Optimization of Gang-operated On-load Tap Changers in Multi-conductor Radial Networks: Formulation and Convex Relaxation

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.