  This paper develops a computationally efficient algorithm which speeds up the
probabilistic power flow (PPF) problem by exploiting the inherently low-rank
nature of the voltage profile in electrical power distribution networks. The
algorithm is accordingly termed the Accelerated-PPF (APPF), since it can
accelerate "any" sampling-based PPF solver. As the APPF runs, it concurrently
generates a low-dimensional subspace of orthonormalized solution vectors. This
subspace is used to construct and update a reduced order model (ROM) of the
full nonlinear system, resulting in a highly efficient simulation for future
voltage profiles. When constructing and updating the subspace, the power flow
problem must still be solved on the full nonlinear system. In order to
accelerate the computation of these solutions, a Neumann expansion of a
modified power flow Jacobian is implemented. Applicable when load bus
injections are small, this Neumann expansion allows for a considerable speed up
of Jacobian system solves during the standard Newton iterations. APPF test
results, from experiments run on the full IEEE 8500-node test feeder, are
finally presented.
