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Power-flow-control techniques that are capable of handling inefficiencies of both the electric motor/generator (EMG) and the internal combustion engine (ICE) are required to fully explore the fuel-saving potential of fully hybridized parallel hybrid electric vehicles (PHEVs). We propose an online power-flow-control strategy for fully hybridized PHEVs based on the power-balancing strategy (PBS), which controls the ICE within its peak-efficiency region by using the electrical system. We introduce a new PHEV assisted by an integrated starter generator (ISG) or ISG-assisted PHEV, in which the ISG supports the downsized EMG to maintain the electrical system's efficiency close to its peak efficiency and, therefore, to enhance the fuel-saving capability of the PBS controller. The key contributions of this study are given as follows: 1) identification of the ICE's peak-efficiency region as a function of the discharging and recharging efficiencies of the electrical system; 2) a new more fuel-efficient HEV architecture; and 3) proper regulation of the state of charge while maintaining infrequent stopping and restarting of the ICE by direct control of the ICE's energy output. Results show that the PBS controller achieves fuel efficiencies similar to the offline benchmark controller using the equivalent consumption minimization strategy. The PBS controller saves up to 9.3% of fuel on the ISG-assisted PHEV, compared with an equally powered PHEV without the ISG.