18-05-2019, 09:35 PM

@Anjana: Please find below my explanations to the equation coefficients:

The input parameter involved in the equations are :

•ACT_EFF(r,y,p,cg,s) – activity efficiency of process p, group cg, timeslice s

•ACT_MINLD(r,y,p) – minimum operating load level

•ACT_LOSPL(r,y,p,cg,'FX') – proportional increase in specific consumption at minimum operating load level

•ACT_LOSPL(r,y,p,cg,'UP') – fraction of feasible load range above the minimum op. level, below which the efficiency losses occur.

•ACT_LOSPL(r,y,p,cg,'LO') – minimum operating level used for the partial load efficiency function, default = MAX(0.1,ACT_MINLD(r,y,p))

The variables involved in the equations are :

• VAR_CAP(r,t,p) – capacity of process p

• VAR_ACT(r,v,t,p,s) – activity of process p, timeslice s

• VAR_FLO(r,v,t,p,c,s) – flow of process p, commodity c, timeslice s

• VAR_UPS(r,v,t,p,s,'N') – off-line capacity of process p, timeslice s

• VAR_UPS(r,v,t,p,s,'FX') – efficiency loss of process p, timeslice s, divided by ACT_LOSPL(r,y,p,cg,'FX')

Note that as you have not defined ACT_LOSPL(LO), the default is MAX(0.1,ACT_MINLD(r,y,p)) = 0.1;

First, your EQE_ACTEFF:

The equation defines the process activity efficiency in 2018, for timeslice SD. You efficiency for TESTELSR is ACT_EFF(ACT)= 0.017288462. The coefficient 57.8420451744059 for VAR_ACT is obtained as the inverse of that, i.e. 57.8420451744059 = 1/0.017288462. The coefficient 1 for VAR_FLO is obtained from the fact that you have not defined any commodity-specific efficiency, and so 1 is assumed. The coefficient 56.8420140553856 for VAR_UPS is obtained as ACT_LOSPL(FX)/ACT_EFF(ACT) = 0.982711 / 0.017288462 = 56.8420140553856. The interpretation is straightforward: The activity is equal to the ELC input flow multiplied by the efficiency and subtracted by the activity loss due to partial load.

Second, your EQ_CAPLOAD(LO):

The equation defines the minimum load in 2018, for timeslice SD. The coefficient is always 1 for VAR_ACT. The coefficient for the online capacity (VAR_CAP−VAR_UPS(S)) is PRC_CAPACT×YRFR×ACT_MINLD = 151.446914485223 × 0.25 × 0.01= 0.378617286213058. The interpretation is straightforward: The load cannot go below the online capacity multiplied by the minimum load level.

Third, your EQ_CAPLOAD(UP):

The equation defines the maximum load in 2018, for timeslice SD. The coefficient is always 1 for VAR_ACT. The coefficient for the online capacity (VAR_CAP−VAR_UPS(S)) is PRC_CAPACT×YRFR×COEF_AF(UP) = 151.446914485223 × 0.25 × 1 = 37.8617286213058. The interpretation is straightforward: The load cannot exceed the online capacity multiplied by the maximum availability.

Fourth , your EQ_ACTPL :

The equation defines the efficiency loss in 2018, for timeslice SD. The loss variable VAR_UPS(FX) always has the coefficient 1. The coefficient for the online capacity (VAR_CAP−VAR_UPS(S)) is defined by ACT_LOSPL(UP), and is obtained as PRC_CAPACT×YRFR × (ACT_LOSPL(UP)+ACT_LOSPL(LO) × (1-ACT_LOSPL(UP))) / (ACT_LOSPL(UP) × (1/ACT_LOSPL(LO)−1)) = 151.446914485223 × 0.25 × (0.2828 + 0.1 × (1−0.2828)) / (0.2828 × (1/0.1−1)) = 5.27374667249148.

The coefficient for the activity VAR_ACT is obtained as 1 / (ACT_LOSPL(UP) × (1/ACT_LOSPL(LO)−1)) = 1 / (0.2828 × (1/0.1−1)) = 0.3928964325.

It is easy to see, by simple calculus, that when the activity is equal to the upper point (ACT_LOSPL(UP)+ACT_LOSPL(LO) × (1-ACT_LOSPL(UP))) = 0.2828+0.1×(1−0.2828))= 0.35452, the loss variable is zero, and when the activity is equal to the lower point ACT_LOSPL(LO), the loss variable is equal (or ≥) to the activity, as designed.

The input parameter involved in the equations are :

•ACT_EFF(r,y,p,cg,s) – activity efficiency of process p, group cg, timeslice s

•ACT_MINLD(r,y,p) – minimum operating load level

•ACT_LOSPL(r,y,p,cg,'FX') – proportional increase in specific consumption at minimum operating load level

•ACT_LOSPL(r,y,p,cg,'UP') – fraction of feasible load range above the minimum op. level, below which the efficiency losses occur.

