This paper presents a typical operation optimization model based on the branch flow model in active distribution system with high penetration of renewable energies and active network management devices. Two types of cutting planes including the total power loss cut and leaf branch current cut are proposed to ensure the exactness of second order cone relaxation in the branch flow model based optimal power flow. The proposed cutting planes are extended to the general conditions where power loss may be excluded in the optimization objectives. The computation performances of cutting planes in different objectives are thoroughly examined to validate the effectiveness of the proposed cutting planes.