AMPS: Collaborative Research: Stochastic Modeling of the Power Grid

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This project will develop mathematical models for the interactions between the economic stake-holders in the modern power grid. While the electricity market is becoming decentralized, understanding the underlying market forces in the presence of fluctuating market conditions and regulations remains inadequate. Providing higher quality information and modeling aids to decision makers is crucial in the drive to achieve grid efficiency and enhanced stability. It is also central to avoiding unintended consequences that have plagued economic policy-making for the grid and for making effective regulations that incentivize aligning stakeholder behavior with societal goals, such as climate change adaptation and investment in new technologies.The project will construct rigorous stochastic models and related numerical algorithms for quantitative assessment and analysis of how to guide the grid in its "smart" evolution. The research will address (i) long-term grid evolution, in particular investment in renewable generation and competition between different producer sectors; (ii) behavior of electricity prices and related financial contracts in the new era of deep renewable penetration, micro-grids, and new requirements on grid stability. The project blends together applied mathematics, game theory, and control, and extends the reach of stochastics to a key application area. The project will contribute to inter-disciplinary training in mathematical sciences at the PhD level and will enhance the exchange of ideas between mathematicians, operations researchers, engineers, and statisticians.