Convergence Analysis of a Parallel Newton Scheme for Dynamic Power Grid Simulations
|Title||Convergence Analysis of a Parallel Newton Scheme for Dynamic Power Grid Simulations|
|Publication Type||Conference Paper|
|Year of Publication||2011|
|Authors||Zavala, VM, Robbins, BA|
|Conference Name||Proc. 1st International Workshop on High Performance Computing, Networking and Analytics for the Power Grid|
In this work, 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 the manifold given by the solution of the nonlinear system at the current time step parameterized in the "moving" iterating solution at the previous step. This property explains why the method can significantly reduce the number of iterations compared to sequential Newton methods. We have also found, however, that 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 developments.