In this work we derive asymptotically stabilizing control laws for electrical power systems
using two nonlinear control synthesis techniques. For this transient stabilization problem the
actuator considered is a power electronic device a controllable series capacitor (CSC). The
power system is described using two different nonlinear models - the second order swing
equation and the third order flux-decay model. To start with the CSC is modeled by the
injection model which is based on the assumption that the CSC dynamics is very fast as compared
to the dynamics of the power system and hence can be approximated by an algebraic equation.
Here by neglecting the CSC dynamics the input vector $g(x)$ in the open loop system takes a
complex form - the injection model. Using this model interconnection and damping assignment
passivity-based control (IDA-PBC) methodology is demonstrated on two power systems: a single
machine infinite bus (SMIB) system and a two machine system. Further IDA-PBC is used to derive
stabilizing controllers for power systems where the CSC dynamics are included as a first order
system. Next we consider a different control methodology immersion and invariance (I&I) to
synthesize an asymptotically stabilizing control law for the SMIB system with a CSC. The CSC is
described by a first order system. As a generalization of I&I we incorporate the power balance
algebraic constraints in the load bus to the SMIB swing equation and extend the design
philosophy to a class of differential algebraic systems. The proposed result is then
demonstrated on another example: a two-machine system with two load buses and a CSC. The
controller performances are validated through simulations for all cases.
