Linear OPF with linearization of quadratic branch flow limits

This paper presents a linear optimal power flow (LOPF) formulation which is developed based on recent advancements in linear flow for analyzing various aspects of piecewise linearization of quadratic branch flow limits. An analytical expression for obtaining the required number of segments for linearization is developed using the geometry of the circle. The expression gives the number of linear constraints to replace the quadratic constraint for a specific error value without introducing any sub-optimization problem. This makes the LOPF solvable without iterations through efficient linear solvers. The variation of linear constraint set size with different line limits for different errors has been shown. Further, a recent method of area reduction in thermal limit linearization is analyzed, and adverse effects of it have been shown using standard test systems. A modified approach for area reduction is also proposed which excludes the problems associated with the present one. Results of LOPF with the linearization strategy obtained for IEEE 30 Bus are promising and motivate further investigations.