The performance of powertrain components in electric vehicles is tightly intertwined with their thermal behavior. In practical applications, their temperature must be monitored and kept below certain thresholds to avoid performance drops and failure. Sensors, however, cannot always be placed at critical locations. Instead, it is possible to use numerical models to estimate relevant magnitudes during system operation. Thermal effects in electric and electronic components can be represented in a compact way using lumped-parameter equivalent circuits. These can be combined with sensor readings from the device under study to develop digital twins and use them to monitor temperatures during test and operation. In this paper, we put forward a method to generate thermal digital twins of e-powertrain elements such as power inverters. The thermal equivalent circuit equations are obtained from a general-purpose simulation software tool and optimized to enable real-time execution. Kalman filters are then used to fuse the simulation results from this model and sensor measurements of component temperatures. The proposed method provides a way to estimate the inputs and parameters of the thermal circuit and can be used to avoid the drift of the simulation away from actual component behavior. The performance of this approach is demonstrated with a simple benchmark example and the thermal equivalent circuit of a three-phase inverter.

The Kalman filter algorithm estimates variables of linear systems combining information from real sensors and a mathematical model of the system. It may be applied to observe nonlinear systems by means of a linearization of the system model. Multibody system dynamics constitutes a methodology for the analysis and design of mechanical systems. During the last twenty years, many ways of employing a multibody model as the Kalman filter model have been explored.This paper gathers up diverse algorithms, from the first ones based on the continuous expressions of the filter, to the indirect methods that enable real-time implementations of the observation of mechanical systems with a large number of variables. A detailed explanation of the methods and a description of the strengths and weaknesses of each one is presented along this paper, including a benchmark evaluating the performance of the methods.An important aspect of the Kalman filter is the characterization of the system uncertainty by means of white Gaussian noise. Sometimes, the statistical properties of the noise are unknown. Several methods to determine these properties are described, and a new methodology to model systems perturbed by colored noise (time-correlated noise) is presented.In Kalman filters based on multibody models, the information from a real mechanical system can be employed to keep the model behaving like the actual system with a great level of accuracy, linking the simulation to the real behavior of the system.