Performance Comparison of Perturbation-Based and Quasi-Newton-Based Extremum-Seeking Control for Frequency Support of Low-Inertia Microgrids

Frequency stability issues are common in low-inertia microgrids due to the dominance of power electronics converter-based resources and comparatively low levels of inertia of synchronous generation. While many methods have been proposed for frequency support in these systems, it is challenging to ensure both stability and an adequate level of support without directly modeling the system. Perturbation-based extremum-seeking control (PESC) is a model-free adaptive control strategy that optimally sets the system's performance measure without requiring a mathematical system model. However, PESC offers poor transient performance due to design limitations, such as an averaging theory. Some modifications have been made to address these limitations; nevertheless, the modified design of PESC operates more as a model-based control. The Quasi-Newton method is a popular class of numerical optimizers attributed with a design procedure similar to model-free control that uses the gradient and an approximate inverse Hessian of the performance measure to run an optimization loop. This paper presents the design and compares the performance of the Quasi-Newton method and a model-based PESC for frequency support of microgrids. The simulation results illustrate the comparable performance of both control schemes and show the model-free control capability of the numerical optimization method for a class of nonlinear dynamic systems.