It is more and more challenging to obtain the global optimal power flow (OPF) information of a whole system with the developing trend of power systems toward hierarchical partition-managed ones. Traditional centralized OPF problems are not adaptive to modern partition-managed power systems because of the emergence of distributed sources and multi-stakeholders and the protection of their private data. This paper extends the traditional OPF to a many-objective optimization problem which is helpful to the independent power flow calculation (PFC) of the various subregions in partition-managed networks. To address the coordination of various regions, the individual distributed PFC problem is transformed into a whole optimization problem through node tearing and line disconnection methods, and then the pattern search algorithm is employed to address its solution. Then, the distributed PFC is integrated into the improved NSGA-III (I-NSGA-III) approach to solve the entire many-objective OPF (Ma-OPF) for partition-managed power systems. The effectiveness and feasibility of the proposed distributed approach are demonstrated in multiple benchmarks of IEEE 30/39/118-bus systems and a practical partitioned power system in Guizhou Province of China. The results show that the average voltage difference between distributed PFC and centralized PFC is within 1.12% while the phase angle difference is within 0.44%. In the application of OPF problems, the proposed distributed approach shows the high ability to yield approximate solutions of the original I-NSGA-III with centralized PFC. It is also found from the simulation that the distributed approach shows competitive performance compared to other considered centralized PFC-based evolutionary algorithms and weighted interior point method while it does not require complete information about various regions and is beneficial to the privacy protection of multi-stakeholders.