*2.2. Quasi-Static Modeling of Vehicle Dynamics*

EV and ECB powertrain models have been presented in detail in previous work [20–22]. A comprehensive physics-based dynamic ECB model is presented and validated with measurement data in [22]. The model was found accurate but computationally intensive, which limited the usefulness of the model for powertrain design.

Quasi-static, or backward progressing, modeling provides a computationally light alternative to dynamic models that make use of differential equations to describe the system. A quasi-static approach is feasible in research and design applications where fast transients are not the central focus. The backward modeling approach means that the input to the model is a specific driving cycle, which is a presentation of the vehicle speed as a function of time. The powertrain load computation flows from the wheels towards the power source, such as a traction motor.

Discrete time is used instead of continuous time for the numerical computation. In each step, the system is interpreted as a static system. This approach is suitable for slow phenomena, such as energy consumption on a driving cycle. Because this approach is computationally light, a large number of topology and component size options can be explored in a short time. This is fitting to the multispeed gearbox selection problem, which requires a search for optimal gear ratios.

The following assumptions are included in the modeling:


The modeled ECB dynamics, gear changing policy, and gear ratio optimization models are introduced in Sections 2.2–2.4. A specific configuration of the model, in which parameter values from the case study are applied, is discussed in Section 3.
