As the proportion of distributed energy resources (DER) continues to grow, it is imperative to enhance the economic and safe operation of the active distribution network (ADN). This paper presents an online distributed optimization model, in which loads and the active distribution network (ADN) operators transfer signals and perform local calculations. In order to significantly reduce the complexity of the model, a novel linear power flow (LPF) model that can be updated online is employed. Furthermore, the high proportion of DER access presents a time-coupled conundrum, thereby creating difficulty in finding the optimal solution. In this study, the Lyapunov drift plus penalty method (LDPPM) is employed to address this challenge by transforming the long-term optimization problem into a current-time one. Additionally, to enhance the calculation efficiency, the iterative optimization algorithm is regarded as a control process and is controlled with the PID controller to form a PID-Lagrange algorithm. The proposed PID-Lagrange algorithm has a clearly defined parameter tuning strategy that aligns with control theory, resulting in a significant reduction in operating costs by 30.27% in the case study. The results of the performance analysis demonstrate the superiority of the proposed method.