remindmodel · fschreyer · Dec 8, 2022 · Dec 8, 2022 · Nov 23, 2022 · Apr 6, 2023
diff --git a/.zenodo.json b/.zenodo.json
@@ -1,6 +1,6 @@
 {
   "title": "REMIND - REgional Model of INvestments and Development",
-  "version": "3.3.0",
+  "version": "3.3.1",
   "creators": [
     {
       "name": "Luderer, Gunnar",
@@ -249,5 +249,5 @@
   "license": {
     "id": "AGPL-3.0-or-later"
   },
-  "publication_date": "2024-03-27"
+  "publication_date": "2024-06-18"
 }
diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -6,6 +6,16 @@ The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/).
 
 ## [Unreleased]
 
+### changed
+
+### added
+
+### fixed
+
+### removed
+
+## [3.3.1] - 2024-06-18
+
 ### changed
 - new inptu data (6.77) including new GDP and population data([#83](https://github.com/pik-piam/mrdrivers/pull/83)) [[#1684]](https://github.com/remindmodel/remind/pull/1684)
 - **37_industry** remove subsector-specific shares of SE

diff --git a/CITATION.cff b/CITATION.cff
@@ -260,7 +260,7 @@ abstract: REMIND (REgional Model of Investment and Development) is a numerical
   technology, policy and climate constraints. It also accounts for regional trade 
   characteristics on goods, energy fuels, and emissions allowances. All greenhouse 
   gas emissions due to human activities are represented in the model.
-version: "3.3.0.dev402"
+version: "3.3.1"
 date-released: 2024-06-18
 repository-code: https://github.com/remindmodel/remind
 keywords:

diff --git a/DESCRIPTION b/DESCRIPTION
@@ -1,7 +1,7 @@
 Package: remindmodel
 Title: REMIND - REgional Model of INvestments and Development
 Version: 0.1
-Date: 2024-03-27
+Date: 2024-06-18
 Description: This is not a package yet, the purpose of this file is to
     document metadata, notably dependencies.
 License: file LICENSE

diff --git a/config/default.cfg b/config/default.cfg
@@ -30,7 +30,7 @@ cfg$extramappings_historic <- ""
 cfg$inputRevision <- "6.77"
 
 #### Current CES parameter and GDX revision (commit hash) ####
-cfg$CESandGDXversion <- "31bbe498c5e0fc19da876e8b543d5aa1fc112015"
+cfg$CESandGDXversion <- "593871ba914d06ec09694ed3719534d6e5cdd94f"
 
 #### Force the model to download new input data ####
 cfg$force_download <- FALSE
@@ -40,7 +40,7 @@ cfg$force_replace <- FALSE
 
 #### list of repositories containing input data
 # defined in your local .Rprofile or on the cluster /p/projects/rd3mod/R/.Rprofile
-cfg$repositories <- getOption("remind_repos")
+cfg$repositories <- c(getOption("remind_repos"), "/p/projects/ariadne/remind/calibration_results")
 
 #### Folder run statistics should be submitted to
 cfg$runstatistics <- "/p/projects/rd3mod/models/statistics/remind"
@@ -71,7 +71,7 @@ cfg$validationmodel_name <- "VALIDATIONREMIND"
 
 #### model version of the overall model (used for run statistics only).
 # automatically generated for development versions, updated by hand for releases
-cfg$model_version <- "3.3.0.dev402"
+cfg$model_version <- "3.3.1"
 
