Biomass (30_biomass)

Description

The biomass module calculates the production costs of all types of primary energy biomass.

Interfaces

Input

Output

Realizations

(A) exogenous

Limitations There are no known limitations.

(B) magpie_40

The costs for purpose grown ligno-cellulosic biomass are the integral under the supplycurve. The supplycurves have been derived from MAgPIE 4.1

The costs for purpose grown ligno-cellulosic biomass are the integral under the supplycurve. The supplycurves have been derived from MAgPIE 4.1

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 convergence by penalizing large jumps in the demand 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)
         + 
         sum(peren2cont30(enty,rlf), vm_fuExtr(ttot,regi,enty,rlf) * pm_costsTradePeFinancial(regi,"use",enty));

MAgPIE EMULATOR: PRICE
This equation calculates the price for purpose grown lignocellulosic biomass as a (linear) function of demand according to the supplycurve as it was derived from MAgPIE. The equation is used by the shift factor calculation in the preloop stage. In the main solve stage the price is only used to apply the bioenergy tax. It contains optional shift and scaling of supply curves in coupled runs.

\[\begin{multline*} vm\_pebiolc\_price(ttot,regi) = \left(v30\_priceshift(ttot,regi) + i30\_bioen\_price\_a(ttot,regi) + i30\_bioen\_price\_b(ttot,regi) \cdot \left(vm\_fuExtr(ttot,regi,"pebiolc","1") + sm\_eps\right) \right) \cdot v30\_pricemult(ttot,regi) \end{multline*}\]

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

\[\begin{multline*} v30\_pebiolc\_costs(ttot,regi) = \left(v30\_priceshift(ttot,regi) + i30\_bioen\_price\_a(ttot,regi) +\frac{ i30\_bioen\_price\_b(ttot,regi) }{ 2 } \cdot \left(vm\_fuExtr(ttot,regi,"pebiolc","1") + sm\_eps\right) \right) \cdot v30\_pricemult(ttot,regi) \cdot vm\_fuExtr(ttot,regi,"pebiolc","1") \end{multline*}\]

Calculate shift factor for bioenergy costs
This applies in coupled runs only to shift the supplycurve according to the price response of MAgPIE. The factor is computed by minimizing least squares (v30_shift_r2) of price differences between actual MAgPIE output (from coupled runs) and the supply curve (aka 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.

\[\begin{multline*} v30\_shift\_r2 = \sum_{regi}\left( \sum_{ttot\$\left(ttot.val ge 2005 \& p30\_pebiolc\_pricemag(ttot,regi) gt 0\right)}\left( \left(\left(p30\_pebiolc\_pricemag(ttot,regi) - vm\_pebiolc\_price(ttot,regi)\right) \cdot pm\_ts(ttot)\right)^{2}\right)\right) \end{multline*}\]

Calculate cost markup factor for coupled runs
Improve convergence of the REMIND-MAgPIE coupling by penalizing deviations from last coupling iteration. This applies in coupled runs only to prevent large jumps in bioenergy demand between coupling iterations. It penalizes deviations in the demand for purpose grown bioenergy from the previous coupling iteration by increasing the costs proportional to the deviation. The factor converges to 1, as the difference between vm_fuExtr and pm_pebiolc_demandmag vanishes when the coupling converges over iterations.

\[\begin{multline*} v30\_multcost(ttot,regi) = \left(\frac{\left(vm\_fuExtr(ttot,regi,"pebiolc","1")-pm\_pebiolc\_demandmag(ttot,regi)\right)}{ \left(pm\_pebiolc\_demandmag(ttot,regi) + 0.15\right)}\right)^{2} \cdot 0.4 + 1 \end{multline*}\]

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

\[\begin{multline*} vm\_Xport(t,regi,"pebiolc") \leq vm\_fuExtr(t,regi,"pebiolc","1") \end{multline*}\]

\[\begin{multline*} \sum_{pe2se(enty,enty2,teBio)\$teCCS(teBio)} vm\_demPe(t,regi,enty,enty2,teBio) \leq 0.5 \cdot p30\_demPe(t,regi) \end{multline*}\]

\[\begin{multline*} v30\_BioPEProdTotal(t,regi) = \sum_{peren2rlf30(enty,rlf)}\left( vm\_fuExtr(t,regi,enty,rlf)\right) + \sum_{peren2cont30(enty,rlf)}\left( vm\_fuExtr(t,regi,enty,rlf)\right) \end{multline*}\]

\[\begin{multline*} v30\_BioPEProdTotal(t,regi) \leq cm\_bioprod\_histlim \cdot v30\_BioPEProdTotal("2015",regi) \end{multline*}\]

The costs for purpose grown ligno-cellulosic biomass are the integral under the supplycurve. The supplycurves have been derived from MAgPIE 4.1

Limitations There are no known limitations.

Definitions

Objects

Sets

Authors

David Klein

See Also

24_trade, core

References