New Stability Region for the Single-Loop AC-Voltage Control in <i>LC</i>-Filtered VSIs and Its Improvement by Means of Voltage Decoupling

Voltage-controlled voltage-source inverters with an output <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i>-filter are used in a wide variety of power supply applications. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i>-filters allow for the attenuation of switching harmonic content, but their resonance can compromise the stability of the system. One of the most common control techniques in these systems consists of a single-loop voltage control with proportional-resonant (PR) or resonant (R) controllers. Numerous previous publications have shown that these systems are only stable for certain ratios between the resonant frequency of the filter (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$f_{n}$</tex-math></inline-formula>) and the sampling frequency (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$f_{s}$</tex-math></inline-formula>), leading to the proposal of different methods to widen this stability region. However, existing methods are based on a continuous-time domain stability analysis, where some approximations are used. This article, after presenting a discrete-time domain stability analysis without approximations that results in a stability region different from that presented in previous publications, demonstrates that the single-loop voltage control with PR controller and capacitor voltage unitary decoupling allows working with positive proportional gains when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$f_{n}$</tex-math></inline-formula> is either above or below <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$f_{s}/3$</tex-math></inline-formula>, improving the performance of existing methods. The article also demonstrates that unitary decoupling of the capacitor voltage is not as effective with an R controller. Experimental tests confirm the theoretical analysis conducted.