Convergence analysis of a parallel newton scheme for dynamic power grid simulations

Abstract

We analyze the convergence properties of a parallel Newton scheme for differential systems. The scheme concurrently solves the time-coupled nonlinear systems arising from the application of implicit discretization schemes. We have found that the scheme acts as a tracking algorithm that converges to a moving manifold given by the solution of the nonlinear system at the current time step parameterized in the iterating solution of the previous step. This property explains why the method can significantly reduce the number of iterations compared with the sequential Newton method that marches forward in time. The method exhibits a theoretical lower bound on the number of iterations equal to the number of discretization points. A numerical study using a detailed dynamic power grid model is provided to demonstrate the scalability of the method.

On-line distributed prediction of traffic flow in a large-scale road network

“…However, a large number of iterations might be needed if the guessed initial states are far away from the actual states. In [26], a parallel Newton method is proposed to reduce 75% of iterations. The method can be interpreted as a Newton-Raphson method applied to a system in a entire simulation horizon instead of each time step.…”