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Voltage sags are an important power quality problem. Enhancing compensating capability is the key technique in voltage sag compensators. In this paper, a transformer-less series voltage sag topology without energy storage capacitors is proposed first. This topology is cost-effective by eliminating the large injection transformer and energy storage capacitors that are used in conventional series injection devices. This topology can both be used in three-phase three-line and three-phase four-line systems, and can compensate symmetrical three-phase voltage sags down to 37%, or one or two phase sags down to zero if other at least one phase is rated. Secondly, this paper proposes and illustrates a new compensation control strategy named as time optimal control which aims to enlarging the compensating time during sags. Using the proposed method, it can be shown that voltage sags can be corrected for much longer time compared to that of existing energy optimal method, and this advantages will be more obvious when the maximum permissible DC link voltage is smaller or in deeper sags. Especially the compensating time during sags by using the proposed control strategy may be several times longer than that of using energy optimal control strategy in the case of lower DC link voltages, deeper sags, and larger load impedance angles. Simulation and experiment results demonstrate the good features.