Power System Dynamic Analysis Using Quantum Linear Differential Equation Solver Oracle

This paper presents a quantum computing framework to solve a system of nonlinear ordinary differential equations (ODEs) used in the power system dynamic analysis. The framework exploits the linearization of power system dynamics’ nonlinear ODEs at particular points of state variable vector to construct a system of linear ODEs (LDE) modeling the system dynamics around considered points within a small time interval. The analytical solution of this LDE system in the matrix exponential form can be simulated and transformed into quantum states using the popular design of a Variational Quantum Circuit (VQC) acting as a quantum LDE solver oracle. The oracle can be used repeatedly to construct the trajectory of the original nonlinear power system dynamics along the time evolution. Obtained numerical results using Julia-based simulatable quantum circuits demonstrate that we can tailor and leverage recent advances in quantum computing algorithms, originally designed for linear systems, to model nonlinear power system dynamics with high accuracy.