The handling of weak networks with asymmetric disturbances implies the accurate handling of the second harmonic component appearing under unbalanced networks. This paper proposes a two-step approach using classic vector control for operating the current controller from the network disturbance. First, both voltage and current must be described in the positive and negative sequence with a proper decoupling. The use of a double frame controller for forcing current balance proves to drastically reduce the second harmonic component in the DC-link voltage. As a second step, a current reference computing method is proposed for fully compensating power oscillations on the DC side that is applicable for phase voltage dips up to 50%.