Accelerated Probabilistic Power Flow in Electrical Distribution Networks via Model Order Reduction and Neumann Series Expansion

TL;DR

This paper introduces the Accelerated-PPF (APPF), a novel algorithm that combines model order reduction and Neumann series expansion to significantly speed up probabilistic power flow calculations in electrical distribution networks.

Contribution

The paper presents a new accelerated algorithm for probabilistic power flow that leverages low-rank voltage profiles and Neumann expansion for efficient computation.

Findings

Achieved faster power flow simulations on IEEE 8500-node test feeder.

Demonstrated the effectiveness of low-rank subspace in reducing computational complexity.

Validated the approach's speedup and accuracy in large-scale networks.

Abstract

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.