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We develop hierarchical coordination frameworks to optimally manage active and reactive power dispatch of number of spatially distributed electric vehicles (EVs) incorporating distribution grid level constraints. The frameworks consist of detailed mathematical models, which can benefit the operation of both entities involved, i.e., the grid operations and EV charging. The first model comprises of a comprehensive optimal power flow model at the distribution grid level, while the second model represents detailed optimal EV charging with reactive power support to the grid. We demonstrate benefits of coordinated dispatch of active and reactive power from EVs using a 33-node distribution feeder with large number of EVs (more than 5,000). Case studies demonstrate that, in constrained distribution grids, coordinated charging reduces the average cost of EV charging if the charging takes place at non-unity power factor mode compared to unity power factor. Similarly, the results also demonstrate that distribution grids can accommodate charging of increased number of EVs if EV charging takes place at non-unity power factor mode compared to unity power factor.