 #### settings ####
 cfg$gms <- list()

diff --git a/config/scenario_config_21_EU11_ARIADNE.csv b/config/scenario_config_21_EU11_ARIADNE.csv
@@ -0,0 +1,16 @@
+title;start;copyConfigFrom;.description;CES_parameters;c_keep_iteration_gdxes;cm_calibration_string;optimization;c_testOneRegi_region;cm_solver_try_max;cm_nash_mode;cm_startIter_EDGET;subsidizeLearning;trade;cm_trade_SE_exog;cm_EnSecScen_price;cm_EnSecScen_limit;cm_Ger_Pol;c_ccsinjecratescen;cm_ccsinjeCost;cm_bioprod_regi_lim;cm_import_tax;cm_1stgen_phaseout;c_agricult_base_shift;cm_altFeEmiFac;cm_PriceDurSlope_elh2;cm_SEtaxRampUpParam;cm_build_H2costAddH2Inv;cm_steel_secondary_max_share_scenario;cm_CESMkup_build;cm_CESMkup_ind;cm_CESMkup_ind_data;cm_exogDem_scen;cm_wasteIncinerationCCSshare;cm_feedstockEmiUnknownFate;cm_FEtax_trajectory_abs;cm_FEtax_trajectory_rel;cm_inco0Factor;cm_adj_coeff_multiplier;cm_adj_seed_multiplier;regionmapping;extramappings_historic;cm_rcp_scen;cm_iterative_target_adj;c_budgetCO2from2020;carbonprice;cm_co2_tax_2020;c_peakBudgYr;c_taxCO2inc_after_peakBudgYr;techpol;regipol;cm_regiExoPrice;cm_emiMktTarget;cm_emiMktTarget_tolerance;cm_NucRegiPol;cm_CoalRegiPol;cm_EDGEtr_scen;cm_emiscen;cm_multigasscen;cm_POPscen;cm_GDPscen;cm_demScen;cm_startyear;path_gdx;path_gdx_ref
+# _____Reference Runs_____;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+Calib_EU_NPi;0;;Calibration Run with National Policies Implemented (NPI);calibrate;;;;;;;;;se_trade;;;;;;;;;;;EUR_regi, NEU_regi;;;;;;;;;;;;;;;;./config/regionmapping_21_EU11.csv;./config/extramapping_EU27.csv;rcp45;;;NPi;1;;;NPi2018;regiCarbonPrice;;;;on;on;Mix1;9;3;;;;2005;;
+NPi;0;Calib_EU_NPi;National Policies implemented;load;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+Calib_EU_Npi_lowDem;0;Calib_EU_NPi;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;NAV_all;;;;;gdp_SSP2EU_NAV_all;;;
+Npi_lowDem;0;Calib_EU_Npi_lowDem;;load;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+# ____ Standard Scenarios______;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+CurrentPolicies;0;NPi;Current Policies Scenario for Germany including latest credible developments from Fit for 55 and Ampel government;;;;;;;;;;;2035.2045.FRA.DEU.seel 0.045, 2035.2045.ESW.DEU.seh2 0.091, 2035.2045.MEA.DEU.seliqsyn 0.091;;;;2;high;DEU 1.1, EU27_regi 7.5;EU27_regi.pebiolc.worldPricemarkup 3.0;1;DEU -0.1;;;;;;fehob 1.75, enhb 0.5;;;ariadne_bal;;;;;;;;;;;;;;;;;;;EU27_regi.(2025 50,2030 100,2035 150,2040 200,2045 250,2050 300,2055 300,2060 300,2070 300,2080 300,2090 300,2100 300,2110 300,2130 300,2150 300);;;;;Mix3;;;;;;2025;;NPi
+KN2045_Bal_v4;0;;Standard Ariadne scenario with -55% GHG in 2030 and GHG neutrality goal in 2050 for EU (incl. EU LULUCF sink), -65% GHG in 2030 and GHG neutrality goal in 2045 for Germany;;;;;;;;;globallyOptimal;se_trade;2035.2045.FRA.DEU.seel 0.183, 2035.2045.ESW.DEU.seh2 0.366, 2035.2045.MEA.DEU.seliqsyn 0.366;;;;2;high;DEU 1.1, EU27_regi 7.5;EU27_regi.pebiolc.worldPricemarkup 3.0;1;DEU -0.1;EUR_regi, NEU_regi;;DEU.elh2.a 0.3, DEU.elh2.b 20;;;fehob 1.75, enhb 0.5;manual;feelhth_otherInd 1.3, fega_steel 0.4;ariadne_bal;;;;;;;;./config/regionmapping_21_EU11.csv;./config/extramapping_EU27.csv;rcp20;9;650;diffCurvPhaseIn2Lin;100;2080;3;;regiCarbonPrice;;2020.2030.DEU.all.year.netGHG_noLULUCF_noBunkers 0.44, 2035.2045.DEU.all.year.netGHG_LULUCFGrassi 0.001;0.003;on;on;Mix4;9;;;;;2025;;NPi
