Rapid Multivariable Identification of Grid Impedance in DQ Domain Considering Impedance Coupling

Abstract

Identifying grid impedance at the point of common coupling is essential for the adaptive control and the online stability analysis of grid-connected converters. A balanced three-phase system is commonly modeled by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> components in the synchronous reference frame. In identification of the synchronous reference-frame impedance components, errors may occur due to the coupling of the system impedances; for example, a measurement injection that is intended to perturb only the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -channel current may also perturb the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -channel current, thus distorting the impedance measurements. Traditionally, sequentially performed measurements, where different injections are performed one after another at the same frequencies, have been required to tackle the impedance coupling. However, the sequential measurements are prone to changes in the operating conditions between the measurements. This article proposes a method to simultaneously obtain all the grid-impedance components within a single measurement cycle with no coupling effect. In the method, two orthogonal binary injections are simultaneously injected into the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> current references of the inverter controller. Then, a frequency-domain interpolation technique is applied to adjust the measured current and voltage responses. As a result, the impedance coupling is avoided in the measured grid impedance. The proposed technique is validated by experimental measurements.