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Learning curve for investment costs: (deactivate learning for tech_stat 4 technologies before 2025 as they are not built before) Learning technologies follow a “one-factor learning curve”[^1] (or “experience curve”). This widely-used formulation derives from empirical observations across different energy technologies of a log-linear relationship between the unit cost \(I\) of the technology and its cumulative production or installed capacity \(C\) (see for example empirical paper[^2]). [^1]: Edward S. Rubin, Iness M.L. Azevedo, Paulina Jaramillo, and Sonia Yeh. A review of learning rates for electricity supply technologies. Energy Policy, 86:198-218, 2015. [^2]: Alan McDonald and Leo Schrattenholzer. Learning rates for energy technologies. Energy Policy, 29(4):255–261, 2001. Learning rate \(\lambda\) is defined as the fractional reduction in cost associated with a doubling of cumulative capacity. Let \(I_0\) be the initial cost when cumulative capacity is \(C_0\), and \(I_d\) be the cost when cumulative capacity is \(C_d=2\times C_0\), then the learning rate is defined as: \[ \lambda = 1 - \frac{I_d}{I_0} \in [0,1] \] Hence relating investment cost \(I\) and cumulative capacity \(C\): \[ \frac{I}{I_0} = \left(1-\lambda \right)^{\log_2\left(\frac{C}{C_0}\right)} = \left(\frac{C}{C_0}\right)^{\log_2(1-\lambda )} \] Defining the learning exponent \(b = \log_2(1-\lambda)\) and the cost of the first unit \(a = \frac{I_0}{C_0^b}\), the learning equation simplifies into: \[ I = a \times C^{b} \] Now suppose there is a floor cost \(F\) such that \(I\geq F\geq 0\), irrespective of the capacity. Then the learning only applies to learnable costs \(I'=I-F\), and the learning equation becomes \[ I = a'\times C^{b'} + F \] with \(a' = \frac{I_0 - F}{C_0^{b'}}\). By design, REMIND learning equations ensure that the initial slope of learning is independent of the floor cost. Mathematically, the slopes are given by the derivative of \(I\) and \(I'\) with respect to \(C\): \[ \frac{dI}{dC} = a \times b \times C^{b-1} = I_0 \times b \times \left(\frac{C}{C_0}\right)^{b-1} \] \[ \frac{dI'}{dC} = a' \times b' \times C^{b'-1} = (I_0-F) \times b' \times \left(\frac{C}{C_0}\right)^{b'-1} \] For the two curves to have the same slope initially, we want the two derivatives to be equal for \(C=C_0\). This means \(I_0 \times b = (I_0-F) \times b'\), that we rewrite as: \[ b' = \frac{I_0}{I_0-F}b \] In datainput.gms, fm_dataglob external data provides the observed learning rate learn (\(\lambda\)), the initial investment costs inco0 (\(I_0\)), the floorcost (\(F\)) and the cumulative capacity in 2015 ccap0 (\(C_0\)). The other learning parameters are computed using the equations described above: learnExp_wFC (\(b'\)), learnMult_wFC (\(a'\)). In equations.gms, the investment costs equation q_costTeCapital corresponds to \(I = a'\times C^{b'} + F\), with variations depending on time period and floor cost scenarios.

q_costTeCapital(t,regi,teLearn) $ (pm_data(regi,"tech_stat",teLearn) < 4 or t.val > 2020) ..
  vm_costTeCapital(t,regi,teLearn)
  =e=
  macro_costGlob $ (t.val <= 2005)
    
  + macro_interpolate(t.val, 2005, 2020, macro_costGlob, macro_costRegi) $ (t.val > 2005 and t.val <= 2020)
$if %cm_floorCostScen% == "pricestruc"  + macro_costRegi $ (t.val > 2020)
$if %cm_floorCostScen% == "gdpBased"    + macro_costRegi $ (t.val > 2020)
$ifthen.default %cm_floorCostScen% == "uniform"
  + macro_costRegi $ (t.val > 2020 and t.val <= c_teLearnConvStartYr)
  + macro_interpolate(t.val, c_teLearnConvStartYr, c_teLearnConvEndYr, macro_costRegi, macro_costGlob) $ (t.val > c_teLearnConvStartYr and t.val < c_teLearnConvEndYr)
  + macro_costGlob $ (t.val >= c_teLearnConvEndYr)
$endif.default
;

Limitations There are no known limitations.

See Also

01_macro, 02_welfare, 04_PE_FE_parameters, 05_initialCap, 11_aerosols, 15_climate, 16_downscaleTemperature, 20_growth, 21_tax, 22_subsidizeLearning, 23_capitalMarket, 24_trade, 25_WACC, 26_agCosts, 29_CES_parameters, 30_biomass, 31_fossil, 32_power, 33_carbonRemoval, 35_transport, 36_buildings, 37_industry, 39_carbonUtilization, 40_techpol, 41_emicapregi, 45_carbonprice, 46_carbonpriceRegi, 47_regipol, 50_damages, 51_internalizeDamages, 70_water, 80_optimization, 81_codePerformance

References