  This paper contributes to modeling and supervision of multi-stage centrifugal
compressors coping with real-gas processes and steady to highly transient
operating conditions. A novel dynamic model is derived, and the incorporation
of the generic Lee-Kesler-Pl\"ocker real-gas equation of state and its
derivatives is presented. The model allows for embedding arbitrarily shaped
performance maps, based on state-of-the-art polytropic change-of-state
compressor characteristics. As the validity of these maps is a key issue for
simulation and model-based monitoring, performance maps are treated as
time-variant, and their shape is to be identified and monitored during
operation. The proposed real-time map estimation scheme comprises an Unscented
Kalman Filter and a newly proposed algorithm, referred to as Recursive Map
Estimation. The combination yields a novel parameter and state estimator, which
is expected to be superior if some parameters are characterized by a distinct
operating point dependency. Two additional time-variant parameters are provided
for monitoring: The first indicates the level of confidence in the local
estimate, and the second points to drastic performance map alterations, which
may be further exploited in fault detection. A modified reference simulation of
a two-stage supercritical carbon dioxide compressor with known state
trajectories, performance maps, and alterations demonstrates the successful
application of the entire monitoring scheme, and serves for a discussion of the
results.
