  Mathematical models are just models. The desire to describe battery energy
storage system (BESS) operation using computationally tractable model
formulations has motivated a long-standing discussion in both the scientific
and industrial communities. Linear BESS models are the most widely used so far.
However, finding suitable linear BESS models has been controversial.
  This paper focuses on the description of linear BESS models. Four linear BESS
formulations are presented, among the most popularly used. A new formulation is
also proposed. The 5 BESS models are tested in 100 random BESS and 1.450 random
samples of daily profiles of renewable generation. Two classical problems of
power systems, namely, the set-point tracking problem and the transmission
expansion planning problem, are selected for numerical analysis. Five thousand
simulations are used to draw a better interpretation of each linear formulation
presented and showcase specific challenges of BESS models. Practical
recommendations are provided based on the findings.
