOMCost: Technology O&M costs (weighted)

2.4.0.34 eqSupAvaUp: Supply availability upper bound

2.4.0.35 eqSupAvaLo: Supply availability lower bound

2.4.0.36 eqSupReserve: Cumulative supply (use of reserve)

2.4.0.37 eqSupReserveUp: Cumulative supply upper constraint

2.4.0.38 eqSupReserveLo: Cumulative supply lower constraint

2.4.0.39 eqSupCost: Supply costs

2.4.0.40 eqDemInp: Demand equation

2.4.0.41 eqAggOutTot: Aggregating-commodity output (weighted)

2.4.0.42 eqEmsFuelTot: Total emissions from commodity consumption (weighted)

2.4.0.43 eqStorageAInp: Storage level

2.4.0.44 eqStorageAOut: Storage availability factor lower

2.4.0.45 eqStorageStore: Storage availability factor upper

2.4.0.46 eqStorageAfLo: Storage output vs level

2.4.0.47 eqStorageAfUp: Storage aux-commodity input

2.4.0.48 eqStorageClear: Storage aux-commodity output

2.4.0.49 eqStorageInpUp: Storage input upper constraint

2.4.0.50 eqStorageInpLo: Storage input lower constraint

2.4.0.51 eqStorageOutUp: Storage output upper constraint

2.4.0.52 eqStorageOutLo: Storage output lower constraint

2.4.0.53 eqStorageCap: Storage capacity

2.4.0.54 eqStorageCapLo: Storage capacity lower bound

2.4.0.55 eqStorageCapUp: Storage capacity upper bound

2.4.0.56 eqStorageNewCapLo: Storage new capacity lower bound

2.4.0.57 eqStorageNewCapUp: Storage new capacity upper bound

2.4.0.58 eqStorageInv: Storage overnight investment costs

2.4.0.59 eqStorageEac: Storage equivalent annual cost

2.4.0.60 eqStorageCost: Storage total costs

2.4.0.61 eqImportTot: Import equation (Ir & ROW)

2.4.0.62 eqExportTot: Export equation (Ir & ROW)

2.4.0.63 eqTradeFlowUp: Trade upper bound

2.4.0.64 eqTradeFlowLo: Trade lower bound

2.4.0.65 eqCostTrade: Total trade costs

2.4.0.66 eqCostRowTrade: Costs of trade with the Rest of the World (ROW)

2.4.0.67 eqCostIrTrade: Costs of import

2.4.0.68 eqExportRowUp: Export to ROW upper constraint

2.4.0.69 eqExportRowLo: Export to ROW lower constraint

2.4.0.70 eqExportRowCum: Cumulative export to ROW

2.4.0.71 eqExportRowResUp: Cumulative export to ROW upper constraint

2.4.0.72 eqImportRowUp: Import from ROW upper constraint

2.4.0.73 eqImportRowLo: Import of ROW lower constraint

2.4.0.74 eqImportRowCum: Cumulative import from ROW

2.4.0.75 eqImportRowResUp: Cumulative import from ROW upper constraint

2.4.0.76 eqTradeCapFlow: Trade capacity

2.4.0.1 `eqTechSng2Sng`: Technology input to output

2.4.0.2 `eqTechGrp2Sng`: Technology group input to output

2.4.0.3 `eqTechSng2Grp`: Technology input to group output

2.4.0.4 `eqTechGrp2Grp`: Technology group input to group output

2.4.0.5 `eqTechShareInpLo`: Technology lower bound on input share

2.4.0.6 `eqTechShareInpUp`: Technology upper bound on input share

2.4.0.7 `eqTechShareOutLo`: Technology lower bound on output share

2.4.0.8 `eqTechShareOutUp`: Technology upper bound on output share

2.4.0.9 `eqTechAInp`: Technology auxiliary commodity input

2.4.0.10 `eqTechAOut`: Technology auxiliary commodity output

2.4.0.11 `eqTechAfLo`: Technology availability factor lower bound

2.4.0.12 `eqTechAfUp`: Technology availability factor upper bound

2.4.0.13 `eqTechAfsLo`: Technology availability factor for sum of slices lower bound

2.4.0.14 `eqTechAfsUp`: Technology availability factor for sum of slices upper bound

