Generalized levelized cost as a metric for explaining model behavior of linear programming-based energy systems models
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Generalized levelized cost as a metric for explaining model behavior of linear programming-based energy systems models Dr. Takuya Hara, IIASA, Toyota Motor Corporation, Japan
Generalized levelized cost as a metric for explaining model behavior of linear programming-based energy systems models
- 1. Generalized levelized cost as a metric for explaining model behavior of linear programming-based energy systems models Takuya Hara1,2, Volker Krey1, Bas van Ruijven1 1IIASA, 2Toyota Motor Corporation ETSAP Workshop, Summer 2025 10. 6. 2025
- 2. | Presentation title 2/14 Motivation “After 2050, …., there is less consensus on how it (=oil) is replaced (…among) electricity, hydrogen and bioenergy” • No explanations as to why a particular model has a specific tendency • The mechanism on “Spread in climate policy scenarios” remains a knowledge gap! Improving the explainability of model behavior Diversity of Hydrogen use in the transport sector (2050) among models/scenarios
- 3. 3/14 | Presentation title Generalized Levelized Cost (GLC) Variable: 𝑥𝑥𝑗𝑗,𝑦𝑦𝑦𝑦 Annual activity (ACT) of tech 𝑗𝑗 (in period 𝑦𝑦𝑦𝑦) (2) Balance of value (for tech 𝑗𝑗 where 𝑥𝑥𝑗𝑗 > 0) Variable Capacity Fuel Conventional Levelized Cost Upper bound Lower bound Value of output commodity from tech j • LP models simultaneously determine both “quantities” and “values” • GLC enables the explanation of: (1) technology selection priorities, and (2) PRICE_COMMODITY behavior (1) GLC corresponds to the objective function coefficient when the original LP is reformulated via Lagrangian relaxation (2) GLC is equivalent to the PRICE_COMMODITY of output, and provides a meaningful decomposition GLC Cost of constraints GLC *levelized_cost (auxilirary parameter in MESSAGE) (1) GLC as the obj. func. coeff. in the subproblem LP
- 4. 4/14 | Presentation title Overview of the MESSAGEix-GLOBIOM Level of energy commodity Commodity (resources, useful service) Technology (conversion, end-use) (from MESSAGEix-GLOBIOM overview ) 12 regions • Global energy systems model combined with a land-use emulator (based on GLOBIOM) • Divides the world into 12 regions and accounts for interregional trade • Represents system behavior in 5- to 10-year intervals up to 2100 • Formulated as a LP model that minimizes total system cost over the entire time horizon
- 5. | Presentation title 5/14 The transport sector in MESSAGEix-GLOBIOM (base model) • Technologies are abstract representations that convert input energy into output energy/service • The model defines a single transport service (no distinction between cars, trucks, rail, or aviation) elec_trp loil_trp Technology name Energy commodity Electricity Lightoil Transport service gas_trp Gas
- 6. 6/14 | Presentation title GLC for MESSAGE Category Cost type Related parameters/constraints Symbol Note Conventional Levelized cost (CLC) Variable cost Coefficient of the Variable 𝑐𝑐𝑗𝑗 Capacity cost Dual of CAPCITY_CONSTRAINT 𝑦𝑦𝑖𝑖𝐴𝐴𝑖𝑖𝑖𝑖 Including investment cost Fuel cost Dual of COMMODITY_BALANCE (input) Including carbon cost Cost of Constraints Upper bound effect Dual of ACTIVITY_BOUND_UP/LO, ACTIVITY_CONSTRAINT_UP/LO, ACTIVITY_SOFT_CONST_UP/LO Lower bound effect Other relations (Upper/Lower) Dual of RELATION_ACTIVITY Cost of Constraint PRICE_COMMODITY of output commodity Dual of COMMODITY_BALANCE (output) 𝑦𝑦𝑖𝑖𝐴𝐴𝑖𝑖𝑖𝑖 (𝑖𝑖 = 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜) GLC Value of output
