  This paper develops a data-driven framework to synthesize local Volt/Var
control strategies for distributed energy resources (DERs) in power
distribution networks (DNs). Aiming to improve DN operational efficiency, as
quantified by a generic optimal reactive power flow (ORPF) problem, we propose
a two-stage approach. The first stage involves learning the manifold of optimal
operating points determined by an ORPF instance. To synthesize local Volt/Var
controllers, the learning task is partitioned into learning local surrogates
(one per DER) of the optimal manifold with voltage input and reactive power
output. Since these surrogates characterize efficient DN operating points, in
the second stage, we develop local control schemes that steer the DN to these
operating points. We identify the conditions on the surrogates and control
parameters to ensure that the locally acting controllers collectively converge,
in a global asymptotic sense, to a DN operating point agreeing with the local
surrogates. We use neural networks to model the surrogates and enforce the
identified conditions in the training phase. AC power flow simulations on the
IEEE 37-bus network empirically bolster the theoretical stability guarantees
obtained under linearized power flow assumptions. The tests further highlight
the optimality improvement compared to prevalent benchmark methods.
