OSeMOSYS v0.8.1

Added authors for Zenodo publication

v0.8

OSeMOSYS GNU MathProg v0.8

OSeMOSYS v1.0.1

OSeMOSYS Change Log

Version 1.0.1

Fixed bug in technology specific discount rate.

Version 1.0.0

This is the first stable version of OSeMOSYS to be reduced using the Semantic Versioning pattern
of numbering. You can read more about semver here.

Multiple alternative versions of OSeMOSYS

Three implementations of OSeMOSYS nicknamed the long, the short and fast versions
of the code are included. All three take the same input parameters, and produce the same
set of results.

The long version is best for teaching, learning and developing extensions to the code.
The formulation almost exactly matches the original description of the mathematical formulation
in the 2011 paper.

The short version is best for stable and accelerated performance. It reduces the size of the
matrix produced through removing intermediate decision variables and combining equations.
The resultant increase in performance comes at the cost of reduced ease of debugging.
However, this allows larger models to be solved, and reduces solution time.

The fast is highest performance, but very terse and uses a number of more complicated tricks to
reduce the size of the matrix and thus increase performance. The fast version is not yet fully
tested and should be considered experimental.

Numerous smaller performance improvements

A number of small performance improvements have been included, reducing the problem size by
implementing conditional operators.

Reintroduced technology specific discount rate

The DiscountRate parameter has been replaced with one containing a technology index
DiscountRate[r,t] and a new parameter for storage has been added DiscountRateStorage[r,s].

OSeMOSYS checks for basic errors in input data

• Thanks to @vignesh1987 for providing check statements for
  • Capacity investment
  • Annual Activity
  • Total capacity
  • Minimum Annual activity
  • Time Slice
  • Model period activity limit

These raise an error if incompatible or incorrect data is presented to the
model prior to attempting a solve step. This saves time, and avoids many
infeasible solutions due to data errors.

Folder of CSV result parameters added

• Results parameters are written out into individual CSV files in long format.
• Headers correspond to the index of the variable, e.g. REGION,FUEL,VALUE

Adds ResultPath parameter to choose location of results

Data files should now include a ResultPath parameter to choose the location of the results

Conditional operators added to 6 parameters

Pull request #30 @tniet, @willu47

Conditional operators were added to five parameters in both short and long versions of the code:

• TotalAnnualMaxCapacity
• TotalAnnualMaxCapacityInvestment
• TotalTechnologyAnnualActivityUpperLimit
• AnnualEmissionLimit
• ModelPeriodEmissionLimit
• TotalTechnologyModelPeriodActivityUpperLimit

If the default value in the corresponding data file is set of -1, then the constraints will no longer be generated,
resulting in a significant improvement in the size of the problem created, and avoiding issues where some constraints
were ignored.

Model osemosys_short.txt with commit hash 7548c08

Modified by Kevin Palmer-Wilson

Changes with respect to previous version commit hash 14cd8cc:

Changes in model file

• Modified objective function to avoid double counting of CapitalCostStorage: The sum{s in STORAGE} was inside the sum{r in REGION, t in TECHNOLOGY, y in YEAR}. Therefore, the storage costs were multiplied by the number of regions times the number of technologies times the number of years. In the corrected version the accounting for storage costs has been moved outside of the sum{r in REGION, t in TECHNOLOGY, y in YEAR} such that sum{r in REGION, s in STORAGE, y in YEAR} are added separately only once.

