In microstructure-resolving lithium-ion batteries simulation the predictions (potential, ion concentration, overpotential) differ from the ones of DFN, which predicts only the local running average, due to the idealization of spherical particle. Accurate theoretical and numerical analysis of the relation between the microscopic model and DFN is needed, possibly a suitable DFN extension that captures the local fluctuations. We provided a theoretical explanation of the models' prediction differences and developed a new computationally effective model as an extension of Newman model with the differences taken into account