Synchronous machine stability analysis using an efficient time domain methodology: unbalanced operation analysis

Abstract

This paper describes a methodology for the efficient stability analysis of the synchronous machine. The state space phase coordinates model of the synchronous machine incorporates the effects of time-varying and inter-spatial harmonic inductances. The dynamics of the synchronous machine are represented by a set of Ordinary Differential Equations (ODEs). The machine behaviour is analyzed under severe unbalanced operation conditions. The level of detail and accuracy obtained with the machine model in phase coordinates can not be achieved with conventional models based on the dq0 framework for unbalanced fault analysis. A Newton technique based on a Numerical Differentiation process is used for the acceleration of the convergence of the state variables to the Limit Cycle to obtain the machine initial conditions and the steady state previous to the fault application and after the fault is removed. The combined response obtained with methodology for swift time domain transient and periodic steady state analysis and the phase domain synchronous machine model is compared in terms of accuracy and computational efficiency against a widely used and accepted machine model of an Electro-Magnetic Transient Program (EMTP-ATP).

Re-examination of Synchronous Machine Modeling Techniques for Electromagnetic Transient Simulations

“…2, the transient responses produced by all models coincide and converge to the reference solutions. This clearly demonstrates that these models are all equivalent and predict the unbalanced operations with acceptable accuracy for the given time step, which is contrary to the conclusions made in [24]- [28].…”

“…The authors of [24]- [26] suggested that the different simulation results obtained by the and PD models may be caused by "different data based on their frames of reference" [24] and listed the machine's internal circuit data and test data in the Appendices of [24], [25]. However, these two sets of data are equivalent, as is shown in [21].…”

“…In [24]- [26], the authors claim that the machine model "assumes perfectly balanced operation conditions in machine" and "cannot accurately describe the transient and steady-state unbalanced operation of the synchronous machine." The authors of [27] and [28] made similar conclusions by comparing the simulation results of the and PD models under unbalanced operation.…”

“…In this paper, computer studies are conducted using the same synchronous machine as in [24]- [26] to demonstrate that the machine model, PD model, and VBR model all give identical simulation results for unbalanced operation, provided that the simulation time-step is sufficiently small. This result is expected as all of these models can be derived from each other and are therefore equivalent in the continuous time domain.…”

“…This result is expected as all of these models can be derived from each other and are therefore equivalent in the continuous time domain. The claims made in [24]- [28] that the machine model cannot represent unbalanced operations are unfounded. The difference in simulation results, however, may possibly arise from inconsistent machine parameters, problems with user interfaces, and/or model implementation.…”