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.

Lumped-parameter thermal networks (LPTNs) are efficient computational models that can be used to replicate the thermal behavior of eMotors in a way that is compatible with real-time execution. The accuracy of the simulation results delivered by LPTNs relies on the selection of an appropriate topology and the accurate tuning of their parameters, namely resistances, capacities and heat sources. It is difficult, however, to obtain an accurate tuning of the parameters starting from theoretical expressions, and these often need to be adjusted based on experimental calibration. Several methods can be used to this end; among these, finite differences are a popular option. This paper presents a methodology for the analytical determination of the sensitivity of LPTN dynamics with respect to its lumped parameters. The obtained analytical sensitivities provide information about the effect of the circuit parameters on the thermal dynamics of the overall system, and can be used to enable the use of gradient-based optimization methods to adjust the LPTN parameters. The proposed method overcomes several limitations of finite difference approaches, like the computational load incurred when the number of parameters to be adjusted is large, and the variability of the results with the increment used to define the finite differences. The analytical sensitivities were tested in the analysis and optimization of a benchmark thermal model and the LPTN representation of a permanent-magnet synchronous motor.

Cable-driven parallel robots are parallel robots where light-weight cables replace rigid bodies to move an end-effector. Their peculiar design allows obtaining large workspaces, high-dynamic handlings, ease of reconfigurability and, in general, low-cost architecture. Knowing the full state variables of a cable robot may be essential to implement advanced control and monitoring strategies and imposes the development of state observers. In this work a general approach to develop nonlinear state observers based on an extended Kalman filter (EKF) is proposed and validated both numerically and experimentally by referring to a cable-suspended parallel robot. The state observer is based on a system model obtained by converting a set of differential algebraic equations into ordinary differential equations through different formulations: the penalty formulation, the Udwadia–Kalaba formulation, and the Udwadia–Kalaba–Phohomsiri formulation, which have been chosen since they can handle the presence of redundant constraints as often happens in cable-driven parallel robots. In the numerical investigation, the EKF is validated simulating encoders heavily affected by quantization errors to demonstrate the filtering capabilities of EKF. In the experimental investigation, a very challenging validation is proposed: only two sensors measuring the rotations of two motors are used to estimate the actual position and velocity of the end-effector. This result cannot be achieved by sole forward kinematics and clearly proves the effectiveness of the proposed observer.

The simulation of complex engineering applications often requires the consideration of component-level dynamics whose nature and time-scale differ across the elements of which the system is composed. Co-simulation offers an effective approach to deal with the modelling and numerical integration of such assemblies by assigning adequate description and solution methods to each component. Explicit co-simulation, in particular, is frequently used when efficient code execution is a requirement, for instance in real-time setups. Using explicit schemes, however, can lead to the introduction of energy artifacts at the discrete-time interface between subsystems. The resulting energy errors deteriorate the accuracy of the co-simulation results and may in some cases develop into the instability of the numerical integration process. This paper discusses the factors that influence the severity of the energy errors generated at the interface in explicit co-simulation applications, and presents a monitoring and correction methodology to detect and remove them. The method uses only the information carried by the variables exchanged between the subsystems and the co-simulation manager. The performance of this energy-correction technique was evaluated in multi-rate co-simulation of mechanical and multiphysics benchmark examples.

Time–domain simulation of electronic and thermal circuits is required by a large array of applications, such as the design and optimization of electric vehicle powertrain components. While efficient execution is always a desirable feature of simulation codes, in certain cases like System-in-the-Loop setups, real-time performance is demanded. Whether real-time code execution can be achieved or not in a particular case depends on a series of factors, which include the mathematical formulation of the equations that govern the system dynamics, the techniques used in code implementation, and the capabilities of the hardware architecture on which the simulation is run. In this work, we present an evaluation framework of numerical methods for the simulation of electronic and thermal circuits from the point of view of their ability to deliver real-time performance. The methods were compared using a set of nontrivial benchmark problems and relevant error metrics. The computational efficiency of the simulation codes was measured under different software and hardware environments, to determine the feasibility of using them in industrial applications with reduced computational power.