Obtaining precise reducer order battery models is a key component in designing lithium-ion battery management systems. In general, with conventional order reduction techniques, low order is followed by low accuracy. To overcome such limitation, this paper presents a frequency-based constructive method to obtain broad-band low-order approximations of the solid-phase lithium-ion diffusion submodel, the core of the reference pseudo-two-dimensional electrochemical model of lithium-ion cells. The proposed method is a combination of an improvement on the residue grouping technique and of standard balancing and truncation/residualization methods borrowed from control systems theory. As main result, dramatic order reductions from 3000th to 5th-order with minimum accuracy losses are obtained. Taking a well-known case-study of a lithium-ion battery model, it is shown that 5th-order models offer approximations with maximum absolute errors of 0.5%, for characteristic times up to 9.54 × 10 4 s . The proposed method will help to obtain accurate real-time estimations of surface concentration and state of charge of lithium-ion batteries. Graphic abstract