+KN2045_Elec_v4;0;KN2045_Bal_v4;Scenario with high electrification, low H2 and synfuel imports;;;;;;;;;;;2035.2045.FRA.DEU.seel 0.183, 2035.2045.ESW.DEU.seh2 0.183, 2035.2045.MEA.DEU.seliqsyn 0.366;;;;;;;;;;;;;;;feelhpb 1.4, fehob 1.75, enhb 0.5;;feh2_otherInd 0.7, feelhth_otherInd 0.9, feh2_cement 2.2, feh2_chemicals 1.05, fega_steel 0.4;;;;;2040.build.feels 0.7, 2040.build.fegas 1.3, 2040.indst.feels 0.7, 2040.indst.fegas 1.3, 2040.indst.fehos 1.3, 2040.trans.feelt 0.7, 2040.trans.fepet 1.3, 2040.trans.fedie 1.3;tdh2s 2, tdh2t 2;;;;;;;;;;;;;;;;;;;;;;;;;;;
+KN2045_H2_v4;0;KN2045_Bal_v4;Scenario with high H2 and synfuel use, high H2 and synfuel imports;;;;;;;;;;;2035.2045.FRA.DEU.seel 0.183, 2035.2045.ESW.DEU.seh2 0.732, 2035.2045.MEA.DEU.seliqsyn 0.366;;;;;;;;;;;20;DEU.elh2.a 0.2, DEU.elh2.b 50;0.1;;feelhpb 2.3, feelrhb 0.87, fehob 1.75, enhb 0.5;;feh2_otherInd 0.01, feelhth_otherInd 1.6, feh2_cement 0.43, feelhth_chemicals 1.6, feh2_chemicals 0.43, feh2_steel 0.1, feli_steel 0.87, fega_steel 0.4;;;;;2040.build.feels 1.3, 2040.build.fegas 1.3, 2040.indst.feels 1.3, 2040.indst.fegas 1.3, 2040.indst.fehos 1.3, 2040.trans.feelt 1.3, 2040.trans.fepet 1.3, 2040.trans.fedie 1.3, 2040.trans.feh2t 0.7;tdh2s 0.5, tdh2t 0.5;;;;;;;;;;;;;;;;;;;HydrHype4;;;;;;;;
+# ____ Energy Security Scenarios___;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+KN2045_EnSov;0;KN2045_Bal_v4;Energy security scenario with limits/taxes on PE gas consumption in Germany and reduced steel demand;;;;;;;;;;;;on;2;ensec;;;;;;;EUR_regi, NEU_regi;;;;;feelhpb 1.4, fehob 1.75, enhb 0.5;;feelhth_otherInd 1.1, fega_steel 0.4;ariadne_ensec;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+# ____ low-demand/high-demand scenarios ____;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
+KN2045plus_EasyRide;0;KN2045_Bal_v4;;;;;;;;;;;;;;;;;;;;;;;;;;;feelhpb 1.4, fehob 1.75, enhb 0.5. feheb 0.01;;feelhth_otherInd 0.9, fega_steel 0.4;ariadne_ensec;;;;;;;;;;;;;;;;;;;;off;;;;NAV_all;;;;;gdp_SSP2EU_NAV_all;;;Npi_lowDem
+# Tests;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
diff --git a/core/datainput.gms b/core/datainput.gms
@@ -1172,7 +1172,6 @@ loop(ttot$(ttot.val ge 2005),
   p_adj_seed_te(ttot,regi,"coalftcrec")      = 0.25;
   p_adj_seed_te(ttot,regi,"coaltr")          = 4.00;
   p_adj_seed_te(ttot,regi,'dac')             = 0.25;
-  p_adj_seed_te(ttot,regi,'geohe')           = 0.33;
 $ifthen.cm_subsec_model_steel "%cm_subsec_model_steel%" == "processes"
   p_adj_seed_te(ttot,regi,"bfcc")            = 0.05;
   p_adj_seed_te(ttot,regi,"idrcc")           = 0.05;
@@ -1182,6 +1181,10 @@ $ifthen.WindOff %cm_wind_offshore% == "1"
   p_adj_seed_te(ttot,regi,"windoff") = 0.5;
 $endif.WindOff
 
