The legacy power grid of the twentieth century has undergone transformational changes in the last two decades -- industry deregulation leading to competitive electricity markets, deep penetration of renewables for reducing the carbon footprint, large scale deployment of sensors such as phasor measurement units and smart meters enabling unprecedented monitoring capabilities and utilizing flexible loads for demand response to close the loop in real-time. These new elements have introduced significant heterogeneous uncertainties in the power systems, requiring the future grid to be not only resilient against these uncertainties, but also to dynamically steer these uncertainties when possible. This research project will deliver a set of novel mathematical algorithms and numerical toolbox to propagate and control the stochastic uncertainties modeled as time-varying joint probability density functions subject to complex interconnected power systems dynamics. The theory and algorithms to be developed in this research project will have impact on multiple applications in power systems including the transient stability analysis under stochastic load perturbations and intermittent renewable generation, as well as the design of controller to steer the state probability density function over finite horizon to achieve desired transient performance under uncertainties. Concomitantly, the mathematical framework will be generic enough to be applicable for ensemble-level prediction and control in any large network of nonlinear oscillators, with potential applications in systems biology, and robotics. Overall, the proposed scientific activities will significantly shift the perspective on how the mathematical analysis and scalable simulation of interconnected uncertain nonlinear systems can be done.
Typically, the joint probability density functions of interest for realistic power systems simulation have high dimensional support, and trajectory-level nonlinearities induce non-Gaussianity, thereby requiring non-parametric computation. For example, transient stability analysis in the presence of stochastic renewables, and uncertainties in the initial conditions and parameters requires scalable yet rigorous predictive algorithms that do not suffer from the "curse-of-dimensionality". The proposed research will enable fast prediction and finite-time minimum effort control of joint probability density functions in power systems simulation by harnessing the emergent theory of optimal mass transport and Schrodinger bridge. The algorithms to be developed in this project will avoid spatial discretization or function approximation, and instead use the novel proximal recursions on the manifold of probability density functions via probability weighted scattered point cloud evolution -- an approach the principal investigator has recently developed. The resulting algorithms will be able to handle real-time stochastic simulation with thousands of interconnected generators and loads. This research will contribute to the development of next-generation algorithmic tools at the confluence of applied probability, optimization and control theory by specifically exploiting the structural nonlinearities in power systems dynamics. From an engineering perspective, this research will catalyze disruptive innovation on power systems stochastic dynamics and control simulation with a general-purpose numerical toolbox permitting rapid proliferation. The project will help build the principal investigator's leadership in education at the University of California Santa Cruz by integrating the research in classrooms and outreach activities. Software toolbox resulting from this research will be released via GitHub.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
