Optimizing the operation of active distribution networks (ADN) has become more challenging because of the uncertainty created by the high penetration level of distributed photovoltaic (PV). From the convex optimization perspective, this paper proposes a two-layer optimization model to simplify the solution of the ADN optimal operation problem. Firstly, to pick out the ADN "key" nodes, a "key" nodes selection approach that used improved K-means clustering algorithm and two indexes (integrated voltage sensitivity and reactive power balance degree) is introduced. Then, a two-layer ADN optimization model is built using various time scales. The upper layer is a long time scale model with on-load tap changer transformer (OLTC) and Capacitor Bank (CB), and the lower layer is a short time scale optimization model with PV inverters and distributed energy storages (ES). To take into account the PV users’ interests, maximizing PV active power output is added to the objective. Afterwards, under the application of the second-order cone programming (SOCP) power flow model, a linearization method of OLTC model and its tap change frequency constraints are proposed. The linear OLTC model, together with the linear models of the other equipment, constructs a mixed-integer second-order cone convex optimization (MISOCP) model. Finally, the effectiveness of the proposed method is verified by solving the IEEE33 node system using the CPLEX solver.