  We consider the problem of learning local Volt/Var controllers in
distribution grids (DGs). Our approach starts from learning separable
surrogates that take both local voltages and reactive powers as arguments and
predict the reactive power setpoints that approximate optimal power flow (OPF)
solutions. We propose an incremental control algorithm and identify two
different sets of slope conditions on the local surrogates such that the
network is collectively steered toward desired configurations asymptotically.
Our results reveal the trade-offs between each set of conditions, with coupled
voltage-power slope constraints allowing an arbitrary shape of surrogate
functions but risking limitations on exploiting generation capabilities, and
reactive power slope constraints taking full advantage of generation
capabilities but constraining the shape of surrogate functions. AC power flow
simulations on the IEEE 37-bus feeder illustrate their guaranteed stability
properties and respective advantages in two DG scenarios.
