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This paper presents a passivity-based controller for a Distribution Static synchronous Compensator (D-Statcom) aimed at compensating reactive power and unbalanced harmonics in the general case of distorted and unbalanced source voltages and load currents. The proposed approach is based on the measurements of line currents, and ensures precise compensation for selected harmonics. Moreover, in order to compensate for the unavoidable uncertainty in certain system parameters, adaptation is added to the passivity-based controller. One of the major advantages of the proposed solution compared to conventional alternatives is that we are able to perform precise tracking (including higher order harmonics) even in the presence of a relatively low switching frequency, i.e., in the presence of an inverter with limited bandwidth. Simulation and experimental results are provided to illustrate the merits of our solution.