A Decoupled Time-Domain Simulation Method via Invariant Subspace Partition for Power System Analysis

Abstract

Abstract-A decoupled method is proposed to deal with timedomain simulation for power system dynamic analysis. Traditionally, there are two main categories of numerical integration methods: explicit methods and implicit methods. The implicit methods are numerically stable but require more computational time to solve the nonlinear equations, while explicit methods are relatively efficient but may cause a numerical stability problem. This paper proposes a new hybrid method to take advantage of both explicit and implicit methods based on the invariant subspace partition. The original power system equations are decoupled into two parts that correspond to the stiff and nonstiff subspaces. For the stiff invariant subspace, the implicit method is applied to achieve numerical stability, and the explicit method is employed to handle nonstiff invariant subspace for the computational efficiency. As a result, the new hybrid method is both numerically stable and efficient. The approach is demonstrated through New England 39-bus and IEEE 118-bus systems.Index Terms-A-stability, decoupled method, differential and algebraic equations (DAE), dynamical simulation, explicit methods, implicit methods, invariant subspace partition, power systems, stiff systems, time-domain simulation.

Semi-implicit Krylov deferred correction methods for differential algebraic equations

“…Electrical power system. Differential algebraic equations have been widely used in the study and engineering of the bulk transfer of electrical power (see e.g., [5,48,60]). Typical electrical power system networks include a large number of dynamic and static components such as generators, exciters, governors, loads, transformers, and other power electronic devices, where the dynamics and constraints for each individual component are often modeled by a system of DAEs.…”

“…When the fault occurs, the shunt admittances of the network are modified and the admittance matrix is recomputed. We neglect further details of this model and techniques to split other systems to stiff and non-stiff in general, and refer interested readers to [5,48,60].…”

“…As explicit schemes are applied to the non-stiff components and algebraic variables in the differential equations, the size of nonlinear system from the SI-KDC scheme is smaller than that from FI-KDC method, and therefore the SI-KDC preconditioning technique is more efficient than FI-KDC for this specific application. There exist many numerical simulation tools and methods for power systems [2,40,60], including the techniques based on splitting the DAE systems to differential and algebraic parts and solving them separately using ODE solvers for the differential parts and a Newton-type method (e.g. Newton-Raphson) for algebraic components.…”

Numerical simulation of Stochastic Differential Algebraic Equations for power system transient stability with random loads

“…An alternative and more practical approach is time-domain simulation, which is utilized in transient stability analysis by both industrial engineers and academic researchers. A considerable amount of effort has been devoted to the numerical solution of DAEs [2]- [3] and the application to power systems [4]- [15]. Considering the large scale of a real power system, the effort to improve the computational efficiency is continually on-going.…”

“…The parallel implementation of the transient stability simulation includes waveform relaxation [4]- [6] and other methods [7]- [9]. Moreover, even in a serial environment, many accelerating techniques are proposed, such as variable-step methods [10]- [11], mutlirate methods [12]- [14], and flexible reconfiguration of explicit or implicit integration methods [11], [15].…”