Munoz, Francisco D.; van der Weijde, Adriaan H.; Hobbs, Benjamin F.; Watson, Jean-Paul W.
We investigate the effects of risk aversion on optimal transmission and generation expansion planning in a competitive and complete market. To do so, we formulate a stochastic model that minimizes a weighted average of expected transmission and generation costs and their conditional value at risk (CVaR). We show that the solution of this optimization problem is equivalent to the solution of a perfectly competitive risk-averse Stackelberg equilibrium, in which a risk-averse transmission planner maximizes welfare after which risk-averse generators maximize profits. This model is then applied to a 240-bus representation of the Western Electricity Coordinating Council, in which we examine the impact of risk aversion on levels and spatial patterns of generation and transmission investment. Although the impact of risk aversion remains small at an aggregate level, state-level impacts on generation and transmission investment can be significant, which emphasizes the importance of explicit consideration of risk aversion in planning models.
Progressive hedging, though an effective heuristic for solving stochastic mixed integer programs (SMIPs), is not guaranteed to converge in this case. Here, we describe BBPH, a branch and bound algorithm that uses PH at each node in the search tree such that, given sufficient time, it will always converge to a globally optimal solution. In addition to providing a theoretically convergent “wrapper” for PH applied to SMIPs, computational results demonstrate that for some difficult problem instances branch and bound can find improved solutions after exploring only a few nodes.
Remote sensing systems have firmly established a role in providing immense value to commercial industry, scientific exploration, and national security. Continued maturation of sensing technology has reduced the cost of deploying highly-capable sensors while at the same time increased reliance on the information these sensors can provide. The demand for time on these sensors is unlikely to diminish. Coordination of next-generation sensor systems, larger constellations of satellites, unmanned aerial vehicles, ground telescopes, etc. is prohibitively complex for existing heuristics- based scheduling techniques. The project was a two-year collaboration spanning multiple Sandia centers and included a partnership with Texas A&M University. We have developed algorithms and software for collection scheduling, remote sensor field-of-view pointing models, and bandwidth- constrained prioritization of sensor data. Our approach followed best practices from the operations research and computational geometry communities. These models provide several advantages over state of the art techniques. In particular, our approach is more flexible compared to heuristics that tightly couple models and solution techniques. First, our mixed-integer linear models afford a rig- orous analysis so that sensor planners can quantitatively describe a schedule relative to the best possible. Optimal or near-optimal schedules can be produced with commercial solvers in opera- tional run-times. These models can be modified and extended to incorporate different scheduling and resource constraints and objective function definitions. Further, we have extended these mod- els to proactively schedule sensors under weather and ad hoc collection uncertainty. This approach stands in contrast to existing deterministic schedulers which assume a single future weather or ad hoc collection scenario. The field-of-view pointing algorithm produces a mosaic with the fewest number of images required to fully cover a region of interest. The bandwidth-constrained al- gorithms find the highest priority information that can be transmitted. All of these are based on mixed-integer linear programs so that, in the future, collection scheduling, field-of-view, and band- width prioritization can be combined into a single problem. Experiments conducted using the de- veloped models, commercial solvers, and benchmark datasets have demonstrated that proactively scheduling against uncertainty regularly and significantly outperforms deterministic schedulers. Acknowledgement We would like to acknowledge John T. Feddema, Brian N. Post, John H. Ganter, and Swaroop Darbha for providing critical project stewardship and fruitful remote sensing utilization discus- sions. A special thanks to Mohamed S. Ebeida for his contributions to the development of the Maximal Poisson Sampling technique. We would also like to thank Kaarthik Sundar and Jianglei Qin for their significant scheduling algorithm and model development contributions to the project. The authors would like to acknowledge the Sandia LDRD program for their support of this work. Sandia National Laboratories is a multi-mission laboratory managed and operated by Sandia Cor- poration, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Energy storage (ES) is a pivotal technology for dealing with the challenges caused by the integration of renewable energy sources. It is expected that a decrease in the capital cost of storage will eventually spur the deployment of large amounts of ES. These devices will provide transmission services, such as spatiotemporal energy arbitrage, i.e., storing surplus energy from intermittent renewable sources for later use by loads while reducing the congestion in the transmission network. This paper proposes a bilevel program that determines the optimal location and size of storage devices to perform this spatiotemporal energy arbitrage. This method aims to simultaneously reduce the system-wide operating cost and the cost of investments in ES while ensuring that merchant storage devices collect sufficient profits to fully recover their investment cost. Finally, the usefulness of the proposed method is illustrated using a representative case study of the ISO New England system with a prospective wind generation portfolio.
Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.; Watson, Jean-Paul W.; Wets, Roger J.B.; Woodruff, David L.
We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. We report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.