Optimization of Gang-operated On-load Tap Changers in Multi-conductor
Radial Networks: Formulation and Convex Relaxation
Abstract
Unbalanced optimal power flow refers to mathematical optimization
problems subject to the physics of grids with phase unbalance. They can
serve as a core technology, or benchmark, for centralized or distributed
optimal control solutions. In recent years, convex relaxations of this
problem have attracted significant interest in the community. For many
common test feeders, it turned out they return exact solutions. However,
more research is needed to study how well this holds up in more
complicated modelling contexts. This paper therefore studies
gang-operated on-load tap changers in detail. Analogous to balanced
optimal power flow, it is possible to reformulate the problem exactly
without an explicit tap variable. This is a non-trivial result that is
discussed in detail. Furthermore, this paper describes in detail how a
solution in the lifted variable space can be projected back to the
original variable space. Best case, it then becomes possible to solve
the problem as a convex optimization problem instead. Worst case, it
provides a lower bound on the objective value. Two numerical case
studies, a simple test case and IEEE13, are included. The case studies
are made publicly available.