+  p_adj_seed_te(ttot,regi,"elh2") = 0.33;
+  p_adj_seed_te(ttot,regi,"MeOH") = 0.5;
+  p_adj_seed_te(ttot,regi,"h22ch4") = 0.5;
+
 *RP: for comparison of different technologies:
 *** pm_conv_cap_2_MioLDV <- 650  # The world has slightly below 800million cars in 2005 (IEA TECO2), so with a global vm_cap of 1.2, this gives ~650
 *** ==> 1TW power plant ~ 650 million LDV
@@ -1207,7 +1210,6 @@ $endif.WindOff
   p_adj_coeff(ttot,regi,"ccsinje")         = 1.0;
   p_adj_coeff(ttot,regi,"spv")             = 0.15;
   p_adj_coeff(ttot,regi,"wind")            = 0.25;
-  p_adj_coeff(ttot,regi,"geohe")           = 0.6;
 $ifthen.cm_subsec_model_steel "%cm_subsec_model_steel%" == "processes"
   p_adj_coeff(ttot,regi,"bfcc")            = 1.0;
   p_adj_coeff(ttot,regi,"idrcc")           = 1.0;
@@ -1221,6 +1223,12 @@ $endif.WindOff
   p_adj_coeff(ttot,regi,"dac")             = 0.8;
   p_adj_coeff(ttot,regi,teGrid)            = 0.3;
   p_adj_coeff(ttot,regi,teStor)            = 0.05;
+
+  p_adj_coeff(ttot,regi,"elh2")            = 0.75;
+  p_adj_coeff(ttot,regi,"MeOH")            = 0.5;
+  p_adj_coeff(ttot,regi,"h22ch4")            = 0.5;
+
+
 );
 
 ***Rescaling adj seed and coeff if adj cost multiplier switches are on

diff --git a/core/declarations.gms b/core/declarations.gms
@@ -94,6 +94,8 @@ pm_shPerm(tall, all_regi)                            "emission permit shares"
 pm_emicapglob(tall)                                  "global emission cap"
 p_adj_coeff(ttot,all_regi,all_te)                    "coefficient for adjustment costs"
 p_adj_coeff_glob(all_te)                             "coefficient for adjustment costs - global scale"
+p_adj_helper_a(ttot,all_regi,all_te)                 "helper parameter that contains different parameters of adjustment cost to facilitate readability of code"
+p_adj_helper_b(ttot,all_regi,all_te)                 "helper parameter that contains different parameters of adjustment cost to facilitate readability of code"
 p_switch_cement(ttot,all_regi)                       "describes an s-curve to provide a smooth switching from the short-term behavior (depending on per capita capital investments) to the long-term behavior (constant per capita emissions) of CO2 emissions from cement production"
 p_cint(all_regi,all_enty,all_enty,rlf)               "additional emissions of GHG from mining, on top of emissions from combustion"
 
