A New Convex Approach for Grid-Supporting Inverter Control Based on DLMIs

The objective of this article is to validate a dynamic output-feedback (DOF) control synthesis methodology to be implemented through digital signal processors in the scope of electrical microgrid applications. The DOF controller, originally designed in continuous-time, is developed aiming to comply with strict transient behavior requirements associated with electrical systems, by using an adaptation of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {D}$</tex-math></inline-formula>-stability concept to handle linear systems affected by time-varying parameters (linear parameter varying model). In order to allow a digital implementation of the control action, a discrete-time equivalent representation of the continuous-time DOF controller is obtained from the Taylor series expansion of the exponential terms associated with the discretization. Additional contributions of this article include: the use of a formulation based on differential linear matrix inequalities to ensure the stability of the hybrid system (composed of the analog plant and the digital controller), and the validation of the redesigned controller performance when applied to a real-time simulation of a three-phase inverter with a grid-supporting configuration emulated via hardware-in-the-loop device. The results demonstrate that the controlled system has achieved a regular operation for all the load cases investigated after the anomalies presented, even regulating a voltage drop of 20%. The proposed method was compared with a method in the literature, showing a decrease of 17.5% in the harmonic distortion of the currents holding similar voltage distortion.