This paper proposes a mathematics model of active distribution network expansion planning (DNEP) integrating the practical operation constraints, which are the OLTC (On-Load Tap Changer) tap adjusting frequency and substation voltage variation. Distributed Generation (DG) curtailment, load curtailment, OLTC tap adjustment, and reactive power compensation are considered as the active management schemes. The expansion model allows alternatives to be considered for new wiring, DG installation, new substation, and substation expansion. The DNEP problem is a mixed integer non-linear programming problem, active management, and uncertainties, especially with the DG integration make the DNEP problem much complex. In order to find the suitable algorithm, this paper converts the DNEP problem to a Second-Order Cone Programming (SOCP) model through distflow equations and constraints relaxation. A modified 33-bus application example is used to verify the proposed model with different active management scenarios.