The energy management of the fast-charging stations (FCSs) in power systems, while maintaining the power quality and the grid codes, can be particularly challenging, given the highly dynamic load curve, the heterogeneous PEV charging, and the inconvenience to the FCS customers. In this article, a consecutive horizon-based energy management (CHEM) process is proposed for the optimal techno-economic operation of the FCSs integrated with battery energy storage systems (ESS). The proposed CHEM process employs a central supervisory control and a resilient distributed control, for the energy management of FCSs and the active and reactive power control to maintain the grid codes. As such, the grid operator can realize and direct the economic and technical operation of the FCSs with low computational burden, without the need for real-time collaboration with the FCSs. Moreover, the FCSs can autonomously cope with the volatility of PEV charging with the use of the ESS. Furthermore, a novel Volt/VAr control is proposed to confine the unpredicted voltage deviations, including voltage sags, within an acceptable limit. The heterogeneous PEV charging is modeled using the queuing theory, while the inherent characteristics of the lithium-ion batteries are considered. Through multiple case studies, it is shown that the developed CHEM process can provide lower costs and a leveled active power profile for the FCSs, while ensuring that the voltage deviations are well confined and the convenience of PEV owners can still be met.