equations.gms

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*** SOF ./modules/30_biomass/magpie_4/equations.gms
***---------------------------------------------------------------------------
***                      FUEL COSTS FOR BIOENERGY
***---------------------------------------------------------------------------

*' @equations
*' 
*' **Total fuel costs for biomass**  
*' The first part, summing over *peren2rlf30*, represents costs for biomass with fixed prices.
*' The second part that includes *v30_pebiolc_costs* represents costs for biomass with continous supply curves from MAgPIE.
*' In coupled runs *v30_multcost* is a cost markup factor improving the optimization performance by penalizing
*' (too) large jumps in the demand in between two coupling iterations. It converges to 1 and therefore does not affect the outcome.
*' The last part, containing *pm_costsTradePeFinancial*, represents additional tradecosts (only for purpose grown lignocellulosic biomass).

q30_costFuBio(ttot,regi)$(ttot.val ge cm_startyear).. 
         vm_costFuBio(ttot,regi)
         =e= sum(peren2rlf30(enty,rlf), p30_datapebio(regi,enty,rlf,"cost",ttot) * vm_fuExtr(ttot,regi,enty,rlf))
         +
$if %cm_MAgPIE_coupling% == "on"  (v30_pebiolc_costs(ttot,regi) * v30_multcost(ttot,regi))
$if %cm_MAgPIE_coupling% == "off" (v30_pebiolc_costs(ttot,regi))
         - p30_pebiolc_costs_emu_preloop(ttot,regi) !! Need to be substracted since they are also inculded in the total agricultural production costs
         + 
         sum(peren2cont30(enty,rlf), vm_fuExtr(ttot,regi,enty,rlf) * pm_costsTradePeFinancial(regi,"use",enty));

*' **Calculate cost markup factor for coupled runs**  
*' It penalizes large jumps from the previous coupling iteration and converges to 1, as the difference between *vm_fuExtr* and 
*' *p30_pebiolc_demandmag* vanish when the coupling converges over iterations.
q30_costAdj(ttot,regi)$(ttot.val ge cm_startyear)..
         v30_multcost(ttot,regi)
         =e=
         power((vm_fuExtr(ttot,regi,"pebiolc","1")-p30_pebiolc_demandmag(ttot,regi))/ (p30_pebiolc_demandmag(ttot,regi) + 0.15),2) * 0.4 + 1
;

***---------------------------------------------------------------------------
***                      MAgPIE EMULATOR
***---------------------------------------------------------------------------

*' **Caclulate bioenergy price according to MAgPIE supply curves**  
*' The equation is mainly used by shift factor calculation in the preloop. In main solve it is only required for bioenergy tax.

q30_pebiolc_price(ttot,regi)$(ttot.val ge cm_startyear)..
         vm_pebiolc_price(ttot,regi)
         =e=
         (v30_priceshift(ttot,regi) 
       + i30_bioen_price_a(ttot,regi) 
       + i30_bioen_price_b(ttot,regi) * (vm_fuExtr(ttot,regi,"pebiolc","1") + sm_eps) )
       * v30_pricemult(ttot,regi);

*' **Calculate bioenergy price according to shifted MAgPIE supply curves**  
*' Required only to calculate the bioenergy tax. For historic reasons there exist both *vm_pebiolc_price_shifted* and 
*' *vm_pebiolc_price*. Could be refactored some time.

q30_pebiolc_price_base(ttot,regi)$(ttot.val ge cm_startyear)..
         vm_pebiolc_price_shifted(ttot,regi)
         =e=
         vm_pebiolc_price(ttot,regi)
;

*' **MAgPIE EMULATOR**  
*' Calculates bioenergy costs of purpose grown lignocellulosic biomass by integrating the linear price supply curve.
*' It contains optional shift and scaling of supply curves in coupled runs. 
*' The equation is used both in preloop and main solve.

q30_pebiolc_costs(ttot,regi)$(ttot.val ge cm_startyear)..
         v30_pebiolc_costs(ttot,regi) 
         =e=
        (v30_priceshift(ttot,regi)
       + i30_bioen_price_a(ttot,regi)
       + i30_bioen_price_b(ttot,regi) / 2 * (vm_fuExtr(ttot,regi,"pebiolc","1") + sm_eps) )
       * v30_pricemult(ttot,regi)
       * vm_fuExtr(ttot,regi,"pebiolc","1")
       
;

***---------------------------------------------------------------------------
***                   SHIFT FACTOR CALCULATOIN
***---------------------------------------------------------------------------

*' **Calculate shift factor for bioenergy costs**  
*' The factor is computed by minimizing least squares (*v30_shift_r2*) of cost differences between MAgPIE output and MAgPIE emulator.
*' It is solved in presolve (*s30_switch_shiftcalc* = 1) and deactivated in main solve (*s30_switch_shiftcalc* = 0).
*' *pm_ts* is used as a weight factor, representing the time step length.

q30_priceshift$(s30_switch_shiftcalc eq 1)..
         v30_shift_r2
         =e=
         sum(regi,
             sum(ttot$(ttot.val ge 2005 AND p30_pebiolc_pricemag(ttot,regi) gt 0), power((p30_pebiolc_pricemag(ttot,regi) - vm_pebiolc_price(ttot,regi))*pm_ts(ttot),2)
             )
         )
;

***---------------------------------------------------------------------------
***          Definition of resource constraints for biomass
***---------------------------------------------------------------------------

*' **Limit export of biomass**  
*' Only purpose grown lignocellulosic biomass may be exported, no residues.

q30_limitXpBio(t,regi)..
         vm_Xport(t,regi,"pebiolc")
         =l=
         vm_fuExtr(t,regi,"pebiolc","1");
		 
*** EOF ./modules/30_biomass/magpie_4/equations.gms