Efficient Distribution Grid Optimal Power Flow with Discrete Control of Legacy Grid Devices

In this work, we present a mathematical model and a computational study of a distribution grid optimal power flow (DOPF) problem with legacy grid devices, i.e., load tap changers (LTCs) and switched capacitors, in active distribution systems. The DOPF model in its original form, with control of LTCs and switched capacitors, is a mixed-integer nonlinear programming (MINLP) problem, which is computationally intractable. Therefore, efficient mixed-integer DOPF models are required for practical feeders to optimally dispatch LTCs and switched capacitors. To this end, utilizing a well known Second Order Cone Programming (SOCP) version of the DOPF formulation, we adopted an exact mixed-integer linear model of LTCs and switched capacitors that leads to an efficient Mixed-Integer SOCP (MISOCP) formulation. The computational performance of the MISOCP DOPF model is evaluated on a modified IEEE 123-node feeder with single-period and multiperiod runs. We showed that MISOCP based OPF formulation provides promising performance in managing legacy grid devices for practical-sized feeder with inter-temporal consideration.