(529f) Capacity Planning with Uncertain Endogenous Technology Learning

Adverse climatic changes and the ever-increasing energy demand have driven us to invest in renewable technology development to make them cost-competitive to traditional fossil-fuel-based energy sources. One of the major factors that dictate the cost reduction of a new technology is the increase in its deployment or cumulative production capacity. This correlation between cost and cumulative capacity falls under a broader concept of endogenous technology learning, which is usually expressed using learning curves [1]. In recent decades, technology learning due to scale-up of operations has driven down solar and wind power costs, making them increasingly economical.

A learning curve's dependence on the availability and reliability of historical data and forecasting tools makes estimating it a challenging task. Thus, often approximate and deterministic learning curves (for tractability purposes) are used to make capacity expansion decisions [2]. However, unanticipated variations in the estimated learning curve could often render the expansion decisions sub-optimal or even infeasible in some cases. To mitigate such scenarios, we extend the idea of incorporating technology learning in capacity planning problems by proposing a multistage stochastic programming [3] model that accounts for uncertainty in learning curves. The proposed mixed-integer linear programming (MILP) model accommodates both capital and operational decisions in a general process network that comprises a set of processes and resources.

For large-scale problems, binary investment decisions and a large number of non-anticipativity constraints (due to a large number of scenarios and endogenous uncertain parameters) often render the proposed stochastic optimization model intractable. Our work investigates the following potential pathways to reduce the computational difficulty for large-scale problems: (1) We explore reduction properties that can decrease the number of constrained scenarios; thus, reducing the model size. (2) We propose a branch-and-price [4,5] decomposition strategy that speeds up the algorithm through parallelization. Additionally, we propose an algorithm for evaluating the value of stochastic solution (VSS) for multistage problems with endogenous uncertainty. The effectiveness of the proposed stochastic optimization framework is demonstrated in a case study involving a technology network for a hydrogen-based economy.

References

[1] Anzanello, M. J., & Fogliatto, F. S. (2011). Learning curve models and applications: Literature review and research directions. International Journal of Industrial Ergonomics, 41(5), 573-583.

[2] Heuberger, C. F., Rubin, E. S., Staffell, I., Shah, N., & Mac Dowell, N. (2017). Power capacity expansion planning considering endogenous technology cost learning. Applied Energy, 204, 831-845.

[3] Apap, R. M., & Grossmann, I. E. (2017). Models and computational strategies for multistage stochastic programming under endogenous and exogenous uncertainties. Computers & Chemical Engineering, 103, 233-274.

[4] Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W., & Vance, P. H. (1998). Branch-and-price: Column generation for solving huge integer programs. Operations research, 46(3), 316-329.

[5] Lübbecke, M. E., & Desrosiers, J. (2005). Selected topics in column generation. Operations research, 53(6), 1007-1023.