  Probabilistic power flow (PPF) plays a critical role in power system
analysis. However, the high computational burden makes it challenging for the
practical implementation of PPF. This paper proposes a model-based deep
learning approach to overcome the computational challenge. A deep neural
network (DNN) is used to approximate the power flow calculation and is trained
according to the physical power flow equations to improve its learning ability.
The training process consists of several steps: 1) the branch flows are added
into the objective function of the DNN as a penalty term, which improves the
approximation accuracy of the DNN; 2) the gradients used in the back
propagation process are simplified according to the physical characteristics of
the transmission grid, which accelerates the training speed while maintaining
effective guidance of the physical model; and 3) an improved initialization
method for the DNN parameters is proposed to improve the convergence speed. The
simulation results demonstrate the accuracy and efficiency of the proposed
method in standard IEEE and utility benchmark systems.