Previous equation

minimize cost: sum{r in REGION, t in TECHNOLOGY, y in YEAR} (((((sum{yy in YEAR: y-yy < OperationalLife[r,t] && y-yy>=0} NewCapacity[r,t,yy])+ ResidualCapacity[r,t,y])*FixedCost[r,t,y] + sum{m in MODE_OF_OPERATION, l in TIMESLICE} RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*VariableCost[r,t,m,y])/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5))+CapitalCost[r,t,y] * NewCapacity[r,t,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))+DiscountedTechnologyEmissionsPenalty[r,t,y]-DiscountedSalvageValue[r,t,y]) + sum{s in STORAGE} (CapitalCostStorage[r,s,y] * NewStorageCapacity[r,s,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))-SalvageValueStorage[r,s,y]/((1+DiscountRate[r])^(max{yy in YEAR} max(yy)-min{yy in YEAR} min(yy)+1))));

New equation

minimize cost: sum{r in REGION, t in TECHNOLOGY, y in YEAR}(((((sum{yy in YEAR: y-yy < OperationalLife[r,t] && y-yy>=0}NewCapacity[r,t,yy])+ResidualCapacity[r,t,y])*FixedCost[r,t,y]+sum{m in MODE_OF_OPERATION, l in TIMESLICE}RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*VariableCost[r,t,m,y])/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5))+CapitalCost[r,t,y] * NewCapacity[r,t,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))+DiscountedTechnologyEmissionsPenalty[r,t,y]-DiscountedSalvageValue[r,t,y]))+sum{r in REGION, s in STORAGE, y in YEAR}(CapitalCostStorage[r,s,y] * NewStorageCapacity[r,s,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))-SalvageValueStorage[r,s,y]/((1+DiscountRate[r])^(max{yy in YEAR} max(yy)-min{yy in YEAR} min(yy)+1)));

1. Model 2017_11_08 and Model 2017_11_08_short

Modified by Francesco Gardumi

Changes with respect to previous version OSeMOSYS_2016_08_01:

• Modified equation E1_AnnualEmissionProductionByMode: technologies with EmissionActivityRatio = 0 would ignore the equation, due to the statement EmissionActivityRatio <>0, giving rise to unsound results in cases where negative emissions are allowed. The statement was therefore removed.

Changes in model file

Previous equation

s.t. E1_AnnualEmissionProductionByMode{r in REGION, t in TECHNOLOGY, e in EMISSION, m in MODE_OF_OPERATION, y in YEAR: EmissionActivityRatio[r,t,e,m,y]<>0}: EmissionActivityRatio[r,t,e,m,y]*TotalAnnualTechnologyActivityByMode[r,t,m,y]=AnnualTechnologyEmissionByMode[r,t,e,m,y];

New equation

s.t. E1_AnnualEmissionProductionByMode{r in REGION, t in TECHNOLOGY, e in EMISSION, m in MODE_OF_OPERATION, y in YEAR}: EmissionActivityRatio[r,t,e,m,y]*TotalAnnualTechnologyActivityByMode[r,t,m,y]=AnnualTechnologyEmissionByMode[r,t,e,m,y];

Changes with respect to previous version OSeMOSYS_2016_08_01_short:

• Modified equations E5_DiscountedEmissionsPenaltyByTechnology, E8_AnnualEmissionsLimit and E9_ModelPeriodEmissionsLimit: the statement EmissionActivityRatio <>0 was removed, in line with the corresponding modification to OSeMOSYS_2016_08_01 (see above).
• Fixed bug in the objective function.
• Fixed bug in the storage constraints SC2_LowerLimit_EndOfDailyTimeBracketOfLastInstanceOfDayTypeInFirstWeekConstraint and SC2_UpperLimit_EndOfDailyTimeBracketOfLastInstanceOfDayTypeInFirstWeekConstraint.
• Fixed bug in the minimum renewable target constraint RE4_EnergyConstraint.