•ACT_LOSPL(r,y,p,cg,'LO') – minimum operating level used for the partial load efficiency function, default = MAX(0.1,ACT_MINLD(r,y,p))

The variables involved in the equations are :

• VAR_CAP(r,t,p) – capacity of process p

• VAR_ACT(r,v,t,p,s) – activity of process p, timeslice s

• VAR_FLO(r,v,t,p,c,s) – flow of process p, commodity c, timeslice s

• VAR_UPS(r,v,t,p,s,'N') – off-line capacity of process p, timeslice s

• VAR_UPS(r,v,t,p,s,'FX') – efficiency loss of process p, timeslice s, divided by ACT_LOSPL(r,y,p,cg,'FX')

Note that as you have not defined ACT_LOSPL(LO), the default is MAX(0.1,ACT_MINLD(r,y,p)) = 0.1;

First, your EQE_ACTEFF:

`EQE_ACTEFF =E= Process Activity Efficiency (=), example equations are:`

EQE_ACTEFF(REG1,2018,2018,TESTELSR,NRG,IN,SD).. - 57.8420451744059*VAR_ACT(REG1,2018,2018,TESTELSR,SD) + VAR_FLO(REG1,2018,2018,TESTELSR,ELC,SD) - 56.8420140553856*VAR_UPS(REG1,2018,2018,TESTELSR,SD,FX) =E= 0 ;EQE_ACTEFF(REG1,2018,2018,TESTELSR,NRG,IN,SD).. - 57.8420451744059*VAR_ACT(REG1,2018,2018,TESTELSR,SD) + VAR_FLO(REG1,2018,2018,TESTELSR,ELC,SD) - 56.8420140553856*VAR_UPS(REG1,2018,2018,TESTELSR,SD,FX) =E= 0 ;

The equation defines the process activity efficiency in 2018, for timeslice SD. You efficiency for TESTELSR is ACT_EFF(ACT)= 0.017288462. The coefficient 57.8420451744059 for VAR_ACT is obtained as the inverse of that, i.e. 57.8420451744059 = 1/0.017288462. The coefficient 1 for VAR_FLO is obtained from the fact that you have not defined any commodity-specific efficiency, and so 1 is assumed. The coefficient 56.8420140553856 for VAR_UPS is obtained as ACT_LOSPL(FX)/ACT_EFF(ACT) = 0.982711 / 0.017288462 = 56.8420140553856. The interpretation is straightforward: The activity is equal to the ELC input flow multiplied by the efficiency and subtracted by the activity loss due to partial load.

Second, your EQ_CAPLOAD(LO):

`EQ_CAPLOAD(REG1,2018,2018,TESTELSR,SD,LO).. VAR_ACT(REG1,2018,2018,TESTELSR,SD) - 0.378617286213058*VAR_CAP(REG1,2018,TESTELSR) + 0.378617286213058*VAR_UPS(REG1,2018,2018,TESTELSR,S,N) =G= 0 ;`The equation defines the minimum load in 2018, for timeslice SD. The coefficient is always 1 for VAR_ACT. The coefficient for the online capacity (VAR_CAP−VAR_UPS(S)) is PRC_CAPACT×YRFR×ACT_MINLD = 151.446914485223 × 0.25 × 0.01= 0.378617286213058. The interpretation is straightforward: The load cannot go below the online capacity multiplied by the minimum load level.

Third, your EQ_CAPLOAD(UP):

`EQ_CAPLOAD(REG1,2018,2018,TESTELSR,SD,UP).. - VAR_ACT(REG1,2018,2018,TESTELSR,SD) + 37.8617286213058*VAR_CAP(REG1,2018,TESTELSR) - 37.8617286213058*VAR_UPS(REG1,2018,2018,TESTELSR,S,N) =G= 0 ;`The equation defines the maximum load in 2018, for timeslice SD. The coefficient is always 1 for VAR_ACT. The coefficient for the online capacity (VAR_CAP−VAR_UPS(S)) is PRC_CAPACT×YRFR×COEF_AF(UP) = 151.446914485223 × 0.25 × 1 = 37.8617286213058. The interpretation is straightforward: The load cannot exceed the online capacity multiplied by the maximum availability.

Fourth , your EQ_ACTPL :

`EQ_ACTPL(REG1,2018,2018,TESTELSR,SD).. 0.392896432500393*VAR_ACT(REG1,2018,2018,TESTELSR,SD) - 5.27374667249148*VAR_CAP(REG1,2018,TESTELSR) + 5.27374667249148*VAR_UPS(REG1,2018,2018,TESTELSR,S,N) + VAR_UPS(REG1,2018,2018,TESTELSR,SD,FX) =G= 0 ;`The equation defines the efficiency loss in 2018, for timeslice SD. The loss variable VAR_UPS(FX) always has the coefficient 1. The coefficient for the online capacity (VAR_CAP−VAR_UPS(S)) is defined by ACT_LOSPL(UP), and is obtained as PRC_CAPACT×YRFR × (ACT_LOSPL(UP)+ACT_LOSPL(LO) × (1-ACT_LOSPL(UP))) / (ACT_LOSPL(UP) × (1/ACT_LOSPL(LO)−1)) = 151.446914485223 × 0.25 × (0.2828 + 0.1 × (1−0.2828)) / (0.2828 × (1/0.1−1)) = 5.27374667249148.

The coefficient for the activity VAR_ACT is obtained as 1 / (ACT_LOSPL(UP) × (1/ACT_LOSPL(LO)−1)) = 1 / (0.2828 × (1/0.1−1)) = 0.3928964325.

It is easy to see, by simple calculus, that when the activity is equal to the upper point (ACT_LOSPL(UP)+ACT_LOSPL(LO) × (1-ACT_LOSPL(UP))) = 0.2828+0.1×(1−0.2828))= 0.35452, the loss variable is zero, and when the activity is equal to the lower point ACT_LOSPL(LO), the loss variable is equal (or ≥) to the activity, as designed.