(544f) Optimal Deployment Under Uncertainty of Negative Emissions Technologies in the European Union Power System

Most scenarios that seek to limit global warming below 2°C rely on negative emissions technologies and practices (NETPs) to remove historical and future anthropogenic emissions. However, the cost, potential, and implications of these technologies at scale are still highly uncertain, especially when predictions are made over a long time horizon. In particular, omitting uncertainties in the modeling of NETPs when assessing the technology readiness level and potential carbon dioxide removal (CDR) may lead to suboptimal deployment paths or even infeasible solutions, particularly in long-term planning.

Uncertainty is broadly classified into exogenous, i.e., decision-independent, and endogenous (type 1 or type 2), i.e., when the realization of the uncertain parameters depends on the decision [1]. In process systems engineering, products demand and prices are examples of exogenous parameters commonly modeled as uncertain. In contrast, technical parameters such as process yield are endogenous – type 2 since their realization is contingent on whether a process is performed or not. Different types of mathematical frameworks can be used to account for uncertainties in optimization problems, such as stochastic programming, chance-constrained programming and robust optimization [2].

In the context of NETPs, Grant and co-authors [3] carried out a pioneering study exploring the feasibility of CDR technologies using stochastic programming. They minimize the expected cost of a selected portfolio of technologies that meets the energy demand in the integrated assessment model TIAM-Grantham [3]. Given an expert-informed probability distribution, they model the uncertain CDR potentials of three selected NETPs, finding that emissions reductions should be performed as fast as possible with renewables that are certain today, instead of relying on uncertain future CDR options.

More recently, Galán-Martín et al. [4] developed a fully deterministic model that identifies the optimal deployment pathway to maximize net carbon dioxide removal [4]. The multi-period linear programming RemovAl oPtImization moDel (RAPID) integrates direct air capture (DAC) and bioenergy with carbon capture and storage (BECCS) in the European power mix. BECCS and DAC can be deployed starting from a given year from 2020 until 2100. Additionally, the authors presented confidence intervals by performing an a posteriori uncertainty analysis on economic and emission parameters.

Here, building on the previously developed RAPID, we apply multi-stage stochastic programming accounting for exogenous uncertainty in the electricity demand, which has to be met as an equality constraint, by dropping the assumption of perfect foresight for the modeling timeframe. The model minimizes the power system's total cost, while meeting a net-zero emissions target in 2050 following a carbon neutrality policy. We introduce fixed-charge costs in the objective function by adding binary variables for the capacity expansion of each technology modeled, which gives rise to the mixed-integer linear program RAPIDU (RemovAl oPtImization moDel under Uncertainty). As a first step to assess the feasibility of NETPs in future scenarios, we apply the methodology developed by Apap and Grossmann [1], adapted to our planning problem. Notably, we define non-anticipativity constraints for the first-stage and recourse variables in all the time periods, excluding the last one. Our study considers two possible realizations of the demand – high and low – for each European Union country, resulting in 64 scenarios.

We relax the constraint on the deployment of the NETPs from a given year, letting the model decide when to install the technologies according to the emissions targets. The minimum cost solution features only BECCS as NETPs starting in 2020, while DAC is never deployed in the given time horizon. Capacity expansions take place in subsequent time periods until 2050. The total cost of the power system increases by roughly 10% compared to the case where uncertainties are omitted.

The problem is implemented in the General Algebraic Modeling System (GAMS) software [5] version 35.2.0 and solved with the CPLEX 20.1.0.1 solver on an Intel i9-9900 CPU, 3.10 GHz computer with 32 GB RAM. RAPIDU features 7,871,425 continuous variables, 300,672 binaries and 4,342,346 equations. The solution time is 24,184 s with a 3% optimality gap using parallel threads. The computational time can be further reduced by applying a decomposition method.

This work highlights the advantages of accounting for uncertainties in NETs deployment planning to meet the climate targets. Our analysis can easily be extended to other uncertain parameters, i.e., carbon dioxide storage and biomass availability. To fully characterize the potential of NETPs under uncertainty, an endogenous analysis must be performed as the next step, where the resolution of the uncertainty depends on whether the technology is installed.

References

[1] Apap, R. M., Grossmann, I. E. Models and computational strategies for multistage stochastic programming under endogenous and exogenous uncertainties. Computers and Chemical Engineering 103, 233–274 (2017). http://dx.doi.org/10.1016/j.compchemeng.2016.11.011

[2] Can, L., Grossmann, I. E. A Review of Stochastic Programming Methods for Optimization of Process Systems Under Uncertainty. Frontiers Chemical Engineering 2, 622241 (2021). https://doi.org/10.3389/fceng.2020.622241

[3] Grant, N., Hawkes, A., Mittal, S., Gambhir, A. The policy implications of an uncertain carbon dioxide removal potential. Joule 5, 2593-2605 (2021). https://doi.org/10.1016/j.joule.2021.09.004

[4] Galán-Martín, Á., Vázquez, D., Cobo, S., Mac Dowell, N., Caballero, J. A., Guillén-Gosálbez, G. Delaying carbon dioxide removal in the European Union puts climate targets at risk. Nature Communications 12, 6490 (2021). https://doi.org/10.1038/s41467-021-26680-3

[5] Brooke, A., Kendrick, D., Meeraus, A. & Raman, R. GAMS—A User'sManual. (GAMS Development Corporation, 1998)