@@ -215,6 +217,8 @@ p_CapFixFromRWfix(ttot,all_regi,all_te)              "parameter for fixing capac
 p_deltaCapFromRWfix(ttot,all_regi,all_te)            "parameter with resulting deltacap values resulting from fixing capacity to real-world values in 2010/2015"
 
 o_margAdjCostInv(ttot,all_regi,all_te)               "marginal adjustment cost calculated in postsolve for diagnostics"
+o_margAdjCostInv_prev(ttot,all_regi,all_te)          "1st term of marginal adjustment cost calculated in postsolve for diagnostics. Refers to marginal cost due to change of vm_deltaCap from previous to current time step."
+o_margAdjCostInv_next(ttot,all_regi,all_te)          "2nd term marginal adjustment cost calculated in postsolve for diagnostics. Refers to marginal cost due to change of vm_deltaCap from current to next time step."
 o_avgAdjCostInv(ttot,all_regi,all_te)                "average adjustment cost calculated in postsolve for diagnostics"
 o_avgAdjCost_2_InvCost_ratioPc(ttot,all_regi,all_te)   "ratio in % of average adj cost compared to direct inv costs"
 

diff --git a/core/equations.gms b/core/equations.gms
@@ -478,9 +478,9 @@ q_costTeCapital(t,regi,teLearn)$(NOT (pm_data(regi,"tech_stat",teLearn) eq 4 AND
 *' EMF27 limits on fluctuating renewables, only turned on for special EMF27 and AWP 2 scenarios, not for SSP
 ***---------------------------------------------------------------------------
 *** this is to prevent that in the long term, all solids are supplied by biomass. Residential solids can be fully supplied by biomass (-> wood pellets), so the FE residential demand is subtracted
-q_limitBiotrmod(t,regi)$(t.val > 2020)..
-    vm_prodSe(t,regi,"pebiolc","sesobio","biotrmod")
-   - sum (in$sameAs("fesob",in), vm_cesIO(t,regi,in) + pm_cesdata(t,regi,in,"offset_quantity"))
+q_limitBiotrmod(t,regi)$(NO).. 
+    vm_prodSe(t,regi,"pebiolc","sesobio","biotrmod") 
+   - sum (in$sameAs("fesob",in), vm_cesIO(t,regi,in) + pm_cesdata(t,regi,in,"offset_quantity")) 
    - sum (fe2es(entyFe,esty,teEs)$buildMoBio(esty), vm_demFeForEs(t,regi,entyFe,esty,teEs) )
     =l=
     (2 +  max(0,min(1,( 2100 - pm_ttot_val(t)) / ( 2100 - 2020 ))) * 3) !! 5 in 2020 and 2 in 2100
@@ -1090,15 +1090,15 @@ q_limitCapFeH2BI(t,regi,sector)$(SAMEAS(sector,"build") OR SAMEAS(sector,"indst"
 *' Enforce historical data biomass share per carrier in sector final energy for buildings and industry (+- 2%)
 ***---------------------------------------------------------------------------
 
-q_shbiofe_up(t,regi,entyFe,sector,emiMkt)$((sameas(entyFe,"fegas") or sameas(entyFe,"fehos") or sameas(entyFe,"fesos")) and entyFe2Sector(entyFe,sector) and sector2emiMkt(sector,emiMkt) and (t.val le 2015))..
+q_shbiofe_up(t,regi,entyFe,sector,emiMkt)$((sameas(entyFe,"fegas") or sameas(entyFe,"fehos") or sameas(entyFe,"fesos")) and entyFe2Sector(entyFe,sector) and sector2emiMkt(sector,emiMkt) and (t.val le 2020))..
   (pm_secBioShare(t,regi,entyFe,sector) + 0.02)
   *
   sum((entySe,te)$se2fe(entySe,entyFe,te), vm_demFeSector(t,regi,entySe,entyFe,sector,emiMkt))
   =g=
   sum((entySeBio,te)$se2fe(entySeBio,entyFe,te), vm_demFeSector(t,regi,entySeBio,entyFe,sector,emiMkt))
 ;
 
