The extensive penetration of open-phase running distributed generators(DGs)such as photovoltaic generators to distribution systems may lead to a serious three-phase unbalanced condition

which is an intrinsic characteristic of distribution systems. The effect of the traditional reactive power optimization method is poor without considering the unbalanced problem. A three-phase unbalanced reactive power optimization model for active distribution networks is presented. The model with the objective of minimizing both the negative sequence system voltages and network losses considers continuous and discrete variables e. g. the under-load tap changers

capacitors banks and static var compensator. The reactive power optimization problem is formulated in rectangular coordinates as a mixed-integer quadratic programming with the quadratic constraint problem. It is solved by the branch-and-bound method and the original problem is divided into a lot of sub-problems without discrete variables

which are solved to get the control strategy of devices. The simulation results of the modified IEEE 33-bus three-phase test system show that the proposed model and method are effective. This work is supported by National Natural Science Foundation of China(No. 51577049)

Specialized Research Fund for the Doctoral Program of Higher Education(SRFDP)of China(No. 20120094110008)and State Grid Corporation of China.