Optimizing Energy Futures: Applying a Novel Technique

1. Application of a novel Optimization technique to Produce Maximally Different Energy Futures Joseph F. DeCarolis, Assistant Professor Department of Civil, Construction, and Environmental Engineering North Carolina State University jdecarolis@ncsu.edu

2. Motivation • Aggressive climate policy will bring about fundamental changes in the way energy is produced and consumed • Energy-related decisions with long-lived consequences must be made today with the best possible information • Energy-focused optimization models have emerged as an important tool to explore different energy futures using a structured and self-consistent set of assumptions

3. The Challenge of Uncertainty Energy and integrated assessment models are used to determine what could or should happen in the future Addressing large future uncertainties a critical challenge for energy modelers Must address 2 types of uncertainty: • Structural: imperfect and incomplete set of equations describing the system being modeled • Parametric: imperfect knowledge of model inputs

4. The Conventional Approach To deal with structural uncertainty, build more complex models that account for additional processes or effects → Add additional objectives, constraints, or processes to address unmodeled issues → Increasing complexity then makes parametric sensitivity analysis more difficult → Run a few detailed scenarios Many large models contribute relatively little insight about alternative ways to structure and solve the problem at hand (Morgan and Henrion, 1990)

5. Limitations of Energy Models Accurate predictions by energy models extending over several decades would require both accurate model structure and precise specification of inputs Large and irreducible uncertainties preclude this possibility Poor performance of past predictions provide validation Better approach would systematically flex models in order to stretch our thinking, challenge preconceptions, and suggest creative solutions

6. Rethinking the Role of Optimization Models Insights from Brill (1979) are remarkably prescient with regard to energy modeling today Models are always a simplification of reality, particularly in complex planning problems Rather than burden models with additional objectives and complexity in an effort to obtain “the answer”, generate near-optimal alternatives that facilitate comparison Approach recognizes that model’s optimal solution is likely to be inaccurate due to structural uncertainty

7. How Optimal is the “Optimal” Solution? Consider an optimization model that only includes Objective 1 and leaves Objective 2 unmodeled. The true optimum is within the feasible, suboptimal region of the model’s solution space. Viable alterative solutions exist within the model’s feasible region. Non-inferior frontier Objective 2 Objective 1 Example adopted from Brill et al. (1990).

8. Modeling to Generate Alternatives Need a method to explore an optimization model’s feasible region → “Modeling to Generate Alternatives”† MGA generates alternative solutions that are maximally different in decision space but perform well with respect to modeled objectives The resultant MGA solutions provide modelers and decision-makers with a set of alternatives for further evaluation †Brill (1979), Brill et al. (1982), Brill et al. (1990)

9. Hop-Skip-Jump (HSJ) MGA Brill et al. (1982) Steps: • Obtain an initial optimal solution by any method • Add a user-specified amount of slack to the value of the objective function • Encode the adjusted objection function value as an additional upper bound constraint • Formulate a new objective function that minimizes the decision variables that appeared in the previous solutions • Iterate the re-formulated optimization • Terminate the MGA procedure when no significant changes to decision variables are observed in the solutions

10. HSJ MGA Mathematical formulation where: Krepresents the set of indices of decision variables with nonzero values in the previous solutions is the jthobjective function Tjis the target specified for the jth modeled objective Xis the set of feasible solution vectors

11. Interpretation of MGA Solutions MGA solutions can be interpreted as equally plausible alternatives to the model’s optimal solution given that structural uncertainty exists Question: Is there a way to reproduce the MGA solution using the original model formulation? Affirmative answer suggests a linkage between MGA and parametric sensitivity analysis of the original model.

12. A Simple MGA Example Original Formulation First MGA Iteration x2 1 slack x1 1

13. Application to a Simple Electric Sector Model What effect might a cap-and-trade proposal have on the electric sector? Cap-and-trade (H.R. 2454) pending in Congress; 83 percent reduction in CO2e emissions by 2050 Suppose this cap applied only to the electric sector without offsets Assume new capacity must be installed to replace all existing fossil-based plants and meet growing demand

14. The Electric Sector Challenge Objective is to deploy new generating capacity in the form of wedges, using the approach outlined in Pacala and Socolow (2004) Model optimizes the number and size of wedges The projection of business-as-usual electric sector electricity generation (TWh) and CO2 emissions is based on a linear extrapolation of CO2 emissions projected in the Annual Energy Outlook 2009 reference case (EIA, 2009a).

15. Model Formulation • Where: • xi is the technology-specific installed capacity • B is the set of baseload technologies • N is the set of non-baseload technologies • F is the set of technologies emitting CO2 emissions • ai is the technology-specific capacity factor • P is total average power production Minimize: Subject to:

16. Technology Costs The cost coefficients in the objective function represent the 2050 annual cost associated with each technology: 13 different energy technologies included in the model Parameters in brackets are drawn directly from the U.S. EIA’s Assumption to the Annual Energy Outlook 2009 Assumed lifetime (T) is 40 years, discount rate (r) is 10% for all technologies

17. Wedges Under the CO2 Constraint Slack set to 25% of the minimum cost in MGA iteration Original Solution 1st MGA Solution

18. MGA Iterations in Carbon Constrained Case Slack = 25% Upper bound constraint on cost binding in all MGA iterations 2050 results

19. Other MGA Objectives

20. Identifying Robust Options Installed capacity across all BAU and CO2-constrained runs

21. Conclusions Large future uncertainties preclude accurate predictions over several decades with energy optimization models Such models are most useful when used to stimulate creative thought about possible solutions MGA provides a way to explore the feasible region to generate solutions that are maximally different in decision space, but perform well with respect to modeled objectives

22. Conclusions (continued) Simple electric sector model developed to illustrate MGA utility; application to a more sophisticated MARKAL model underway Modeling is an art; when to increase model complexity and when to rely on MGA is a subjective judgment by the modeler.

23. Thanks for your time! I’d like to acknowledge Downey Brill and Ranji Ranjithan for very useful discussions regarding the use of MGA techniques