## 1 Introduction  
Due to fossil fuel depletion and environmental pollution around the world, the development of renewable energy, such as wind and photovoltaic, has attracted much attention [1; 2; 3; 4]. The distributed generation (DG) systems based on renewable energy can be connected in parallel with each other to form a micro-grid. The analysis of field data of photovoltaic (PV) plants indicates that the harmonics at point of common coupling (PCC) in weak grid can exist stably for a long time and the line impedances of low-voltage power distribution systems cannot be ignored [5]. Harmonics in micro-grid may cause abnormality of distribution system and even damage of power facilities, further reducing power quality and even causing the shutdown of PV inverters [6]. In [7; 8], the PV inverters operated in parallel can shift the resonant frequency to a low frequency band, and these resonances of inverters can take place at the frequencies of 5 th and 7 th harmonics. With the high penetration of nonlinear power electronics devices, the impact harmonic resonance between inverters and grid is more complicated. Traditionally, many studies are only implemented for a single power electronic equipment and single renewable energy penetration level, neglecting the interaction between new devices and micro-grids, as well as revealing little generation mechanisms about the PCC harmonic of renewable energy. In [9; 10], the generation mechanisms of multi-inverter resonances are studied by establishing inverter parallel models, and a virtual impedance method was proposed to suppress these resonances. On the other hand, the serial resonant frequencies between PV inverters and line impedances can also shift to the lower band because of the high line impedance in weak grid. The output harmonics of grid-tied PV inverters are generally concentrated in low-frequency bands, and it is probable to cause resonances at PCC [11]. In [12; 13; 14], the impedance matching analysis method of serial resonances between power converter groups and grid impedances is proposed, and a harmonic linearization model is studied. In [15; 16; 17; 18], the companion harmonic circuit modeling is adopted to develop an electronic device and micro-grid combine model, which can analyze the adverse effects of harmonic distortion in weak grids. It also produces a very easy solution method. For renewable energy generations, almost all dispatched loads and parallel reactive power compensating devices work in a frequently changing way [19]. The parameters of equivalent admittance/impedance of fundamental and harmonics of these equipment exist in uncertainty, which will significantly change the harmonic network admittance matrix of micro-grid [20]. Due to the rapid increase of photovoltaic systems in micro-grids, the problem of power quality associated with the intermittent nature of these systems had become more and more serious, and many efforts have been made already [21; 22]. Most of the strategies about harmonic suppression in micro-grid focus on the power grid models containing one PV inverter, hence it is necessary to establish a model associated with a multi-inverter-based micro-grid [23; 24]. In [25; 26; 27; 28; 29], a composite method to study the impact of harmonic sources on the distribution system is proposed. This approach combines a bottom-up stochastic modeling of the local loads with harmonic waveform data and power-flows all based on a scenario analysis. Based on the analysis of the measurement data, a prediction of the harmonic current level in a residential area can be performed by the method on the current situation. The purpose of this research is to study the harmonic generation mechanism and suppression method by establishing a combined model of micro-grid. In [30; 31], it is mentioned that the phase-locked loop (PLL) is the most important grid synchronization technique in grid-connected power converter applications. However, its phase-tracking performance is affected seriously by the unbalances and distortions of micro-grid voltage.