  For proper planning, operation, control, and protection of the power system,
the development of a suitable steady-state mathematical model of FACTS devices
is a key issue. The Fast and Flexible Holomorphic Embedding (FFHE) method
converges faster and provides the flexibility to use any state as an initial
guess. But to investigate the effect and ability of FACTS devices using FFHE
technique, it is necessary to develop an embedded system for these devices.
Therefore, this paper presents an FFHE-based embedded system for VSC-based
FACTS controllers, such as SSSC and IPFC. The embedded system is also proposed
for their controlling modes.
  The introduced embedded system is flexible which allows to take any state as
an initial guess instead of fixed state, which leads towards the reduced
runtime and decreases the required number of terms, as compared to standard
HELM. To demonstrate the effectiveness and practicability, the proposed
FFHE-based models of FACTS devices have been tested for several cases. Further,
the developed recursive formulas for power balance equations, devices' physical
constraints, and their controlling modes are thoroughly investigated and
examined. From several tests, it is found that the proposed FFHE-based FACTS
models require less execution time and reduce the error at higher rate.
