Reactive power optimization for distribution network with distributed generators is a complicated nonconvex nonlinear mixed integer programming problem. A new method is proposed to solve the reactive power optimization problem for distribution network. The original mathematical model of reactive power optimization ignoring discrete variables is transformed and relaxed into a convex semi-definite programming (SDP) model by this method to guarantee global optimality of the solution and the problem solved within polynomial time. Then the model is extended into a mixed integer semi-definite programming (MISDP) model with discrete variables. Benders’ decomposition is used to decompose the MISDP model into a simple mixed integer linear programming (MILP) master problem and an SDP sub-problem without discrete variables. The optimal solution is obtained by alternately iterating the master problem and the sub-problem. Numerical tests on a modified IEEE 33-bus system show that the method has the advantages of accurate relaxation

high efficiency and global optimality. This work is supported by National High Technology Research and Development Program of China (863 Program) (No. 2015AA050102) and State Grid Corporation of China (No. NY71-14-040).