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152 Power flows in compensation and control studies

4.8 Conclusion

This chapter has presented the mathematical modelling of plant components used to
control active and reactive power flows and voltage magnitude in high-voltage
transmission networks. The emphasis has been on positive sequence power flow
modelling of both conventional equipment and modern power systems controllers.
The main steady state characteristics of the most prominent FACTS and Custom
Power controllers were discussed with a view to developing simple and yet com-
prehensive power flow models for this new generation of power systems equipment.
The following FACTS controllers received attention in this chapter: the SVC, the
STATCOM, the SPS, the TCSC, the DVR, the UPFC, and the HVDC Light.
The theory of power flows and the fundamental equations used in electrical power
circuits have been covered in depth, with plenty of detailed numerical examples. The
Newton±Raphson power flow algorithm has been singled out for full treatment due
to its high reliability towards the convergence. Numerical methods with strong
convergence characteristics are mandatory when solving FACTS upgraded power
systems networks. This is due to the difficulty involved in solving the highly non-
linear equations used to represent such equipment and the very large-scale system
that the power network represents.