Discretisation-free battery fast-charging optimisation using the measure-moment approach

The development of safe and reliable battery fast-charging protocols is one of the key technologies needed to reduce our over-reliance on fossil fuel energy storage. Existing charging algorithms are typically generated by discretising a lumped parameter battery model in time and then solving a constrained numerical optimisation problem. One of the main limitations with this approach is that its performance is reliant upon the granularity of the time discretisation; too coarse a discretisation gives an inaccurate solution where the constraints may be violated between time steps; too fine a discretisation gives a rapid growth in computational complexity. To overcome this trade-off, a discretisation-free approach to solving the optimisation problem is proposed. By exploiting recent developments in the field of measure-moment theory, the method is able to generate discontinuous charging profiles from numerical solutions of a convex optimisation problem, which intrinsically satisfy the physical conservation laws of the model. Numerical examples highlight the potential of the approach for efficiently generating fast-charging protocols.