Emissions accounting equations

Previous equations

s.t. E5_DiscountedEmissionsPenaltyByTechnology{r in REGION, t in TECHNOLOGY, y in YEAR}: sum{e in EMISSION, l in TIMESLICE, m in MODE_OF_OPERATION: EmissionActivityRatio[r,t,e,m,y]<>0} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*EmissionsPenalty[r,e,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5)) = DiscountedTechnologyEmissionsPenalty[r,t,y];

s.t. E8_AnnualEmissionsLimit{r in REGION, e in EMISSION, y in YEAR}: sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION: EmissionActivityRatio[r,t,e,m,y]<>0} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]+AnnualExogenousEmission[r,e,y] <= AnnualEmissionLimit[r,e,y];

s.t. E9_ModelPeriodEmissionsLimit{r in REGION, e in EMISSION}:  sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION, y in YEAR: EmissionActivityRatio[r,t,e,m,y]<>0} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y] + ModelPeriodExogenousEmission[r,e] <= ModelPeriodEmissionLimit[r,e] ;

New equations

s.t. E5_DiscountedEmissionsPenaltyByTechnology{r in REGION, t in TECHNOLOGY, y in YEAR}: sum{e in EMISSION, l in TIMESLICE, m in MODE_OF_OPERATION} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*EmissionsPenalty[r,e,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5)) = DiscountedTechnologyEmissionsPenalty[r,t,y];

s.t. E8_AnnualEmissionsLimit{r in REGION, e in EMISSION, y in YEAR}: sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]+AnnualExogenousEmission[r,e,y] <= AnnualEmissionLimit[r,e,y];

s.t. E9_ModelPeriodEmissionsLimit{r in REGION, e in EMISSION}:  sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION, y in YEAR} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y] + ModelPeriodExogenousEmission[r,e] <= ModelPeriodEmissionLimit[r,e] ;

Objective function

Previous equation

minimize cost: sum{r in REGION, t in TECHNOLOGY, y in YEAR} (((((sum{yy in YEAR: y-yy < OperationalLife[r,t] && y-yy>=0} NewCapacity[r,t,yy])+ ResidualCapacity[r,t,y])*FixedCost[r,t,y] + sum{m in MODE_OF_OPERATION, l in TIMESLICE} RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*VariableCost[r,t,m,y])/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5))+CapitalCost[r,t,y] * NewCapacity[r,t,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))+DiscountedTechnologyEmissionsPenalty[r,t,y]-DiscountedSalvageValue[r,t,y]) + sum{s in STORAGE} (CapitalCostStorage[r,s,y] * NewStorageCapacity[r,s,y]/((1+...

v1.0

OSeMOSYS Change Log

Version 1.0.0

This is the first stable version of OSeMOSYS to be released using Semantic Versioning. You can read more about semver here. A number of new features and additions have been made to the formulation since the last release of OSeMOSYS. These should be considered breaking changes, and you will likely need to modify some aspect of your datafiles to make use of this release. Please make note of the key changes below.

Multiple alternative versions of OSeMOSYS

Three implementations of OSeMOSYS nicknamed the long, the short and fast versions
of the code are included. All three take the same input parameters, and produce the same
set of results.

The long version is best for teaching, learning and developing extensions to the code.
The formulation almost exactly matches the original description of the mathematical formulation
in the 2011 paper.

The short version is best for stable and accelerated performance. It reduces the size of the
matrix produced through removing intermediate decision variables and combining equations.
The resultant increase in performance comes at the cost of reduced ease of debugging.
However, this allows larger models to be solved, and reduces solution time.

The fast is highest performance, but very terse and uses a number of more complicated tricks to
reduce the size of the matrix and thus increase performance. The fast version is not yet fully
tested and should be considered experimental.

Numerous smaller performance improvements

A number of small performance improvements have been included, reducing the problem size by
implementing conditional operators.

Reintroduced technology specific discount rate

The DiscountRate parameter has been replaced with one containing a technology index
DiscountRate[r,t] and a new parameter for storage has been added DiscountRateStorage[r,s].

OSeMOSYS checks for basic errors in input data

• Thanks to @vignesh1987 for providing check statements for
  • Capacity investment
  • Annual Activity
  • Total capacity
  • Minimum Annual activity
  • Time Slice
  • Model period activity limit

These raise an error if incompatible or incorrect data is presented to the
model prior to attempting a solve step. This saves time, and avoids many
infeasible solutions due to data errors.

