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. Parametric models of the main powertrain components are implemented in FACE and GRAB-ECO. Coefficients of these parametric models are expressed as a function of typical dimensioning parameters through analyzing characteristics of several engines, motors, and batteries belonging to similar technologies. Similarly, the common design constraints (i.e. acceleration and gradeability metrics) are scaled with the dimensioning parameters as well. Both virtual-light- and real-heavy-duty series hybrid electric powertrains are applied to assess the performance of FACE and GRAB-ECO by comparing with a benchmark based on Pontryagin's Minimum Principle. Optimization of powertrain dimensioning parameters are performed on both series hybrid powertrains to demonstrate the effectiveness of FACE and GRAB-ECO in the powertrain optimal design application.