The optimal power flow problem of the active distribution network with distributed generators and various discrete adjustable devices is essentially a non-convex

nonlinear mixed integer optimization problem. The solving speed of this kind of problem is slower. This paper proposes a three-phase optimal power flow model for distribution network based on the constant Hessian matrix. In the model

the second-order model of the three-phase transformer

the distributed generator with three-phase coupling characteristics and the voltage regulator are considered

which guarantee a constant Hessian matrix throughout iterations. By adding the branch current into the demand variables

the second-order model of three-phase transformer under Cartesian coordinate system is proposed

which makes the Hessian matrix of the optimization model become a constant matrix

thus reducing the computing time of optimal power flow. The three-phase optimal power flow model for active distribution network with three-phase power coupling characteristics of distributed generators is developed. The effects of the quadratic penalty function and Gaussian penalty function on the discrete control variables are compared

and the optimization model is solved by the prediction-correction primal-dual interior point method. Meanwhile

the two-stage iterative optimal power flow strategy with the voltage regulator is proposed to further optimize the target value. The correctness and effectiveness of the proposed model and method are verified by an example.