Reduced-Order Modelling for Thermal–Mechanical Analysis of Power Electronic Modules

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This paper introduces a compact and time-efficient reduced-order modelling method for conducting thermal–mechanical analyses and studying material nonlinearities in power electronic modules (PEMs). Thermal–mechanical analyses in reduced-order modelling research typically follow a sequential coupling approach, where the thermal model is solved first, allowing the resulting temperature distributions to serve as loads in the mechanical system. In this study, a direct coupling method is employed for the thermomechanical analysis, enabling the simultaneous evaluation of the thermal and structural governing equations to determine thermal and directional deformation distributions, with temperature and deformations as the degrees of freedom (DOFs) of the coupled system. A novel approach, utilising the Krylov subspace-based model order reduction (MOR) process, the Newmark and Newton–Raphson algorithms within the reduced-order modelling framework, have been developed for analysing material nonlinearity in PEMs. The time domain responses, i.e., the transient ROM solutions, align remarkably well with the corresponding FOM solutions. The inelastic strains and plastic work results demonstrate strong consistency for materials having time-independent (plasticity) and time-dependent (creep and viscoplasticity) nonlinearities. Responses of the reduced-order model (ROM) in the frequency (Laplace) domain are analysed in contrast to its full-order model (FOM) to evaluate its characteristics and show suitability within the required expansion points. The MOR process provides a significantly compact ROM order of just 20 × 20 for reduced-dimensional computation, achieving up to an 83% reduction in computational time compared to its FOM order of approximately 400,000 × 400,000. The reduced-order modelling approach is implemented using the MATLAB coding environment. • A new modelling approach is introduced for thermal–mechanical analysis of PEMs. • A new way is offered for material nonlinearity analysis of PEM wires and solders. • A Krylov subspace algorithm is integrated with Newmark and Newton–Raphson methods. • The process offers a computing time reduction of 83% while retaining its accuracy.

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