Folder of CSV result parameters added

• Results parameters are written out into individual CSV files in long format.
• Headers correspond to the index of the variable, e.g. REGION,FUEL,VALUE

Adds ResultPath parameter to choose location of results

Data files should now include a ResultPath parameter to choose the location of the results

Conditional operators added to 6 parameters

Pull request #30 @tniet, @willu47

Conditional operators were added to five parameters in both short and long versions of the code:

• TotalAnnualMaxCapacity
• TotalAnnualMaxCapacityInvestment
• TotalTechnologyAnnualActivityUpperLimit
• AnnualEmissionLimit
• ModelPeriodEmissionLimit
• TotalTechnologyModelPeriodActivityUpperLimit

If the default value in the corresponding data file is set of -1, then the constraints will no longer be generated,
resulting in a significant improvement in the size of the problem created, and avoiding issues where some constraints
were ignored.

Model osemosys_short.txt with commit hash 7548c08

Modified by Kevin Palmer-Wilson

Changes with respect to previous version commit hash 14cd8cc:

Changes in model file

• Modified objective function to avoid double counting of CapitalCostStorage: The sum{s in STORAGE} was inside the sum{r in REGION, t in TECHNOLOGY, y in YEAR}. Therefore, the storage costs were multiplied by the number of regions times the number of technologies times the number of years. In the corrected version the accounting for storage costs has been moved outside of the sum{r in REGION, t in TECHNOLOGY, y in YEAR} such that sum{r in REGION, s in STORAGE, y in YEAR} are added separately only once.

Previous equation

minimize cost: sum{r in REGION, t in TECHNOLOGY, y in YEAR} (((((sum{yy in YEAR: y-yy < OperationalLife[r,t] && y-yy>=0} NewCapacity[r,t,yy])+ ResidualCapacity[r,t,y])*FixedCost[r,t,y] + sum{m in MODE_OF_OPERATION, l in TIMESLICE} RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*VariableCost[r,t,m,y])/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5))+CapitalCost[r,t,y] * NewCapacity[r,t,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))+DiscountedTechnologyEmissionsPenalty[r,t,y]-DiscountedSalvageValue[r,t,y]) + sum{s in STORAGE} (CapitalCostStorage[r,s,y] * NewStorageCapacity[r,s,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))-SalvageValueStorage[r,s,y]/((1+DiscountRate[r])^(max{yy in YEAR} max(yy)-min{yy in YEAR} min(yy)+1))));

New equation

minimize cost: sum{r in REGION, t in TECHNOLOGY, y in YEAR}(((((sum{yy in YEAR: y-yy < OperationalLife[r,t] && y-yy>=0}NewCapacity[r,t,yy])+ResidualCapacity[r,t,y])*FixedCost[r,t,y]+sum{m in MODE_OF_OPERATION, l in TIMESLICE}RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*VariableCost[r,t,m,y])/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5))+CapitalCost[r,t,y] * NewCapacity[r,t,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))+DiscountedTechnologyEmissionsPenalty[r,t,y]-DiscountedSalvageValue[r,t,y]))+sum{r in REGION, s in STORAGE, y in YEAR}(CapitalCostStorage[r,s,y] * NewStorageCapacity[r,s,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))-SalvageValueStorage[r,s,y]/((1+DiscountRate[r])^(max{yy in YEAR} max(yy)-min{yy in YEAR} min(yy)+1)));

1. Model 2017_11_08 and Model 2017_11_08_short

Modified by Francesco Gardumi

Changes with respect to previous version OSeMOSYS_2016_08_01:

• Modified equation E1_AnnualEmissionProductionByMode: technologies with EmissionActivityRatio = 0 would ignore the equation, due to the statement EmissionActivityRatio <>0, giving rise to unsound results in cases where negative emissions are allowed. The statement was therefore removed.

