Publication
Solving Differential-Algebraic Equations in Power System Dynamic Analysis with Quantum Computing
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 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 non-linearity 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, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.
AI Summary
This journal article develops a quantum-computing framework for solving the differential-algebraic equations used in power-system dynamic simulation. The method first converts the original DAEs to nonlinear ODEs through index reduction, then uses amplitude encoding, polynomial approximation, tensor representations, Hamiltonian simulation, and quantum linear-equation solvers to map the time-domain computation into a form suitable for quantum algorithms. The framework is evaluated on both a single-machine-infinite-bus model and a WSCC three-machine nine-bus system, including simplified internal-node and more detailed generic DAE formulations with load disturbances and governor response. Quantum-formulated results closely track classical simulations across the reported cases, including a transformed generic model with dozens of states. The work extends the earlier conference formulation by demonstrating the approach on more complete power-system models and showing how symbolic scientific-computing tools can automate DAE transformation and support scalable quantum dynamic simulation.
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