  Compressed air energy storage (CAES) is suitable for large-scale energy
storage and can help to increase the penetration of wind power in power
systems. A CAES plant consists of compressors, expanders, caverns, and a
motor/generator set. Currently used cavern models for CAES are either accurate
but highly non-linear or linear but inaccurate. Highly non-linear cavern models
cannot be directly utilized in power system optimization problems. In this
regard, an accurate bi-linear cavern model for CAES is proposed in this first
paper of a two-part series. The charging and discharging processes in a cavern
are divided into several virtual states and then the first law of
thermodynamics and ideal gas law are used to derive a cavern model, i.e., model
for the variation of temperature and pressure in these processes. Thereafter,
the heat transfer between the air in the cavern and the cavern wall is
considered and integrated into the cavern model. By subsequently eliminating
several negligible terms, the cavern model reduces to a bi-linear (linear)
model for CAES with multiple (single) time steps. The accuracy of the proposed
cavern model is verified via comparison with an accurate non-linear model.
