Modeling adaptation as a flow and stock decision with mitigation

An effective policy response to climate change will include, among other things, investments in lowering greenhouse gas emissions (mitigation), as well as short-term temporary (flow) and long-lived capital-intensive (stock) adaptation to climate change. A critical near-term question is how investments in reducing climate damages should be allocated across these elements of a climate policy portfolio, especially in the face of uncertainty in both future climate damages and also the effectiveness of yet-untested adaptation efforts. We build on recent efforts in DICE-based integrated assessment modeling approaches that include two types of adaptation—short-lived flow spending and long-lived depreciable adaptation stock investments—along with mitigation, and we identify and explore the uncertainties that impact the relative proportions of policies within a response portfolio. We demonstrate that the relative ratio of flow adaptation, stock adaptation, and mitigation depend critically on interactions among: 1) the relative effectiveness in the baseline of stock versus flow adaptation, 2) the degree of substitutability between stock and flow adaptation types, and 3) whether there exist physical limits on the amount of damages that can be reduced by flow-type adaptation investments. The results indicate where more empirical research on adaptation could focus to best inform near-term policy decisions, and provide a first step towards considering near-term policies that are flexible in the face of uncertainty

A stochastic minimum principle and an adaptive pathwise algorithm for stochastic optimal control

We present a numerical method for finite-horizon stochastic optimal control models. We derive a stochastic minimum principle (SMP) and then develop a numerical method based on the direct solution of the SMP. The method combines Monte Carlo pathwise simulation and non-parametric interpolation methods. We present results from a standard linear quadratic control model, and a realistic case study that captures the stochastic dynamics of intermittent power generation in the context of optimal economic dispatch models.National Science Foundation (U.S.) (Grant 1128147)United States. Dept. of Energy. Office of Science (Biological and Environmental Research Program Grant DE-SC0005171)United States. Dept. of Energy. Office of Science (Biological and Environmental Research Program Grant DE-SC0003906

Technology Variation vs. R&D Uncertainty: What Matters Most for Energy Patent Success?

R&D is an uncertain activity with highly skewed outcomes. Nonetheless, most recent empirical studies and modeling estimates of the potential of technological change focus on the average returns to research and development (R&D) for a composite technology and contain little or no information about the distribution of returns to R&D—which could be important for capturing the range of costs associated with climate change mitigation policies—by individual technologies. Through an empirical study of patent citation data, this paper adds to the literature on returns to energy R&D by focusing on the behavior of the most successful innovations for six energy technologies, allowing us to determine whether uncertainty or differences in technologies matter most for success. We highlight two key results. First, we compare the results from an aggregate analysis of six energy technologies to technology-by-technology results. Our results show that existing work that assumes diminishing returns but assumes one generic technology is too simplistic and misses important differences between more successful and less successful technologies. Second, we use quantile regression techniques to learn more about patents that have a high positive error term in our regressions – that is, patents that receive many more citations than predicted based on observable characteristics. We find that differences across technologies, rather than differences across quantiles within technologies, are more important. The value of successful technologies persists longer than those of less successful technologies, providing evidence that success is the culmination of several advances building upon one another, rather than resulting from one single breakthrough. Diminishing returns to research efforts appear most problematic during rapid increases of research investment, such as experienced by solar energy in the 1970s.

Heterogeneous Unit Clustering for Efficient Operational Flexibility Modeling for Strategic Models

The increasing penetration of wind generation has led to significant improvements in unit commitment models. However, long-term capacity planning methods have not been similarly modified to address the challenges of a system with a large fraction of generation from variable sources. Designing future capacity mixes with adequate flexibility requires an embedded approximation of the unit commitment problem to capture operating constraints. Here we propose a method, based on clustering units, for a simplified unit commitment model with dramatic improvements in solution time that enable its use as a submodel within a capacity expansion framework. Heterogeneous clustering speeds computation by aggregating similar but non-identical units thereby replacing large numbers of binary commitment variables with fewer integers that still capture individual unit decisions and constraints. We demonstrate the trade-off between accuracy and run-time for different levels of aggregation. A numeric example using an ERCOT-based 205-unit system illustrates that careful aggregation introduces errors of 0.05-0.9% across several metrics while providing several orders of magnitude faster solution times (400x) compared to traditional binary formulations and further aggregation increases errors slightly (~2x) with further speedup (2000x). We also compare other simplifications that can provide an additional order of magnitude speed-up for some problems

Electricity Investments under Technology Cost Uncertainty and Stochastic Technological Learning

