Convexified OPF in Multiphase Low Voltage Radial Distribution Networks including Neutral Conductor

Optimal power flow problem for low-voltage radial distribution networks including neutral conductor is considered in this paper. The standard semi-definite programming based relaxation, initially proposed for three-phase networks, is extended to such multi-phase networks by taking into account the coupled phase-neutral power injections. An approach based upon correction current injection is utilized which incorporates the network loads into the system admittance matrix by representing them through constant admittances. Furthermore, the impact of neutral-ground impedance has also been taken into account. Simulations are carried out on real low-voltage unbalanced distribution networks for minimization of slack-bus power injection and power losses objective functions. It has been shown that the proposed approach is numerically exact under a large range of the value of neutral-ground impedance and can be successfully solved by a generic optimization solver such as MOSEK. The exactness of the proposed scheme has also been verified for the time-varying load and generation profiles, whereas the accuracy of the recovered solution is also confirmed by root-mean-square-error parameter.