## 5 Discussion  
According to the study above, the main characteristics of the harmonics at PCC of the PV plant are summarized as follows:  
1. The harmonics at PV PCC are steady-state inter-harmonics.
2. The spectra of PV PCC harmonics are isolated spectral lines.
3. The transition times of the harmonic appearance and fading are all very short.
4. The frequencies and amplitudes of the harmonics are insensitive to external conditions.  
It is proposed that the inter-harmonics at PCC of PV plant in field were generated by nonlinear self-oscillation of the \"inverter-weak grid\" system. A stable self-oscillation occurs inside the grid-tied PV inverters, and the harmonic frequencies did not depend on the linear characteristics of the inverters and the micro-grid. The nonlinear properties leading to nonlinear self-oscillations of the \"inverter-weak grid\" system are related to the integral saturation of inverter controller, PLL, hysteresis loop of grid-tied transformers, and dead-zones of IGBT-bridge of PV inverters.  
The nonlinear dynamics also explain that the self-oscillations of nonlinear systems mainly include two categories: (1) periodic/quasi-periodic/chaotic oscillation with larger amplitude; and (2) weakly damped oscillation near the equilibrium with small amplitude. The nonlinear self-oscillation studied in  
Figure 13: Waveforms and spectra of the harmonics at PV PCC of simulation: (**a**) voltages at PV PCC; (**b**) currents at PV PCC; (**c**) spectra of the voltages (THDU = 5.60%); and (**d**) spectra of the currents (THDI = 24.56%).  
this project belongs to the first type. In fact, the \"grid-tied inverter-weak grid\" system has the necessary conditions for self-oscillation: the energy conversion and energy supplement loop correspond to the invert-units and the DC sources of PV inverters; the frequency selective network corresponds to the output impedances of PV inverters, filter circuit equivalent impedances, and the line impedances of micro-grid; and the amplitude stable mechanism involves all the nonlinear properties in PV inverter-grid system. Therefore, the nonlinear self-oscillation theory proposed here reveals the essential mechanism of the harmonic generation at PV PCC in a micro-grid.  
As discussed in the Introduction, the conventional methodologies of micro-grid harmonic research all include theoretical analysis, modeling, simulation and experiments. The preset of these studies was that the micro-grid and grid-tied inverters were linear systems. If any nonlinear characteristics were encountered, they should be treated by linearization. Most publications have reported from theoretical point of view, but there is no field verification in a real PV plant. In this study, the field waveforms were captured in a high-power PV plant to figure out the nonlinear self-oscillation mechanism of the harmonic phenomena in micro-grid. In fact, almost all the power quality problems in micro-grid including PV PCC harmonics come from real projects, therefore, field testing, real-time measurements and detailed data analysis are necessary for harmonic analysis and harmonic mitigations. The nonlinear self-oscillation theories proposed here and the research methodologies based on field data are worth being discussed.