Given that electricity generation investments are expected to operate for 40 or more years, the decisions we make today can have long-term impacts on the electricity system and the ability and cost of meeting long-term environmental goals. This research investigates socially optimal near-term electricity investment decisions under uncertainty in future technology costs and policy by formulating a computable general equilibrium (CGE) model of the U.S. as a two-stage stochastic dynamic program. The unique feature of the study is a stochastic formulation of technological learning. Most studies that include technological learning utilize deterministic learning curves in which a given amount of investment, production or capacity leads to a given cost reduction. In a stochastic framework, investment in a technology in the current period depends on uncertain learning that will result and lower future costs of the technology. Results under stochastic technological learning suggest that additional near-term investment relative to what is optimal under no learning can be justified at technological learning rates as low as 10–15%, and at the 20–25% rates commonly found in literature for advanced non-carbon technologies, significant additional near-term investment can be justified. We also find it can be socially optimal to invest more in non-carbon technology when the rate of learning is uncertain compared to the case where the learning rate is certain. Increasing marginal costs produce an asymmetric loss function that under uncertainty leads to more near-term non-carbon investment in attempt to avoid the situation of high non-carbon costs and an external economic environment that creates high demand for non-carbon technology.The authors gratefully acknowledge the financial support for this work provided by the U.S. Department of Energy, Office of Science under grants DE-SC0003906 and DE-FG02-94ER61937; the U.S. Environmental Protection Agency under grant XA-83600001-1; and other government, industry, and foundation sponsors of the Joint Program on the Science and Policy of Global Change

Impact of unit commitment constraints on generation expansion planning with renewables

Growing use of renewables pushes thermal generators against operating constraints - e.g. ramping, minimum output, and operating reserves - that are traditionally ignored in expansion planning models. We show how including such unit-commitment-derived details can significantly change energy production and optimal capacity mix. We introduce a method for efficiently combining unit commitment and generation expansion planning into a single mixed-integer optimization model. Our formulation groups generators into categories allowing integer commitment states from zero to the installed capacity. This formulation scales well, runs much faster (e.g. 5000×) than individual plant binary decisions, and makes the combined model computationally tractable for large systems (hundreds of generators) at hourly time resolutions (8760 hours) using modern solvers on a personal computer. We show that ignoring these constraints during planning can result in a sub-optimal capacity mix with significantly higher operating costs (17%) and carbon emissions (39%) and/or the inability to meet emissions targets

Second-best instruments for near-term climate policy: Intensity targets vs. the safety valve

Current proposals for greenhouse gas emissions regulations in the United States mainly take the form of emissions caps with tradable permits. Since Weitzman's (1974) [3] study of prices vs. quantities, economic theory predicts that a price instrument is superior under uncertainty in the case of stock pollutants. Given the general belief in the political infeasibility of a carbon tax in the US, there has been recent interest in two other policy instrument designs: hybrid policies and intensity targets. We extend the Weitzman model to derive an analytical expression for the expected net benefits of a hybrid instrument under uncertainty. We compare this expression to one developed by Newell and Pizer (2006) [6] for an intensity target, and show the theoretical minimum correlation between GDP and emissions required for an intensity target to be preferred over a hybrid. In general, we show that unrealistically high correlations are required for the intensity target to be preferred to a hybrid, making a hybrid a more practical instrument in practice. We test the predictions by performing Monte Carlo simulation on a computable general equilibrium model of the US economy. The results are similar, and we show with the numerical model that when marginal abatement costs are non-linear, an even higher correlation is required for an intensity target to be preferred over a safety valve.Doris Duke Charitable Foundatio

An approximate dynamic programming framework for modeling global climate policy under decision-dependent uncertainty

Analyses of global climate policy as a sequential decision under uncertainty have been severely restricted by dimensionality and computational burdens. Therefore, they have limited the number of decision stages, discrete actions, or number and type of uncertainties considered. In particular, other formulations have difficulty modeling endogenous or decision-dependent uncertainties, in which the shock at time t+1 depends on the decision made at time t. In this paper, we present a stochastic dynamic programming formulation of the Dynamic Integrated Model of Climate and the Economy (DICE), and the application of approximate dynamic programming techniques to numerically solve for the optimal policy under uncertain and decision-dependent technological change. We compare numerical results using two alternative value function approximation approaches, one parametric and one non-parametric. Using the framework of dynamic programming, we show that an additional benefit to near-term emissions reductions comes from a probabilistic lowering of the costs of emissions reductions in future stages, which increases the optimal level of near-term actions