Computational Methods for Stability Assessment of Power Systems with High Penetration of Clean Renewal Energy

The electrical power grid is currently undergoing the architectural revolution with the increasing penetration of renewable and distributed energy sources and the presence of millions of active endpoints. Introduction of these novel components affects the stability of the system, i.e. its ability to return to normal operating conditions after disturbances. Lack of stability may compromise the reliable power supply and result in cascading blackouts in the most dramatic scenarios. The key intellectual merit of the project will be demonstrated through the development of a theoretical foundation for the problem of stability assessment of future power grids with high levels of renewable energy penetration. Interdisciplinary team of researchers from 3 US institutions will bring in cutting edge innovations from a number of fields like power systems dynamics and control, numerical algebraic geometry, and nonlinear systems in order to develop the computational tools to analyze the highly nonlinear dynamic behaviors and to certify stability/feasibility of operating points in the next generation power grids. From broader impact perspective the project addresses some of the most difficult and important challenges of modern society. The technology transfer of the results to public and private companies will provide direct benefit to the society by providing new open source tools for better economic decision making, protection of national security and informing of public policy. Other broader impacts include but are not limited to: 1) raising awareness of the stability related problems among applied mathematics and controls community, 2) Organization of a joint seminar between the applied mathematics and electrical engineering departments at University of Notre Dame, 3) Organization of special sessions and workshops on power system modeling and control in upcoming conferences, namely American Control Conference 2016 in Boston 4) engagement of underrepresented groups in research and education activities and development of custom tailored summer research projects for interested students. 5) Development of new graduate level specialized classes on advanced topics in smart grids.

In heavily stressed operating conditions, the nonlinear interactions play a critical role in power system dynamics and its response to disturbances. Introduction of renewable generation will affect both the structure of operating points and their stability properties. Implicit assumptions in traditional stability analysis techniques developed for conventional hierarchical nature of power grid structure may be violated and the techniques may not be applicable to future power grids. The goal of this project is to develop a new generation of computationally tractable but engineering wise accurate approaches to help the operators to assess the stability of operating points in renewable-integrated power systems. More specifically, the project will develop new techniques for constructing Lyapunov functions-based stability certificates for large-scale power systems, and novel ways of representing the complicated switch-type nonlinearities in polynomial form. New generation of efficient and robust homotopy algorithms will be developed and applied to practical problems in power systems. PI Chakrabortty and his group will be responsible for the development and validation of tractable but at the same time accurate dynamic models of power systems with renewable generations. The group of Turitsyn and Vu will be studying and exploring new approaches to construction of stability certificates for large scale dynamic model of power systems, and will be analyzing the nonlinear sensitivities of operating point with respect to generation levels of renewable generators and other uncertain parameters. PI Mehta will be leading the effort on the advancement of recently developed Numerical Polynomial Homotopy Continuation algorithms that will be used for the analysis of operating conditions of nonlinear systems developed in the first two thrusts.