An algorithm is presented that exploits the maximum parallelism that the transient stability analysis problem can offer. By applying a stable integration method such as the trapezoidal rule, the overall algebraic-differential set of equations is usually transformed into a unique algebraic problem at each time step. By utilizing an indirect method for the solution of the set of nonlinear equations, a parallelism in space (that is, for all equations) and in time (that is, for all time steps) is obtained. The formulation permits, easily, the implementation of multigrid techniques. Theoretical aspects of the existence, uniqueness, and convergence of the algorithm are discussed.
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