2.4.0.15 `eqTechRampUp`: Technology ramp up

2.4.0.16 `eqTechRampDown`: Technology ramp down

2.4.0.17 `eqTechActSng`: Technology activity to commodity output

2.4.0.18 `eqTechActGrp`: Technology activity to group output

2.4.0.19 `eqTechAfcOutLo`: Technology commodity availability factor lower bound

2.4.0.20 `eqTechAfcOutUp`: Technology commodity availability factor upper bound

2.4.0.21 `eqTechAfcInpLo`: Technology commodity availability factor lower bound

2.4.0.22 `eqTechAfcInpUp`: Technology commodity availability factor upper bound

2.4.0.23 `eqTechCap`: Technology capacity

2.4.0.24 `eqTechCapLo`: Technology capacity lower bound

2.4.0.25 `eqTechCapUp`: Technology capacity upper bound

2.4.0.26 `eqTechNewCapLo`: __

2.4.0.27 `eqTechNewCapUp`: __

2.4.0.28 `eqTechRetiredNewCap`: Retirement of new capacity

2.4.0.29 `eqTechRetiredStockCum`: Retirement of stock cumulative

2.4.0.30 `eqTechRetiredStock`: Retirement of stock

2.4.0.31 `eqTechEac`: Technology Equivalent Annual Cost (EAC)

2.4.0.32 `eqTechInv`: Technology overnight investment costs

2.4.0.33 `eqTechOMCost`: Technology O&M costs (weighted)

2.4.0.34 `eqSupAvaUp`: Supply availability upper bound

2.4.0.35 `eqSupAvaLo`: Supply availability lower bound

2.4.0.36 `eqSupReserve`: Cumulative supply (use of reserve)

2.4.0.37 `eqSupReserveUp`: Cumulative supply upper constraint

2.4.0.38 `eqSupReserveLo`: Cumulative supply lower constraint

2.4.0.39 `eqSupCost`: Supply costs

2.4.0.40 `eqDemInp`: Demand equation

2.4.0.41 `eqAggOutTot`: Aggregating-commodity output (weighted)

2.4.0.42 `eqEmsFuelTot`: Total emissions from commodity consumption (weighted)

2.4.0.43 `eqStorageAInp`: Storage level

2.4.0.44 `eqStorageAOut`: Storage availability factor lower

2.4.0.45 `eqStorageStore`: Storage availability factor upper

2.4.0.46 `eqStorageAfLo`: Storage output vs level

2.4.0.47 `eqStorageAfUp`: Storage aux-commodity input

2.4.0.48 `eqStorageClear`: Storage aux-commodity output

2.4.0.49 `eqStorageInpUp`: Storage input upper constraint

2.4.0.50 `eqStorageInpLo`: Storage input lower constraint

2.4.0.51 `eqStorageOutUp`: Storage output upper constraint

2.4.0.52 `eqStorageOutLo`: Storage output lower constraint

2.4.0.53 `eqStorageCap`: Storage capacity

2.4.0.54 `eqStorageCapLo`: Storage capacity lower bound

2.4.0.55 `eqStorageCapUp`: Storage capacity upper bound

2.4.0.56 `eqStorageNewCapLo`: Storage new capacity lower bound

2.4.0.57 `eqStorageNewCapUp`: Storage new capacity upper bound

2.4.0.58 `eqStorageInv`: Storage overnight investment costs

2.4.0.59 `eqStorageEac`: Storage equivalent annual cost

2.4.0.60 `eqStorageCost`: Storage total costs

2.4.0.61 `eqImportTot`: Import equation (Ir & ROW)

2.4.0.62 `eqExportTot`: Export equation (Ir & ROW)

2.4.0.63 `eqTradeFlowUp`: Trade upper bound

2.4.0.64 `eqTradeFlowLo`: Trade lower bound

2.4.0.65 `eqCostTrade`: Total trade costs

2.4.0.66 `eqCostRowTrade`: Costs of trade with the Rest of the World (ROW)

2.4.0.67 `eqCostIrTrade`: Costs of import

2.4.0.68 `eqExportRowUp`: Export to ROW upper constraint

2.4.0.69 `eqExportRowLo`: Export to ROW lower constraint

2.4.0.70 `eqExportRowCum`: Cumulative export to ROW

2.4.0.71 `eqExportRowResUp`: Cumulative export to ROW upper constraint

2.4.0.72 `eqImportRowUp`: Import from ROW upper constraint

2.4.0.73 `eqImportRowLo`: Import of ROW lower constraint

2.4.0.74 `eqImportRowCum`: Cumulative import from ROW

2.4.0.75 `eqImportRowResUp`: Cumulative import from ROW upper constraint

2.4.0.76 `eqTradeCapFlow`: Trade capacity

2.4.0.77 `eqTradeCap`: Trade capacity lower bound

2.4.0.78 `eqTradeCapLo`: Trade capacity upper bound

2.4.0.79 `eqTradeCapUp`: Trade new capacity lower bound

2.4.0.80 `eqTradeNewCapLo`: Trade new capacity upper bound