Solving Differential-Algebraic Equations in Power System Dynamic Analysis with Quantum Computing

TL;DR

This paper explores how quantum computing can efficiently solve complex differential-algebraic equations in power system dynamics, potentially transforming large-scale power grid analysis.

Contribution

It introduces a quantum algorithm framework for converting DAEs to ODEs, encoding data into qubits, and solving them with quantum linear solvers, advancing power system analysis methods.

Findings

Quantum algorithms solve power system DAEs with polynomial complexity in log(system size).

The approach accurately captures system nonlinearity using Hamiltonian simulation.

Advanced scientific machine learning tools facilitate implementation of quantum solutions.

Abstract

Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system nonlinearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, i.e. Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.