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Parallel Hybrid Electric Vehicle consists of internal combustion engine, engine clutch, motor, automatic transmission, Integrated Starter Generator (ISG), and battery. Due to hybridizations such as using engine clutch to disengage the internal combustion engine and omitting torque converter from the automatic transmission to increase fuel economy, drivability will not be same as conventional vehicle. To ensure drivability comparable to conventional vehicle, dynamic simulation has been utilized to foresee the drivability issues for the proposed hybrid system and ideas for improvements are tested in simulation. CoSimulation of AMESim vehicle model and Simulink Hybrid Control Unit (HCU) model has been used to test and improve HCU logic.