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 d and q 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 d-channel current may also perturb the q-channel current thus distorting the impedance measurements. Traditionally sequentially performed measurements, where different injections are performed one after another at 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. The present paper 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 d and q 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.

Grid characteristics have a drastic impact on the stability and control performance of grid-connected systems. Because the grid conditions typically vary over time, online measurements are most desirable for the stability assessment, protection design, and control-system optimization of the systems. Previous studies have presented methods based on Fourier techniques and broadband sequences with which the frequency responses of the grid-connected systems, such as the grid impedance or inverter control loops, can be measured. However, online measurements under unbalanced grids with harmonic voltages have not been comprehensively considered. The present paper demonstrates how the previously applied online-measurement methods fail in the presence of unbalanced grid and voltage harmonics due to the spectral leakage caused by Fourier transform. This work also proposes a simple signal-design method to avoid the leakage. Experimental results based on a high-power grid-connected system are shown to demonstrate the effectiveness of the proposed method.

Impedance-ratio-based interaction analyses in terms of stability and performance of DC-DC converters is well established. Similar methods are applied to grid-connected three-phase converters as well, but the multivariable nature of the converters and the grid makes these analyses very complex. This paper surveys the state of the interaction analyses in the grid-connected three-phase converters, which are used in renewable-energy applications. The surveys show clearly that the impedance-ratio-based stability assessment are usually performed neglecting the cross-couplings between the impedance elements for reducing the complexity of the analyses. In addition, the interactions, which affect the transient performance, are not treated usually at all due to the missing of the corresponding analytic formulations. This paper introduces the missing formulations as well as explicitly showing that the cross-couplings of the impedance elements have to be taken into account for the stability assessment to be valid. In addition, this paper shows that the most accurate stability information can be obtained by means of the determinant related to the associated multivariable impedance ratio. The theoretical findings are also validated by extensive experimental measurements.

Modern electric distribution systems typically contain several feedback-controlled parallel inverters that together form a complex power distribution system. Consequently, a number of issues related to stability arise due to interactions among multiple inverter subsystems. Recent studies have presented methods where the stability and other dynamic characteristics of a paralleled inverter system can be effectively analyzed using impedance measurements. This paper presents implementation techniques for a comprehensive online stability analysis of grid-connected paralleled inverters using power hardware-in-the-loop measurements based on an OPAL-RT real-time simulator. The analysis is based on simultaneous online measurements of current control loop gains of the inverters and the grid impedance, and aggregated terminal admittance measurements of the inverters. The analysis includes the measurement of the inverters’ aggregated output impedance, inverters’ loop gains, global minor loop gain, and grid impedance. The presented methods make it possible to rapidly evaluate the system on both global and local level in real time, thereby providing means for online stability monitoring or adaptive control of such systems. Experimental measurements are shown from a high-power energy distribution system recently developed at DNV GL, Arnhem, Netherlands.

The utility-scale wind and solar electricity production is typically connected to the power grid through multiple parallel three-phase inverters. One of the main issues in such grid-connected systems is the harmonic resonance caused by interactions between the grid and inverters. A common method for the analysis of these systems has been the impedance-based stability criterion. However, in systems that have multiple parallel inverters, the system complexity and challenges in obtaining the required impedance measurements may deteriorate the accuracy of the impedance-based approach. This paper discusses the aggregation of parallel inverters and the stability analysis of such grid-connected system. A simple method, based on impedance measurements, is shown for defining the allowable number of paralleled inverters so that the system remains stable. Experimental results are shown from power hardware-in-the-loop setup recently developed at DNV GL Flexible Power Grid Lab.