Network Power System
In applications involving network power systems, our research work is focused on a couple of different problems, which include real-time stability monitoring, stochastic stability and performance analysis of power systems in the presence of uncertain renewable, robust distributed optimization of a distributed system, data-driven analytics involving linear operator theoretic methods for reduced order modeling, and cyber security of power grid.
We have discovered data-driven methods based on the dynamical system theory for the real-time rotor angle and power system voltage stability monitoring using time-series data from Phasor Measurement Units (PMUs).
Our theoretical research on characterizing fundamental limitations for estimating and controlling nonlinear systems has led to systematic tools for analyzing the mean square stability and synthesizing network power systems with stochastic disturbances.
In particular, small signal stochastic stability of the network power system is analyzed to understand the effects of an increase in the penetration of renewable energy resources. Similarly, the distributed controller is designed to be robust to stochastic fluctuations in loads in demand response control problems.
Linear operator theoretic methods involving the Koopman operator are employed for the identification and reduced order modeling of power system dynamics using sensor data. The problem of uncertainty propagation and domain of attraction computation are also formulated and solved using spectral analysis of the Koopman operator.
The novel dynamical system-based approach we developed for solving robust optimization problems is applied to solving robust optimal power flow (OPF) problems in the presence of renewable uncertainty. The uncertainty from renewable is modeled as an uncertain parameter in the OPF problem. The dynamic system-based approach for solving the RO problem is also used to solve the robust OPF problem in a distributed manner and to design distributed real-time voltage control strategies in the distribution power system.