Stability evaluation of a DC micro-grid and future interconnection to an AC system a, * , a a, b Santiago Sanchez Marta Molinas , Marco Degano , Pericle Zanchetta b a Department of Electrical Power Engineering, Norwegian University of Science and Technology, Trondheim NO 7491, Norway b Department of Electrical and Electronic Engineering, University of Nottingham, University Park, Nottingham, UK abstract This paper presents the stability analysis of a DC micro-grid fed by renewable sources and the future interconnection with an AC micro-grid. This interconnection is realized through a voltage source con- verter, and the operation of the micro-grid is in island mode. The stability is analyzed by the Nyquist criteria with the impedance relation method. The frequency response of the models was obtained by the injection of a perturbation current at the operation point. Where this perturbation was at the input of the converter used to export power from the DC grid. Other perturbation was applied at the node of the micro-grid to evaluate its impedance. Finally the simulations show the impedance representation of the systems, and the stability for the interconnection of them. The experimental verification shows the impedance of the converter with the same tendency as the representation obtained by the analytical and simulation. 1. Introduction The stable behavior is one of the most important factors in po- wer systems. Its correct analysis ensures to the designer or operator that the system is going to be under normal conditions. Small signal techniques were developed for classical power systems, where generator to load current flow is always assumed [1]. But, future grids can present a system with power injection into the grid from the side of the costumer. These future grids will exhibit more nonlinear behavior and difficult coordination than the classical power system. In the case of DC distributed power electronics systems used in telecommunications, aircraft or ships the stability had been studied in Refs. [2e5]. Where stable region operation was identified. These methods employ frequency response and Nyquist criteria to present stability analysis. Linearization has been done, due to its simplicity and success record [6,7]. The wide spread choice to predict instability by the application of small signal analysis such as the Nyquist criterion or eigenvalues in AC systems with power electronics has been presented in Refs. [1,8e14]. However, it is necessary to analyze the stability of the distribution system with one of its prominent topology, in this work it is presented a variant of the CIGRE AC benchmark [15] for a DC resi- dential low voltage micro-grid, and its stability has been studied at one of the power exchange nodes. The paper is organized as follows: the Section 2 describes the modeling by impedance representation, Section 3 presents the grid structure and the method employed to control the DC voltage, and Section 4 describes the numerical results obtained from the simulations. 2. Impedance representation methods The impedance is determined by the application of an ideal source with a frequency component. This source is a sinusoidal current or voltage type (i p or v p respectively), and is denominated the perturbation. The magnitude has to be small with respect to the nominal operation value of the system. The frequency is chosen as f p varying in a range. The input voltage and current are measured at the DC side of the grid or the VSC. Their Fourier transform is computed. Finally the values at the perturbation frequency determine the input impedance of the inverter for small signal stability analysis or output impedance of the grid [2,8,9]. The cur- rent or voltage injection to obtain the impedance for the VSC is presented in Fig. 1 . The stability is analyzed with the Nyquist criteria used in Refs. [14,12]. Where the full system is partitioned into a source and a load subsystem, described by a Thevenin equivalent system in the case in which the source is considered