The present study investigates how different charge injection functions impact electrohydrodynamic-driven flows within a latent heat thermal storage system (LHTSS). To this end, three injection models are examined: the Heaviside step function, the Schottky injection, and autonomous injection. Previous research has largely utilized autonomous charge injection, which neglects the influence of the electric field, thus producing space charge density distributions that do not mimic the realistic charge injection phenomena. In this work, the lattice Boltzmann method (LBM) is applied to simulate the behavior of paraffin wax in an LHTSS under both autonomous and non-autonomous charge injection based on an experimental current–voltage curve. The governing equations were solved using an LBM solver, with the results being verified against multiple experimental and numerical benchmarks. Initially, the paraffin wax began to melt due to thermal conduction from the hot top wall. Electro-convection was then generated by injecting charges via a central circular electrode in the LHTSS, thereby enhancing the heat transfer rate. LBM results demonstrated an electrohydrodynamic enhancement factor of 1.57 using the experimental current–voltage curve presented by Hassan and Cotton [Int. J. Heat Mass Transfer 204, 123831 (May 2023)]. The liquid fraction, heat transfer coefficient, and velocity for the Schottky and Heaviside step functions of injection were very close; however, despite using identical current in all cases, the results for autonomous injection showed deviations of up to 30%, 16%, and 42%, respectively. Furthermore, increasing the material's permittivity worsens the deviations. This study provides insights into how to use charge injection to design LHTSSs and predict heat transfer augmentation in LHTSSs.