In order to elimate the disadvantages of low calculation efficiency of traditional ordered charging method and not taking the three-phase imbalance of distribution network

constraints of node voltage and branch power flow into account

the branch power flow equations of three-phase balanced and unbalanced distribution networks are derived. The linearization methods for the nonlinear terms of equations are proposed. The ordered charging model of electric vehicles is developed

which takes minimum charging cost of owners as objective function

takes node voltage

branch power and charging power as the inequality constraints

and takes branch power flow equations and charging demand as equality constraints. The solving method is proposed by using two-stage linear programming. The linear programming of the first stage calculates the estimated optimized active power

reactive power and node voltage of the branch as linearized initial points of nonlinear terms for branch power flow equations by using simplified linear model

which ignores the nonlinear terms of branch power flow equations. The linear programming of the second stage calculates the optimal charging power by using the linearized branch power flow equations. The capabilities of the proposed method are verified by using three simulation cases compared with the selected methods.