  Joint chance-constrained optimal power flow (JCC-OPF) is a promising tool to
manage uncertainties from distributed renewable generation. However, most
existing works are based on power flow equations, which require accurate
network parameters that may be unobservable in many distribution systems. To
address this issue, this paper proposes a learning-based surrogate model for
JCC-OPF with renewable generation. This model equivalently converts joint
chance constraints in quantile-based forms and introduces deep quantile
regression to replicate them, in which a multi-layer perceptron (MLP) is
trained with a special loss function to predict the quantile of constraint
violations. Another MLP is trained to predict the expected power loss. Then,
the JCC-OPF can be formulated without network parameters by reformulating these
two MLPs into mixed-integer linear constraints. To further improve its
performance, two pre-processing steps, i.e., data augmentation and calibration,
are developed. The former trains a simulator to generate more training samples
for enhancing the prediction accuracy of MLPs. The latter designs a positive
parameter to calibrate the predictions of MLPs so that the feasibility of
solutions can be guaranteed. Numerical experiments based on the IEEE 33- and
123-bus systems validate that the proposed model can achieve desirable
feasibility and optimality simultaneously with no need for network parameters.
