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Voltage swell and overvoltage compensation problems in a diode-bridge rectifier supported transformerless-coupled dynamic voltage restorer (DVR) are discussed. When swell or overvoltage happens, applying conventional in-phase or phase-invariant boosting method causes a rapid rise in dc-link voltage, which may damage the storage capacitors and switching devices, and increase the switching loss. This paper illustrates the inability of the minimum energy injection scheme to solve these problems during unbalanced situations. Therefore, we propose a novel unidirectional power flow control algorithm with DVR maximum compensation limit consideration, which can effectively suppress problems of continuous rising in dc-link voltage. Progressive phase rotating method is applied to prevent compensated load voltage distortion or discontinuity. Appropriate and practical design of the dc storage capacitor's rating is also discussed. Simulation and experimental results for unbalanced voltage swell compensation are given to prove the validity and superior performance of the proposed algorithm.