  In distribution networks, there are slow controlling devices and fast
controlling devices for Volt-VAR regulation. These slow controlling devices,
such as capacitors or voltage regulators, cannot be operated frequently and
should be scheduled tens of minutes ahead (Hereafter named as slow control).
Since of the uncertainties in predicting the load and distributed generation,
the voltage violations cannot be eliminated by fast controlling devices with
improper schedule of the slow controlling devices. In this paper we propose
dual time-scale coordination for the Volt-VAR control scheme, corresponding to
slow and fast control. In the case of slow control, a robust voltage and
reactive power optimization model is developed. This guarantees that subsequent
fast controls can maintain the system's voltage security if the uncertain
parameters vary within predefined limits. This nonconvex optimization problem
is relaxed to a mix integer second order conic problem, and the dual form of
its sub-problem is also derived. Then a column-and-constraint generation
algorithm was used to solve the robust convexified model. A conventional
deterministic optimization model can be used to determine the fast control
mechanism. Numerical tests were conducted on a real distribution feeder in
China, a balanced IEEE 69-bus and unbalanced 123-bus benchmark distribution
networks. The simulation results show that solving the deterministic model is
not always feasible and voltage violation may occur. The robust model was shown
to be effective with respect to all possible scenarios in the uncertainty set,
with little compromise in terms of network losses.
