W e addressed the problem of developing a model to simulate at a high level of detail the movements of over 6,000 drivers for Schneider National, the largest truckload motor carrier in the United States. The goal of the model was not to obtain a better solution but rather to closely match a number of operational statistics. In addition to the need to capture a wide range of operational issues, the model had to match the performance of a highly skilled group of dispatchers while also returning the marginal value of drivers domiciled at different locations. These requirements dictated that it was not enough to optimize at each point in time (something that could be easily handled by a simulation model) but also over time. The project required bringing together years of research in approximate dynamic programming, merging math programming with machine learning, to solve dynamic programs with extremely high-dimensional state variables. The result was a model that closely calibrated against real-world operations and produced accurate estimates of the marginal value of 300 different types of drivers.

We address the problem of modeling long-term energy policy and investment decisions while retaining the important ability to capture fine-grained variations in intermittent energy and demand, as well as storage. In addition, we wish to capture sources of uncertainty such as future energy policies, climate, and technological advances, in addition to the variability as well as uncertainty in wind energy, demands, prices and rainfall. Accurately modeling the value of all investments such as wind and solar requires handling fine-grained temporal variability and uncertainty in wind and solar, as well as the use of storage. We propose a modeling and algorithmic strategy based on the framework of approximate dynamic programming (ADP) that can model these problems at hourly time increments over a multidecade horizon, while still capturing different types of uncertainty. This paper describes initial proof of concept experiments for an ADP-based model, called SMART, by describing the modeling and algorithmic strategy, and providing comparisons against a deterministic benchmark as well as initial experiments on stochastic datasets.

The purpose of this two-part study is to model the effects of large penetrations of offshore wind power into a large electric system using realistic wind power forecast errors and a complete model of unit commitment, economic dispatch, and power flow. The chosen electric system is PJM Interconnection, one of the largest independent system operators in the U.S. with a generation capacity of 186 Gigawatts (GW). The offshore wind resource along the U.S. East Coast is modeled at five build-out levels, varying between 7 and 70 GW of installed capacity, considering exclusion zones and conflicting water uses. This paper, Part I of the study, describes in detail the wind forecast error model; the accompanying Part II describes the modeling of PJM's sequencing of decisions and information, inclusive of day-ahead, hour-ahead, and real-time commitments to energy generators with the Smart-ISO simulator and discusses the results. Wind forecasts are generated with the Weather Research and Forecasting (WRF) model, initialized every day at local noon and run for 48 hours to provide midnight-to-midnight forecasts for one month per season. Due to the lack of offshore wind speed observations at hub height along the East Coast, a stochastic forecast error model for the offshore winds is constructed based on forecast errors at 23 existing PJM onshore wind farms. PJM uses an advanced, WRF-based forecast system with continuous wind farm data assimilation. The implicit (and conservative) assumption here is that the future forecast

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