A direct method for power system corrective control to relieve current violation in transient with UPFCs by barrier functions

• A direct method based corrective control with UPFCs is proposed to releve current violation in transient.
• A barrier function approach is proposed to avoided undesirable relay trips caused by current violation in transient.
• A control Lyapunov function consistsed of an energy function and a barrier function, is introduced.
• A sufficient condition of mathematical guarantee for stability and security (for current violation) have been derived and proved.

A direct method based new control scheme for corrective control with unified power flow controllers (UPFCs) is proposed to avoid mal-operation of transmission-line relay trips caused by current violation so as to prevent possible cascaded element failure by overloads of the parallel transmission-line. Undesirable relay trips are avoided by decreasing the dynamic currents near the thresholds thanks to the barrier function penalty, because the value of the barrier function approaches infinity as current of the transmission line approaches pre-set threshold. A control Lyapunov function (CLF), which consists of an energy function and barrier functions, is introduced to derive the control law that exploits the non-positive time derivative of the energy function and the large value of the barrier function as trajectories approach the boundary of constraints. In particular, the feedback control exercised by the UPFC results in the negative time derivative of the Control Lyapunov Function in the reshaped attraction region, with the consequence that the state trajectory converges to the desired stable equilibrium point (SEP). Ultimately, the resulting reshaped attraction region for the desired operating point is analyzed, and illustrative numerical simulations are carried out using a 3-bus and the IEEE 162 Bus test system, demonstrating the effectiveness of the proposed method.