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Chase Dowling

During the 2016-17 academic year I plan to explore novel mathematical tools to solve the AC optimal power flow (OPF) problem. Cycles in a power grid network as well as stochastic variations in resources like wind and solar make solving the AC OPF problem difficult. With a better theoretical understanding, renewable power could be made more accessible to grid operators from moment to moment by providing assurances that, if an operator attenuates the state of specific buses in the grid, the rest of the grid can achieve an efficient state. Specifically, I believe that recent results in combinatorial Hodge theory can provide power engineers with a means of A) understanding the feasible solution region of the AC OPF problem over complex grid topologies and B) approximating individual bus potentials with respect to the grid’s feasible solution region. These tools will aid in future distributed control and efficient energy storage utilization.

Advisor Baosen Zhang- Electrical Engineering