A Second-Order Singular Perturbation for Model Simplification for a Microgrid

As the integration of electronic-interfaced devices have increased, microgrid models have become too complex to perform a stability analysis. Thus, an effective model simplification method keeping most dynamics of the system becomes very essential. Singular perturbation is a common way for model simplification. However, its accuracy is insufficient when nonlinear properties dominate. This is caused by the "Quasi-Steady State Assumption" that traditional singular perturbation holds. By assuming that microgrid can only be stabilized when fast variables stop variating, the traditional method ignores some common phenomena before a stabilization occurs, leading to a loss of dynamics. To improve the accuracy, this paper proposes a "second-order singular perturbation". Here, the traditional "Quasi-Steady State" is updated to a scenario that third-order derivatives of fast variables become zero before the microgrid stabilizes. The updated assumption covers more common phenomena before a stabilization occurs. This leads to a more precise simplification. Simulation results indicate that the proposed method outperforms traditional singular perturbation in accuracy.