14,224 research outputs found
Optimizing Service Restoration in Distribution Systems with Uncertain Repair Time and Demand
This paper proposes a novel method to co-optimize distribution system
operation and repair crew routing for outage restoration after extreme weather
events. A two-stage stochastic mixed integer linear program is developed. The
first stage is to dispatch the repair crews to the damaged components. The
second stage is distribution system restoration using distributed generators,
and reconfiguration. We consider demand uncertainty in terms of a truncated
normal forecast error distribution, and model the uncertainty of the repair
time using a lognormal distribution. A new decomposition approach, combined
with the Progressive Hedging algorithm, is developed for solving large-scale
outage management problems in an effective and timely manner. The proposed
method is validated on modified IEEE 34- and 8500-bus distribution test
systems.Comment: Under review in IEEE Transactions on Power System
The Resolvent Average for Positive Semidefinite Matrices
We define a new average - termed the resolvent average - for positive
semidefinite matrices. For positive definite matrices, the resolvent average
enjoys self-duality and it interpolates between the harmonic and the arithmetic
averages, which it approaches when taking appropriate limits. We compare the
resolvent average to the geometric mean. Some applications to matrix functions
are also given
- …