Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Huynh Trung Thanh Tran, Hieu T. Nguyen, Long T Vu, Samuel T. Ojetola

Abstract: Power system dynamics are generally modeled by high dimensional non-linear 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 dis-tributed energy resources, whereas their computation time becomes sensitive due to theincreasing interconnection of the power grid with other energy systems. This paper demon-strates the use of quantum computing algorithms to solve DAEs for power system dynamicanalysis. We leverage a symbolic programming framework to equivalently convert thepower system’s DAEs into ordinary differential equations (ODEs) using index reductionmethods and then encode their data into qubits using amplitude encoding. The system non-linearity is captured by Hamiltonian simulation with truncated Taylor expansion so thatstate variables can be updated by a quantum linear equation solver. Our results show thatquantum computing can solve the power system’s DAEs accurately with a computationalcomplexity polynomial in the logarithm of the system dimension. We also illustrate the useof recent advanced tools in scientific machine learning for implementing complex com-puting concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantumcomputing solver with abstract representation for power engineering applications.