  To cope with fast-fluctuating distributed energy resources (DERs) and
uncontrolled loads, this paper formulates a time-varying optimization problem
for distribution grids with DERs and develops a novel non-iterative algorithm
to track the optimal solutions. Different from existing methods, the proposed
approach does not require iterations during the sampling interval. It only
needs to perform a single one-step calculation at each interval to obtain the
evolution of the optimal trajectory, which demonstrates fast calculation and
online-tracking capability with an asymptotically vanishing error.
Specifically, the designed approach contains two terms: a prediction term
tracking the change in the optimal solution based on the time-varying nature of
system power, and a correction term pushing the solution toward the optimum
based on Newton's method. Moreover, the proposed algorithm can be applied in
the absence of an accurate network model by leveraging voltage measurements to
identify the true voltage sensitivity parameters. Simulations for an
illustrative distribution network are provided to validate the approach.
