Direct current (DC) power grids based on flexible high-voltage DC technology have become a common solution of facilitating the large-scale integration of distributed energy resources (DERs) and the construction of advanced urban power grids. In this study, a typical topology analysis is performed for an advanced urban medium-voltage DC (MVDC) distribution network with DERs, including wind, photovoltaic, and electrical energy storage elements. Then, a multi-time scale optimal power flow (OPF) strategy is proposed for the MVDC network in different operation modes, including utility grid-connected and off-grid operation modes. In the utility grid-connected operation mode, the day-ahead optimization objective minimizes both the DER power curtailment and the network power loss. In addition, in the off-grid operation mode, the day-ahead optimization objective prioritizes the satisfaction of loads, and the DER power curtailment and the network power loss are minimized. A dynamic weighting method is employed to transform the multi-objective optimization problem into a quadratically constrained quadratic programming (QCQP) problem, which is solvable via standard methods. During intraday scheduling, the optimization objective gives priority to ensure minimum deviation between the actual and predicted values of the state of charge of the battery, and then seeks to minimize the DER power curtailment and the network power loss. Model predictive control (MPC) is used to correct deviations according to the results of ultra short-term load forecasting. Furthermore, an improved particle swarm optimization (PSO) algorithm is applied for global intraday optimization, which effectively increases the convergence rate to obtain solutions. MATLAB simulation results indicate that the proposed optimization strategy is effective and efficient.