In their award-winning paper, titled “Uncertainty Propagation in Power System Dynamics with the Method of Moments,” the researchers address the problem of propagating state and parameter uncertainty in dynamic simulations of electrical power systems.
“As the amount of variable energy resources grows in the U.S grid, scientists and engineers need new frameworks to quantify the uncertainty that this will entail,” said Maldonado, a postdoctoral associate in Argonne’s Mathematics and Computer Science Division. “Researchers often employ Monte Carlo methods due to their generality, but they suffer from slow convergence in this type of problem. The method of moments offers an attractive alternative by computing an approximation using higher-order derivatives.”
Specifically, the Argonne researchers used the automatic differentiation package ForwardDiff written in Julia, a numerical computing language for high-performance computing. This conveniently allows the efficient and accurate computation of the Jacobian, Hessian, and higher-order tensors of the propagating function. With this strategy, uncertainty propagation can be incorporated into existing simulation tools.
The researchers compared their method of moments approach with a Monte Carlo simulation where, even for a small system, convergence was slow. To obtain the same accuracy as the method of moments, Monte Carlo required thousands of simulation runs. Furthermore, it was found that using higher-order derivatives significantly improved the precision in the computation of the first-order moments.
“We hope that scientists will find our method of moments approach useful not only for propagating uncertainties in power system dynamics but also for providing a basis for new stochastic optimization and control methods that can handle variable resources within the electrical power mix,” said Maldonado.
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