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For grid-connected voltage-source converters (VSCs), it is commonly required that its power outputs can track the power references given by operators under various grid conditions. To achieve this objective, this article presents a Lyapunov-based nonlinear power control algorithm. The system dynamics is developed in the stationary frame, which facilitates the design of the control algorithm in the absence of phase-locked loops that may cause instability issues in ultraweak grids. A virtual resistance is then introduced to allow fast power tracking performance and relax the requirement on accurate system parameters. Furthermore, to simplify the control design, the quasi-stationary line impedance model is applied, based on which a nonlinear control algorithm that only utilizes the output voltage and current information is developed. Afterward, the stability of the closed-loop system is analyzed via the Lyapunov theory. The theoretical results illustrate that the power regulation goal can be achieved and the VSC can maintain synchronization with the power grid. Finally, experimental results demonstrate the effectiveness of the proposed control algorithm under temporary grid faults and various short-circuit ratios.