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This paper proposes a novel static Var generator (SVG), which employs series-connected IGBTs in each leg of the bridge for medium voltage blocking capability. The SVG is used to compensate reactive power, negative sequence current, current harmonics and unbalanced source voltages. The configuration of the AC power system with the SVG is firstly introduced. Then the operation principles of the SVG to compensate the current or voltage distortions and unbalances are described. Two types of control strategies of the whole system, i.e., controlling the SVG operating as a voltage controlled voltage source (VCVS) and controlling the SVG as a current source (VCCS), are analyzed and discussed in detail. Especially, the approaches to generating the reference signal of for the SVG control circuit is presented according to the different compensation objectives mentioned above. All these control strategies and algorithms are realized in digital circuits based on a DSP controller. The simulation investigations and experiments on a low voltage prototype were carried out. The results showed that the behavior of the SVG is satisfactory both in steady state and in transient process. The proposed control strategies and algorithms are verified.