1D PDE Model for Thermal Dynamics in Fluid-Cooled Battery Packs: Numerical Methods and Sensor Placement

This paper addresses the problem of modeling and estimating state dynamics in coupled battery and thermal cooling systems. We present a coupled diffusion-advection PDE model for fluid-cooled battery packs. A novel numerical method is proposed to simulate this PDE system. The technique is a monolithic integration of the method of characteristics and the Crank-Nicolson update scheme. The numerical scheme is validated with thermal energy conservation and shown to be conservative. We then leverage this numeric scheme to examine the optimal sensor placement problem. We formulate and solve the optimal sensor placement problem by designing the “C matrix” such that the mean square error of the Kalman filter state estimate is minimized.