A highly parallel method for transient stability analysis

Abstract

In this paper, a new method for transient stability simulation is presented. The objective of this work is to exploit the maximum degree of parallelism that the problem presents. The transient stability problem can be seen as a coupled set of nonlinear algebraic and differential equations; by applying a discretization method such as the trapezoidal rule, the overall algebraicdifferential set of equations is transformed into an unique algebraic problem a t each time step. A solution that considers every time step, not in a sequential way, but concurrently, is suggested. The solution of this set of equations with a relaxation-type indirect method gives rise to a highly parallel algorithm. This parallelism consists of a parallelism in space (that is in the equations at each time step) and a parallelism in time. Another characteristic of the algorithm is that the time step can be changed between iterations using a nested iteration multigrid technique from a coarse time grid to the desired fine time grid to enhance the convergence of the algorithm. Also, this new method can handle all the typical dynamic models of realistic power system components. Test results are presented and compared with the sequential dishonest Newton algorithm for realistic power systems. KEY WORDSTrasient stability, parallel processing, dynamic simulation, parallel algorithm. assessment study of near term computer capabilities and their impact on power flow and stability simulation program". EPRI-TPS-77-749 , Final Report 2) H.

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

“…Parallel-in-time simulation strategies have been reported in [5,12,13,20]. Similar to space partitioning, these relaxation (e.g., Gauss-Jacobi) methods allow the time horizon to be partitioned and solved concurrently by dropping the coupling terms in the Newton system between neighboring times steps.…”

Making use of BDF-GMRES methods for solving short and long-term dynamics in power systems

“…A literature review on iterative methods and power systems problems revealed a majority of steady-state studies [3][4][5][6][7][8][9][10][11][12][13][14][15]. Despite time domain simulation be an important tool for dynamic assessment of power systems [16][17][18], the application of iterative methods have been focused only on the solution of short-term phenomena (transient stability) through implicit integration methods with fixed step sizes, taking advantage of parallel or distributed computing [3,4,13,14].…”

“…Despite time domain simulation be an important tool for dynamic assessment of power systems [16][17][18], the application of iterative methods have been focused only on the solution of short-term phenomena (transient stability) through implicit integration methods with fixed step sizes, taking advantage of parallel or distributed computing [3,4,13,14]. Besides, the reasons for the lower number of references related to time-domain analyses may be associated to the high computational cost when solving complex Differential Algebraic Equations (DAEs) due to the slow or non-convergence presented by earlier unpreconditioned iterative methods, or even by the use of low quality preconditioners.…”

Parallel dynamic simulation of power systems

“…The basic idea of using simultaneous implicit method using trapezoidal integration method for parallel processing is due to Alvarado [l]. He proposed Newton's method to solve the algebraic equations while LaScala et a1 [2] use the relaxation method on a hypothetical computer. We modify Alvarado's method in two respects (i) consider a detailed multi-machine system resulting in algebraic differential equations and (ii) use the supercomputer Cray 2 with multiple processors.…”