Collaborative Research: AMPS: New sensitivity and control theory and tools for systems exhibiting extreme behaviors and faults with application to wind turbines

University Of Cincinnati Main Campus, Cincinnati OH

Investigators

Abstract

Many modern power systems, including wind turbines, exhibit irregular behavior due to exposure to uncontrollable conditions (e.g., extreme weather) and transitions between different operating conditions (e.g., different modes of power generation). It is desirable to minimize the negative consequences associated with power systems undergoing these extreme events, while maintaining system objectives/targets during normal operating times. However, standard mathematical tools and computational methods cannot be applied in such scenarios with acceptable guarantees of accuracy and robustness. Motivated by this, the PIs seek to develop a novel theoretical and numerical toolkit with the following broad aims in mind: (i) it is suitable for analysis, design, control, and optimization of dynamic systems that exhibit irregular behavior such as but not limited to modern power systems; and (ii) it is accurate, robust, and user-friendly. The developed tools will be tested through application to modern wind turbine power systems, with goals of maximizing power generation and minimizing extreme behavior effects for the power delivered to the grid. Additional broader impacts of this multidisciplinary research include its usefulness/relevance to many fields of systems control and its overlap with issues in emerging technological and implementation challenges found in green energy, sustainability, and global warming. Moreover, this project will train graduate and undergraduate students, including those from underrepresented populations, in STEM fields. Recent advances in generalized derivatives theory now allow for a computationally-relevant sensitivity theory for nonsmooth modeling frameworks, including nonsmooth ordinary-differential equations (ODEs) and differential-algebraic equations (DAEs). This sensitivity theory is practically implementable and provides first-order generalized derivative information that may be supplied to dedicated numerical methods with guaranteed convergence rates. Moreover, it allows for the development of tools for system analysis, control, and optimization. Other approaches, such as smoothing approximations, necessarily introduce user-defined parameters and numerical error and do not typically come with guarantees of recovering the true behavior of the system in the limit. Since nonsmooth ODEs and DAEs are an appropriate modeling framework for many systems, such as but not limited to modern wind turbine power systems (WTPSs), that exhibit nonsmoothness due to uncontrollable conditions and/or transitions between operating conditions, this nonsmooth ODE and DAE theory is relevant to this project, which has three broad goals: First, the PIs aim to develop a dynamic sensitivity theory for nonsmooth/discontinuous ODE and DAE systems that is computationally relevant and applicable to a wide class of systems. This includes extending existing smooth sensitivity-based dynamic and control system analysis methods to the nonsmooth and/or discontinuous setting. Second, they seek to extend the theory and application of control theory and methods for a wide class of nonsmooth and/or discontinuous ODE and DAE systems. Third, the project apply the developed theory and tools to improve the analysis and control capabilities of WTPSs, in order to increase the resilience of WTPSs, which are quite different from traditional power systems, and the power grid. That is, the application goal will be minimizing, or suppressing, negative consequences resulting from WTPSs exposed to extreme situations and maintaining system objectives/targets desirable in normal times as much as possible (i.e., with the least possible disruption due to extreme events). 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.