Changes in model file

Previous equation

s.t. E1_AnnualEmissionProductionByMode{r in REGION, t in TECHNOLOGY, e in EMISSION, m in MODE_OF_OPERATION, y in YEAR: EmissionActivityRatio[r,t,e,m,y]<>0}: EmissionActivityRatio[r,t,e,m,y]*TotalAnnualTechnologyActivityByMode[r,t,m,y]=AnnualTechnologyEmissionByMode[r,t,e,m,y];

New equation

s.t. E1_AnnualEmissionProductionByMode{r in REGION, t in TECHNOLOGY, e in EMISSION, m in MODE_OF_OPERATION, y in YEAR}: EmissionActivityRatio[r,t,e,m,y]*TotalAnnualTechnologyActivityByMode[r,t,m,y]=AnnualTechnologyEmissionByMode[r,t,e,m,y];

Changes with respect to previous version OSeMOSYS_2016_08_01_short:

• Modified equations E5_DiscountedEmissionsPenaltyByTechnology, E8_AnnualEmissionsLimit and E9_ModelPeriodEmissionsLimit: the statement EmissionActivityRatio <>0 was removed, in line with the corresponding modification to OSeMOSYS_2016_08_01 (see above).
• Fixed bug in the objective function.
• Fixed bug in the storage constraints SC2_LowerLimit_EndOfDailyTimeBracketOfLastInstanceOfDayTypeInFirstWeekConstraint and SC2_UpperLimit_EndOfDailyTimeBracketOfLastInstanceOfDayTypeInFirstWeekConstraint.
• Fixed bug in the minimum renewable target constraint RE4_EnergyConstraint.

Emissions accounting equations

Previous equations

s.t. E5_DiscountedEmissionsPenaltyByTechnology{r in REGION, t in TECHNOLOGY, y in YEAR}: sum{e in EMISSION, l in TIMESLICE, m in MODE_OF_OPERATION: EmissionActivityRatio[r,t,e,m,y]<>0} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*EmissionsPenalty[r,e,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5)) = DiscountedTechnologyEmissionsPenalty[r,t,y];

s.t. E8_AnnualEmissionsLimit{r in REGION, e in EMISSION, y in YEAR}: sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION: EmissionActivityRatio[r,t,e,m,y]<>0} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]+AnnualExogenousEmission[r,e,y] <= AnnualEmissionLimit[r,e,y];

s.t. E9_ModelPeriodEmissionsLimit{r in REGION, e in EMISSION}:  sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION, y in YEAR: EmissionActivityRatio[r,t,e,m,y]<>0} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y] + ModelPeriodExogenousEmission[r,e] <= ModelPeriodEmissionLimit[r,e] ;

New equations

s.t. E5_DiscountedEmissionsPenaltyByTechnology{r in REGION, t in TECHNOLOGY, y in YEAR}: sum{e in EMISSION, l in TIMESLICE, m in MODE_OF_OPERATION} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*EmissionsPenalty[r,e,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5)) = DiscountedTechnologyEmissionsPenalty[r,t,y];

s.t. E8_AnnualEmissionsLimit{r in REGION, e in EMISSION, y in YEAR}: sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]+AnnualExogenousEmission[r,e,y] <= AnnualEmissionLimit[r,e,y];

s.t. E9_ModelPeriodEmissionsLimit{r in REGION, e in EMISSION}:  sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION, y in YEAR} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y] + ModelPeriodExogenousEmission[r,e] <= ModelPeriodEmissionLimit[r,e] ;

Objective function

Previous equation

minimize cost: sum{r in REGION, t in TECHNOLOGY, y in YEAR} (((((sum{yy in YEAR: y-yy < OperationalLife[r,t] && y-yy>=0} NewCapacity[r,t,yy])+ ResidualCapacity[r,t,y])*FixedCost[r,t,y] + sum{m in MODE_OF_OPERATION, l in TIMESLICE} RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*VariableCost[r,t,m,y])/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5))+CapitalCost[r,t,y] * NewCapacity[r,t,y]/((1+Disco...

