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Fuel consumption is an essential factor that requires to be minimized in the design of a vehicle powertrain. Simple energy models can be of great help - by clarifying the role of powertrain dimensioning parameters and reducing the computation time of complex routines aiming at optimizing these parameters. In this paper, a Fully Analytical fuel Consumption Estimation (FACE) is developed based on a novel GRaphical-Analysis-Based fuel Energy Consumption Optimization (GRAB-ECO), both of which predict the fuel consumption of light- and heavy-duty series hybrid-electric powertrains that is minimized by an optimal control technique. When a drive cycle and dimensioning parameters (e.g. vehicle road load, as well as rated power, torque, volume of engine, motor/generators, and battery) are considered as inputs, FACE predicts the minimal fuel consumption in closed form, whereas GRAB-ECO minimizes fuel consumption via a graphical analysis of vehicle optimal operating modes.