Dynamic phasors modeling for a single phase two stage inverter

Photovoltaic systems, wind turbines and battery storage systems are all commonly present in energy self-sufficiency and independent producers schemes, since they support distributed generation designs. For both cases, single phase inverters provide power conditioning in order to inject micro-sources power to the grid, demanding multiple tasks such as maximum power tracking, DC to AC voltage conversion, electrical signal filtering and network synchronization, among others. The massive integration of such devices demands an assessment on their impact over the low voltage distribution network to which they are connected to. Hence, an accurate and efficient mathematical modeling is required, for both steady and transient state, in order to provide a robust dynamical simulation to support the designing of coordinated protection schemes and operational control algorithms. The analysis also contributes to ensure network stability within the required quality issues. Therefore, this paper extends the dynamic phasors technique that is a widely employed method for modeling oscillatory systems, in order to develop, simulate and analyze the mathematical model of single phase full bridge inverter. A comparison between different types of numeric methods is made, to find the better option depending of the finality of the study. The technique focuses on three frequencies of interest: the network rate, the boost and the inverter stage frequencies. Based on dynamic phasors information, two PI controls are designed to control the DC an AC voltages, and new formulas for calculation of DC and AC powers are presented. Simulation results in Matlab and Simulink demonstrate the effectiveness of the work.