v1.0.0-alpha.12

OSeMOSYS Change Log

Version 1.0.0

Folder of CSV result parameters added

• Results parameters are written out into individual files in long format.
• Headers correspond to the index of the variable, e.g. REGION,FUEL,VALUE

Adds ResultPath parameter to choose location of results

Data files should now include a ResultPath parameter to choose the location of the results

Conditional operators added to 6 parameters

Pull request #30 @tniet, @willu47

Conditional operators were added to five parameters in both short and long versions of the code:

• TotalAnnualMaxCapacity
• TotalAnnualMaxCapacityInvestment
• TotalTechnologyAnnualActivityUpperLimit
• AnnualEmissionLimit
• ModelPeriodEmissionLimit
• TotalTechnologyModelPeriodActivityUpperLimit

If the default value in the corresponding data file is set of -1, then the constraints will no longer be generated,
resulting in a significant improvement in the size of the problem created, and avoiding issues where some constraints
were ignored.

Model osemosys_short.txt with commit hash 7548c08

Modified by Kevin Palmer-Wilson

Changes with respect to previous version commit hash 14cd8cc:

Changes in model file

• Modified objective function to avoid double counting of CapitalCostStorage: The sum{s in STORAGE} was inside the sum{r in REGION, t in TECHNOLOGY, y in YEAR}. Therefore, the storage costs were multiplied by the number of regions times the number of technologies times the number of years. In the corrected version the accounting for storage costs has been moved outside of the sum{r in REGION, t in TECHNOLOGY, y in YEAR} such that sum{r in REGION, s in STORAGE, y in YEAR} are added separately only once.

Previous equation

minimize cost: sum{r in REGION, t in TECHNOLOGY, y in YEAR} (((((sum{yy in YEAR: y-yy < OperationalLife[r,t] && y-yy>=0} NewCapacity[r,t,yy])+ ResidualCapacity[r,t,y])*FixedCost[r,t,y] + sum{m in MODE_OF_OPERATION, l in TIMESLICE} RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*VariableCost[r,t,m,y])/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5))+CapitalCost[r,t,y] * NewCapacity[r,t,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))+DiscountedTechnologyEmissionsPenalty[r,t,y]-DiscountedSalvageValue[r,t,y]) + sum{s in STORAGE} (CapitalCostStorage[r,s,y] * NewStorageCapacity[r,s,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))-SalvageValueStorage[r,s,y]/((1+DiscountRate[r])^(max{yy in YEAR} max(yy)-min{yy in YEAR} min(yy)+1))));

New equation

minimize cost: sum{r in REGION, t in TECHNOLOGY, y in YEAR}(((((sum{yy in YEAR: y-yy < OperationalLife[r,t] && y-yy>=0}NewCapacity[r,t,yy])+ResidualCapacity[r,t,y])*FixedCost[r,t,y]+sum{m in MODE_OF_OPERATION, l in TIMESLICE}RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*VariableCost[r,t,m,y])/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5))+CapitalCost[r,t,y] * NewCapacity[r,t,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))+DiscountedTechnologyEmissionsPenalty[r,t,y]-DiscountedSalvageValue[r,t,y]))+sum{r in REGION, s in STORAGE, y in YEAR}(CapitalCostStorage[r,s,y] * NewStorageCapacity[r,s,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))-SalvageValueStorage[r,s,y]/((1+DiscountRate[r])^(max{yy in YEAR} max(yy)-min{yy in YEAR} min(yy)+1)));

1. Model 2017_11_08 and Model 2017_11_08_short

Modified by Francesco Gardumi

Changes with respect to previous version OSeMOSYS_2016_08_01:

• Modified equation E1_AnnualEmissionProductionByMode: technologies with EmissionActivityRatio = 0 would ignore the equation, due to the statement EmissionActivityRatio <>0, giving rise to unsound results in cases where negative emissions are allowed. The statement was therefore removed.