-q_shbiofe_lo(t,regi,entyFe,sector,emiMkt)$((sameas(entyFe,"fegas") or sameas(entyFe,"fehos") or sameas(entyFe,"fesos")) and entyFe2Sector(entyFe,sector) and sector2emiMkt(sector,emiMkt) and (t.val le 2015))..
+q_shbiofe_lo(t,regi,entyFe,sector,emiMkt)$((sameas(entyFe,"fegas") or sameas(entyFe,"fehos") or sameas(entyFe,"fesos")) and entyFe2Sector(entyFe,sector) and sector2emiMkt(sector,emiMkt) and (t.val le 2020))..
   (pm_secBioShare(t,regi,entyFe,sector) - 0.02)
   *
   sum((entySe,te)$se2fe(entySe,entyFe,te), vm_demFeSector(t,regi,entySe,entyFe,sector,emiMkt))

diff --git a/core/input/generisdata_tech.prn b/core/input/generisdata_tech.prn
@@ -70,7 +70,7 @@ luse
 
 
 +                  elh2         dot         dhp       h2turb      h2curt       h2turbVRE  elh2VRE      h22ch4      MeOH
-tech_stat            4                                    5           5            5                     3          3
+tech_stat            3                                    5           5            5                     3          3  
 inco0               1350         480         360         510         700          510      0.1          700       1300
 constrTme            2            2           1           2           2            2        1            2          2
 mix0

diff --git a/core/postsolve.gms b/core/postsolve.gms
@@ -556,16 +556,38 @@ loop(ttot$(ttot.val ge 2005),
 pm_GDPGross(tall,regi)$(tall.val ge 2150) = pm_GDPGross("2149",regi); 
 
