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Photovoltaic (PV) grid-connected system requires the inverter possesses excellent dynamic and static characteristics. In view of the mathematical model of the inverter is nonlinear, we will adopt a kind of nonlinear control strategy called Passivity-Based Control (PBC) based on current model. First we establish the standard Euler-Lagrange (EL) current mode for inverter, then we also prove that this inverter is strictly passive. Based on passivity of inverter, we can redistribute the system energy, and adopt the approaches of injecting damping and decoupling to improve system performance. In this paper, we can make the power factor of inverter achieve one, and current of inverter output can fast track the grid voltage, we can also make the active power of system fast track the PV array maximum power point. Usually, we can use Single Chip Microcomputer or other kinds of computer with this algorithm for our design, this algorithm can be programmed with the computer language, such as C/C++ and assembly language, etc. Simulation results show that passivity-based control based on current model method can make the inverter possess better robustness and dynamic.