  The handling of weak networks with asymmetric loads and disturbances implies
the accurate handling of the second-harmonic component that appears in an
unbalanced network. This paper proposes a classic vector control approach using
a PI-based controller with superior decoupling capabilities for operation in
weak networks with unbalanced phase voltages. A synchronization method for weak
unbalanced networks is detailed, with dedicated dimensioning rules. The use of
a double-frame controller allows a current symmetry or controlled imbalance to
be forced for compensation of power oscillations by controlling the negative
current sequence. This paper also serves as a useful reminder of the proper way
to cancel the inherent coupling effect due to the transformation to the
synchronous rotating reference frame, and of basic considerations of the
relationship between switching frequency and control bandwidth.