Changes in model file

Previous equation

s.t. E1_AnnualEmissionProductionByMode{r in REGION, t in TECHNOLOGY, e in EMISSION, m in MODE_OF_OPERATION, y in YEAR: EmissionActivityRatio[r,t,e,m,y]<>0}: EmissionActivityRatio[r,t,e,m,y]*TotalAnnualTechnologyActivityByMode[r,t,m,y]=AnnualTechnologyEmissionByMode[r,t,e,m,y];

New equation

s.t. E1_AnnualEmissionProductionByMode{r in REGION, t in TECHNOLOGY, e in EMISSION, m in MODE_OF_OPERATION, y in YEAR}: EmissionActivityRatio[r,t,e,m,y]*TotalAnnualTechnologyActivityByMode[r,t,m,y]=AnnualTechnologyEmissionByMode[r,t,e,m,y];

Changes with respect to previous version OSeMOSYS_2016_08_01_short:

• Modified equations E5_DiscountedEmissionsPenaltyByTechnology, E8_AnnualEmissionsLimit and E9_ModelPeriodEmissionsLimit: the statement EmissionActivityRatio <>0 was removed, in line with the corresponding modification to OSeMOSYS_2016_08_01 (see above).
• Fixed bug in the objective function.
• Fixed bug in the storage constraints SC2_LowerLimit_EndOfDailyTimeBracketOfLastInstanceOfDayTypeInFirstWeekConstraint and SC2_UpperLimit_EndOfDailyTimeBracketOfLastInstanceOfDayTypeInFirstWeekConstraint.
• Fixed bug in the minimum renewable target constraint RE4_EnergyConstraint.

Emissions accounting equations

Previous equations

s.t. E5_DiscountedEmissionsPenaltyByTechnology{r in REGION, t in TECHNOLOGY, y in YEAR}: sum{e in EMISSION, l in TIMESLICE, m in MODE_OF_OPERATION: EmissionActivityRatio[r,t,e,m,y]<>0} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*EmissionsPenalty[r,e,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5)) = DiscountedTechnologyEmissionsPenalty[r,t,y];

s.t. E8_AnnualEmissionsLimit{r in REGION, e in EMISSION, y in YEAR}: sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION: EmissionActivityRatio[r,t,e,m,y]<>0} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]+AnnualExogenousEmission[r,e,y] <= AnnualEmissionLimit[r,e,y];

s.t. E9_ModelPeriodEmissionsLimit{r in REGION, e in EMISSION}:  sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION, y in YEAR: EmissionActivityRatio[r,t,e,m,y]<>0} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y] + ModelPeriodExogenousEmission[r,e] <= ModelPeriodEmissionLimit[r,e] ;

New equations

s.t. E5_DiscountedEmissionsPenaltyByTechnology{r in REGION, t in TECHNOLOGY, y in YEAR}: sum{e in EMISSION, l in TIMESLICE, m in MODE_OF_OPERATION} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*EmissionsPenalty[r,e,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5)) = DiscountedTechnologyEmissionsPenalty[r,t,y];

s.t. E8_AnnualEmissionsLimit{r in REGION, e in EMISSION, y in YEAR}: sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y]+AnnualExogenousEmission[r,e,y] <= AnnualEmissionLimit[r,e,y];

s.t. E9_ModelPeriodEmissionsLimit{r in REGION, e in EMISSION}:  sum{l in TIMESLICE, t in TECHNOLOGY, m in MODE_OF_OPERATION, y in YEAR} EmissionActivityRatio[r,t,e,m,y]*RateOfActivity[r,l,t,m,y]*YearSplit[l,y] + ModelPeriodExogenousEmission[r,e] <= ModelPeriodEmissionLimit[r,e] ;

