The power grid is undergoing probably the most transformative transition in the last 50 years. Introduction of clean, but intermittent (sporadic) renewable generation introduces an unprecedented level of uncertainty in power system operation. At the same time, the society becomes more and more dependent on reliable supply of power and more sensitive to power outages. Maintaining power system security i.e. its ability to withstand most probable disturbances is an extremely challenging computational problem. Millions of scenarios have to be fast screened by operators and contingency plans prepared for the most dangerous of them. The key objective of this project is to develop a new generation of computational techniques that would allow fast identification of safe operating conditions that ensure system resiliency. This goal is achieved by targeted advancement and adaptation of the modern optimization and nonlinear analysis techniques to specific challenges faced by the power industry. The latter include but are not limited to: estimation of the reserve levels necessary for operation in the presence of intermittent wind power, identification of the most dangerous line failure scenarios, design of the most effective remedial action plans. The research activities will be tightly interwoven with educational and outreach efforts. Undergraduate and high-school students from underrepresented minorities will be engaged in the group research and educational activities. A set of simple power-grid inspired puzzles will be developed that will help explaining the kids and the broad audience the technical trade-offs and decisions that the power industry faces today. Finally, a new EdX introductory class on power systems with interactive problems will be developed to help in educating the future engineering workforce for power industry.
The technical approach of the research part of the project is based on the idea of constructing safe operation regions in parameter space where the solution is guaranteed to exist and satisfy operational constraints. These "certificates" are formally an inner approximation of the feasibility set and can be constructed via a variety of techniques with the most general relying on Sum-of-Squares approaches. The project will explore possible representations of the mathematical problems appearing in the context of power system operations and security assessment. Specific problems that will be naturally addressed with the developed mathematical tools include computation of do-not-exceed limits, screening of N-1 and N-2 contingencies for AC power flow model, verification of the remedial actions, assessment of voltage stability margins in the presence of distributed reactive power control. A hierarchy of certificates will be constructed covering the conservativeness - complexity trade-off curve and their effectiveness demonstrated on standard IEEE testcases. The implementations of the codes will be linked to the mostpopular academic analysis packages and release under open source license in public domain.
