This paper addresses the state-variable stabilising control of the power system using such series FACTS devices as TCPAR installed in the tie-line connecting control areas in an interconnected power system. This stabilising control is activated in the transient state and is supplementary with respect to the main steady-state control designed for power flow regulation. Stabilising control laws, proposed in this paper, have been derived for a linear multi-machine system model using direct Lyapunov method with the aim to maximise the rate of energy dissipation during power swings and therefore maximisation their damping. The proposed control strategy is executed by a multi-loop controller with frequency deviations in all control areas used as the input signals. Validity of the proposed state-variable control has been confirmed by modal analysis and by computer simulation for a multi-machine test system.