Objective function

Previous equation

minimize cost: sum{r in REGION, t in TECHNOLOGY, y in YEAR} (((((sum{yy in YEAR: y-yy < OperationalLife[r,t] && y-yy>=0} NewCapacity[r,t,yy])+ ResidualCapacity[r,t,y])*FixedCost[r,t,y] + sum{m in MODE_OF_OPERATION, l in TIMESLICE} RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*VariableCost[r,t,m,y])/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5))+CapitalCost[r,t,y] * NewCapacity[r,t,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))+DiscountedTechnologyEmissionsPenalty[r,t,y]-DiscountedSalvageValue[r,t,y]) + sum{s in STORAGE} (CapitalCostStorage[r,s,y] * NewStorageCapacity[r,s,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))-CapitalCostStorage[r,s,y] * NewStorageCapacity[r,s,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))));

New equation

minimize cost: sum{r in REGION, t in TECHNOLOGY, y in YEAR} (((((sum{yy in YEAR: y-yy < OperationalLife[r,t] && y-yy>=0} NewCapacity[r,t,yy])+ ResidualCapacity[r,t,y])*FixedCost[r,t,y] + sum{m in MODE_OF_OPERATION, l in TIMESLICE} RateOfActivity[r,l,t,m,y]*YearSplit[l,y]*VariableCost[r,t,m,y])/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)+0.5))+CapitalCost[r,t,y] * NewCapacity[r,t,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))+DiscountedTechnologyEmissionsPenalty[r,t,y]-DiscountedSalvageValue[r,t,y]) + sum{s in STORAGE} (CapitalCostStorage[r,s,y] * NewStorageCapacity[r,s,y]/((1+DiscountRate[r])^(y-min{yy in YEAR} min(yy)))-SalvageValueStorage[r,s,y]/((1+DiscountRate[r])^(max{yy in YEAR} max(yy)-min{yy in YEAR} min(yy)+1))));

Storage constraints

Previous equations

s.t. SC2_LowerLimit_EndOfDailyTimeBracketOfLastInstanceOfDayTypeInFirstWeekConstraint{r in REGION, s in STORAGE, ls in SEASON, ld in DAYTYPE, lh in DAILYTIMEBRACKET, y in YEAR}: 0 <= if ld > min{ldld in DAYTYPE} min(ldld) then (StorageLevelDayTypeStart[r,s,ls,ld,y]-sum{lhlh in DAILYTIMEBRACKET:lh-lhlh<0} (((sum{t in TECHNOLOGY, m in MODE_OF_OPERATION, l in TIMESLICE:TechnologyToStorage[r,t,s,m]>0} RateOfActivity[r,l,t,m,y] * TechnologyToStorage[r,t,s,m] * Conversionls[l,ls] * Conversionld[l,ld] * Conversionlh[l,lhlh]) - (sum{t in TECHNOLOGY, m in MODE_OF_OPERATION, l in TIMESLICE:TechnologyFromStorage[r,t,s,m]>0} RateOfActivity[r,l,t,m,y] * TechnologyFromStorage[r,t,s,m] * Conversionls[l,ls] * Conversionld[l,ld] * Conversionlh[l,lhlh])) * DaySplit[lhlh,y]))-MinStorageCharge[r,s,y]*(sum{yy in YEAR: y-yy < OperationalLifeStorage[r,s] && y-yy>=0} NewStorageCapacity[r,s,yy]+ResidualStorageCapacity[r,s,y]);

s.t. SC2_UpperLimit_EndOfDailyTimeBracketOfLastInstanceOfDayTypeInFirstWeekConstraint{r in REGION, s in STORAGE, ls in SEASON, ld in DAYTYPE, lh in DAILYTIMEBRACKET, y in YEAR}: if ld > min{ldld in DAYTYPE} min(ldld) then (StorageLevelDayTypeStart[r,s,ls,ld,y]-sum{lhlh in DAILYTIMEBRACKET:lh-lhlh<0} (((...