  The increasing penetration of renewables in distribution networks calls for
faster and more advanced voltage regulation strategies. A promising approach is
to formulate the problem as an optimization problem, where the optimal reactive
power injection from inverters are calculated to maintain the voltages while
satisfying power network constraints. However, existing optimization algorithms
require the exact topology and line parameters of underlying distribution
system, which are not known for most cases and are difficult to infer. In this
paper, we propose to use specifically designed neural network to tackle the
learning and optimization problem together. In the training stage, the proposed
input convex neural network learns the mapping between the power injections and
the voltages. In the voltage regulation stage, such trained network can find
the optimal reactive power injections by design. We also provide a practical
distributed algorithm by using the trained neural network. Theoretical bounds
on the representation performance and learning efficiency of proposed model are
also discussed. Numerical simulations on multiple test systems are conducted to
illustrate the operation of the algorithm.
