Frequency Robust Control Application in Islanded Microgrids Considering Parametric Uncertainties and Distinct Photovoltaic Penetration Rate Scenarios

In this paper, a cascaded two-level hybrid control scheme based on multi-variable robust
$\mathcal {H}_{\infty }$
and proportional integral control is proposed for primary frequency control of an island mode microgrid consisting of a diesel engine generator, a photovoltaic energy source, an energy storage system, and an aggregated static load. Topological and nonlinear averaged models of each subsystem are introduced, followed by linearized frequency-control-oriented modelling of the entire system. Then, for currents control, conventional proportional-integral-based tracking controllers placed on a lower control level are designed, with their reference values generated from the output of an
$\mathcal {H}_{\infty } $
-control-based upper level. A comprehensive methodology that casts the specific engineering demands of microgrid operation into the
$\mathcal {H}_{\infty }$
control formalism is outlined. Additionally, it is demonstrated how closed-loop dynamic performance requirements must at their turn be taken into account in the initial microgrid setup and sizing, namely in appropriately choosing and rating the energy storage system. Numerical simulations performed with MATLAB®/Simulink® show the validity and effectiveness of the proposed frequency robust control technique in the presence of multiple photovoltaic power step changes on a kVA-rated microgrid. A robust performance analysis of the previously designed
$\mathcal {H}_{\infty }$
controller is performed under numerous uncertainty levels in the steady-state value of the supercapacitor state of charge and multiple photovoltaic power step changes to determine if the closed-loop system remains robust from a performance standpoint around its nominal design. The
$\mathcal {H}_{\infty }$
control design procedure allows a further investigation on how to link time-domain dynamic performance specifications (e.g., desired control objectives) and frequency-domain specifications (e.g., via so-called weighting functions) in a systematic and optimal manner (i.e., automation for their design or expert modelling), from which an useful guide can be created for practical control engineers in the future. Distinct photovoltaic penetration rate scenarios together with respective computed
$\mathcal {H}_{\infty } $
controllers, on the other hand, are examined to determine whether or not an
$\mathcal {H}_{\infty } $
optimal control solution that is robust in performance to a variety of photovoltaic power step variations relative to the rated operating point can always be generated.