Compact modeling of microbatteries using behavioral linearization and model-order reduction

Thin-film, solid-state microbatteries represent now a viable alternative for powering small form-factor microsystems or storing the power harvested by energy microsensors. One major obstacle to their widespread use in integrated systems has been the absence of a high-fidelity, physics-based, compact model describing their operation and enabling their design and verification in the same CAD environment as integrated systems or energy harvesters. In this work, we develop and validate such a model using a thorough analysis of the electrochemistry of a thin-film, solid-state lithium-ion microbattery. Our compact model is based on a behavioral linearisation step where the nonlinear partial differential equations (PDEs) describing the microbattery electrochemistry are replaced with linear ones without virtually any loss in accuracy. Unlike Taylor series and other local techniques, our behavioral linearisation is global and is based on the careful examinations and validation of global electroneutrality in the thin-film, solid-state electrolyte. We then apply the well-established methodology of Arnoldi-based model-order reduction (MOR) techniques to develop a compact microbattery model capable of reproducing its input(current)-output(voltage) electrical behavior with less than 1% error with respect to the full discretised PDEs. The use of the reduced-order model results in more than 30X speedup in transient simulation.