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.

9 pages, 10 figures. This work has been submitted to the IEEE for possible publication