 
-*** CG: calculate marginal adjustment cost for capacity investment: d(vm_costInvTeAdj) / d(vm_deltaCap)  !!!! the closed formula only holds when v_adjFactorGlob.fx(t,regi,te) = 0;
-o_margAdjCostInv(ttot,regi,te)$(ttot.val ge max(2010, cm_startyear) AND teAdj(te)) =  vm_costTeCapital.l(ttot,regi,te) * p_adj_coeff(ttot,regi,te)
-    * 2 * (sum(te2rlf(te,rlf), vm_deltaCap.l(ttot,regi,te,rlf)) - sum(te2rlf(te,rlf), vm_deltaCap.l(ttot-1,regi,te,rlf)))
-    / power((pm_ttot_val(ttot) - pm_ttot_val(ttot-1)), 2)
-    / (sum(te2rlf(te,rlf), vm_deltaCap.l(ttot-1,regi,te,rlf)) + p_adj_seed_reg(ttot,regi) * p_adj_seed_te(ttot,regi,te)
-      + p_adj_deltacapoffset("2010",regi,te)$(ttot.val eq 2010) + p_adj_deltacapoffset("2015",regi,te)$(ttot.val eq 2015)
-      + p_adj_deltacapoffset("2020",regi,te)$(ttot.val eq 2020) + p_adj_deltacapoffset("2025",regi,te)$(ttot.val eq 2025)
-    )
-    * (1 + 0.02/pm_ies(regi) + pm_prtp(regi)) ** (pm_ts(ttot) / 2)
-;
+*** Marginal Adjustment Cost Calculation
+*** Marginal adjustment cost consist of two terms.
+*** 1st term: d(v_costInvTeAdj(vm_deltaCap(t),vm_deltaCap(t-1))) / d(vm_deltaCap(t))
+*** This calculates marginal adjustment cost due to the change in vm_deltaCap between the current time step t and the previous time step t-1. (same as o_margAdjCostInv above)
+*** 2nd term: d(v_costInvTeAdj(vm_deltaCap(t+1),vm_deltaCap(t))) / d(vm_deltaCap(t))
+*** This calculates marginal adjustment cost due to the change in vm_deltaCap between the next time step t+1 and the current time step.
+*** calculate some helper parameters first to ease readability
+p_adj_helper_a(ttot,regi,te) = p_adj_coeff(ttot,regi,te) * (1.02 + pm_prtp(regi) ) ** (pm_ts(ttot) / 2);
+p_adj_helper_b(ttot,regi,te) = p_adj_seed_reg(ttot,regi) * p_adj_seed_te(ttot,regi,te)
+                                          + p_adj_deltacapoffset("2010",regi,te)$(ttot.val eq 2010) + p_adj_deltacapoffset("2015",regi,te)$(ttot.val eq 2015)
+                                          + p_adj_deltacapoffset("2020",regi,te)$(ttot.val eq 2020) + p_adj_deltacapoffset("2025",regi,te)$(ttot.val eq 2025);
+*** With those helper parameters a and b, adjustment cost v_costInvTeAdj can be written as (see q_eqadj and q_costInvTeAdj equations):
+*** v_costInvTeAdj(vm_deltaCap(t),vm_deltaCap(t-1)) = vm_costTeCapital * a * [ (vm_deltaCap(t) - vm_deltaCap(t-1)) / (pm_ttot_val(t) - pm_ttot_val(t-1)) ]^2 / (vm_deltaCap(t-1)+b)
+*** 1st term, marginal adjustment cost due to previous time step:
+o_margAdjCostInv_prev(ttot,regi,te)$(ttot.val ge max(2010, cm_startyear) AND teAdj(te)) = vm_costTeCapital.l(ttot,regi,te)
+                                                                                            * p_adj_helper_a(ttot,regi,te)
+                                                                                            / power((pm_ttot_val(ttot) - pm_ttot_val(ttot-1)), 2)
+                                                                                            * 2 * ( sum(te2rlf(te,rlf), vm_deltaCap.l(ttot,regi,te,rlf)) - sum(te2rlf(te,rlf), vm_deltaCap.l(ttot-1,regi,te,rlf)) )
+                                                                                            / ( sum(te2rlf(te,rlf), vm_deltaCap.l(ttot-1,regi,te,rlf)) + p_adj_helper_b(ttot,regi,te));
+*** 2nd term, marginal adjustment cost due to next time step:
+o_margAdjCostInv_next(ttot,regi,te)$(ttot.val ge max(2010, cm_startyear) AND teAdj(te)) = - vm_costTeCapital.l(ttot,regi,te)
+                                                                                              * p_adj_helper_a(ttot,regi,te)
+                                                                                              / power((pm_ttot_val(ttot+1) - pm_ttot_val(ttot)), 2)
+                                                                                              / power(  sum(te2rlf(te,rlf), vm_deltaCap.l(ttot,regi,te,rlf)) + p_adj_helper_b(ttot,regi,te), 2 )
+                                                                                              * ( 2 * ( sum(te2rlf(te,rlf), vm_deltaCap.l(ttot+1,regi,te,rlf)) - sum(te2rlf(te,rlf), vm_deltaCap.l(ttot,regi,te,rlf))  )
+                                                                                                * ( sum(te2rlf(te,rlf), vm_deltaCap.l(ttot,regi,te,rlf)) + p_adj_helper_b(ttot,regi,te) )
+                                                                                              + power( sum(te2rlf(te,rlf), vm_deltaCap.l(ttot+1,regi,te,rlf)) - sum(te2rlf(te,rlf), vm_deltaCap.l(ttot,regi,te,rlf))  , 2)  );
+
+
+
+*** total marginal adjustment cost are sum of marginal adjustment cost of change from previous time step and marginal adjustment cost of change to next time step
+o_margAdjCostInv(ttot,regi,te) = o_margAdjCostInv_prev(ttot,regi,te) + o_margAdjCostInv_next(ttot,regi,te);
 
 *** CG: calculate average adjustment cost for capacity investment: vm_costInvTeAdj / vm_deltaCap
 o_avgAdjCostInv(ttot,regi,te)$(ttot.val ge 2010 AND teAdj(te) AND