Geometry of Power Flows in Tree Networks

Details Geometry of Power Flows in Tree Networks Geometry of Power Flows in Tree Networks

2012-04-19

arxiv.org/abs/1204.4419v1

Mathematics

Optimization and Control

To appear in PES general meeting 2012

Scientific paper

We investigate the problem of power flow and its relationship to optimization in tree networks by looking at the injection regions of the networks. The injection region is the set of all vectors of bus power injections that satisfy the network and operation constraints. The geometrical object of interest is the set of Pareto-optimal points of the injection region, since they are the solutions to the minimization of increasing functions. If the voltage magnitudes are fixed, the injection region of a tree network can be written as a linear transformation of the product of two-bus injection regions, one for each line in the network. Using this decomposition, we show that under the practical condition that the angle difference across each line is not too large, the set of Pareto-optimal points of the injection region remains unchanged by taking the convex hull. Therefore, the optimal power flow problem can be convexified and efficiently solved. This result improves upon earlier works by removing the assumptions on active power lower bounds. Partial results are presented for the variable voltage magnitude case.

Affiliated with

Also associated with

No associations

Rating

Geometry of Power Flows in Tree Networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Geometry of Power Flows in Tree Networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometry of Power Flows in Tree Networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-35451