- 7. | Presentation title 7/14 • Electricity increases and then plateaus • Behavior of transportation service prices (sharp drop in 2055) Output Example for the Demo: Transport Sector in the 1.5°C Scenario 2020 2030 2040 2050 2060 2070 2080 2090 2100 -10 0 10 20 30 40 50 60 GHG emissions (GtCO 2 eq) NetGHG NetCO 2 Final Energy (EJ/yr) electricity gas lightoil ethanol MESSAGEix-base + 250 GtCO2 carbon budget (2026-2110, cumulative) Transport Final Energy and PRICE_COMMODITY of transport (R12_NAM) Carbon and GHG emissions (Global) methanol PRICE_COMMODITY of transport PRICE_COMMODITY ($/MJ) Observation
- 8. | Presentation title 8/14 Behavior of PRICE_COMMODITY: two mechanisms • From 2030 to 2050, PRICE_COMMODITY aligns with CLC of techs without constraints (lightoil ⇨ ethanol ⇨ methanol). • From 2055, electricity reaches the upper share limit, activating the share constraint, and PRICE_COMMODITY aligns with the weighted average cost of all deployed technologies, including electricity electricity gas lightoil ethanol *0.03 $/MJ ~ 0.1 $/kWh ~ 1 $/L Conventional LC and PRICE_COMMODITY (R12_NAM) Conventional LC and PRICE_COMMODITY ($/MJ)* PRICE_COMMODITY of transport electricity ethanol methanol lightoil PRICE_COMMODITY of transport
- 9. 9/14 | Presentation title Breakdown of GLC Generalized Levelized Cost ($/MJ) 2030 elec trp eth ic trp gas trp loil trp meth ic trp coal trp eth fc trp foil trp h2 fc trp meth fc trp -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 2040 elec trp eth ic trp gas trp loil trp meth ic trp coal trp eth fc trp foil trp h2 fc trp meth fc trp -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 2050 elec trp eth ic trp gas trp loil trp meth ic trp coal trp eth fc trp foil trp h2 fc trp meth fc trp -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 2055 elec trp eth ic trp gas trp loil trp meth ic trp coal trp eth fc trp foil trp h2 fc trp meth fc trp -0.05 0 0.05 0.1 0.15 0.2 2080 elec trp eth ic trp gas trp loil trp meth ic trp coal trp eth fc trp foil trp h2 fc trp meth fc trp -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 2100 elec trp eth ic trp gas trp loil trp meth ic trp coal trp eth fc trp foil trp h2 fc trp meth fc trp -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 var&capa fuel constraint PRICE C OMMODITY lightoil ethanol methanol (1) CLC of Marginal tech determines PRICE_COMMODITY (2) The weighted average of CLC of introduced techs. determines PRICE_COMMODITY h2_fc
- 10. 10/14 | Presentation title Identifying Technology Contributions to PRICE_COMMODITY 𝑦𝑦𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 = � 𝑗𝑗∈𝐽𝐽0 𝑔𝑔𝑗𝑗 � 𝐵𝐵−1 𝑗𝑗,𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜 (where B denotes the optimal basis matrix of the subproblem)
- 11. | Presentation title 11/14 To sum… • Conventional Levelized Cost (CLC) is a metric that represents the priority of technology selection • Generalized Levelized Cost (GLC) supplements the cost of constraints • GLC of input technologies provides the price of output energy and services • and its breakdown helps in understanding their behavior
- 12. | Presentation title 12/14 Key takeaways • The key constraints determine the model output, i.e. the ‘characteristics’ of the model can change if the assumptions of such constraints change • Generalized Levelized Cost (GLC) is useful to explain the model behavior • This approach can facilitate more detailed comparisons across different LP-based models
- 13. 13/14 | Presentation title Related work Uwe Remme (Univ. Stuttgart -> IEA ) • One previous study that has applied duality theory to the analysis of TIMES model • The draft of working paper has been published in ETSAP web site, but it has not been published as an journal paper • The results of applying the method to actual model outputs have not been shown
- 14. International Institute for Applied Systems Analysis (IIASA) Schlossplatz 1, A-2361 Laxenburg, Austria iiasa.ac.at @IIASAVienna iiasa.ac.at/contact @IIASALive IIASA @iiasavienna iiasa-vienna Thank you for your attention !