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Compared with current-controlled grid-connected inverters (CCIs), voltage-controlled grid-connected inverters (VCIs) have shown stronger stability in very weak grids. Therefore, in the future power system with renewable energy as the main energy source, VCI has a wide application prospect. However, the power control bandwidth of VCIs is usually very low under very weak grids. It is difficult for the VCI to track renewable energy changes in time and may lead to DC side power imbalance or even DC voltage instability. First, this paper proposes a VCI rapid power control method based on pre-filtering control, which can effectively increase the VCI active power control bandwidth, and without affecting the control stability in the weak grid. Then, this paper proposes a corresponding MPPT control strategy, which can achieve MPPT efficiency equivalent to CCI even in the very weak grid and maintain DC voltage stability. Finally, experimental results validate the analysis and the proposed method.