Renewable energy sources including wind farms and solar sites, have been rapidly integrated within power systems for economic and environmental reasons. Unfortunately, many renewable energy sources suffer from variability and uncertainty, which may jeopardize security and stability of the power system. To face this challenge, it is necessary to develop new methods to manage increasing supply-side uncertainty within operational strategies. In modern power system operations, the optimal power flow (OPF) is essential to all stages of the system operational horizon; underlying both day-ahead scheduling and real-time dispatch decisions. The dispatch levels determined are then implemented for the duration of the dispatch interval, with the expectation that frequency response and balancing reserves are sufficient to manage intra-interval deviations. To achieve more accurate generation schedules and better reliability with increasing renewable resources, the OPF must be solved faster and with better accuracy within continuous time intervals, in both day-ahead scheduling and real-time dispatch. To this end, we formulate a multi-period dispatch framework, that is, progressive period optimal power flow (PPOPF), which builds on an interval optimal power flow (IOPF), which leverages median and endpoints on the interval to develop coherent coordinations between day-ahead and real-time period optimal power flow (POPF). Simulation case studies on a practical PEGASE 13,659-bus transmission system in Europe have demonstrated implementation of the proposed PPOPF within multi-stage power system operations, resulting in zero dispatch error and violation compared with traditional OPF.