Boundary values methods for time-domain simulation of power system dynamic behavior

Time-domain solution of a large set of coupled algebraic and ordinary differential equations is an important tool for many applications in power system analysis. The urgent need for online applications as well as the necessity of integrating transient and long-term analysis in a unique code is the main motivation for developing more reliable and fast algorithms. In this paper, a class of algorithms which exploits the so-called parallel-in-time formulation is considered. These algorithms, developed to run on vector/parallel computers, also give the opportunity to develop new integration rules sharing interesting properties. Parallel-in-time boundary value methods (BVMs) are proposed for implementation in power system transient stability analysis. These methods are characterized by some advantages such as: the possibility to have high accuracy; to use efficiently the same method for stable and unstable problems; to treat stiff problems; and to be implemented efficiently on vector/parallel computers. Their application to the solution of linear differential algebraic equations (DAEs) has been proposed in the mathematical literature. In this paper, the authors extend their use to nonlinear DAEs and demonstrate the existence and uniqueness of the numerical solution as well as the convergence properties of the proposed algorithms. The theoretical results are utilized for the implementation of Newton/relaxation algorithms on a vector/parallel computer. Test results on a realistic network characterized by 662 buses and 91 generators are reported.