The existing transmission network is becoming increasingly overloaded due to rapidly growing electricity demand, deregulation, and limited investment in transmission network expansion. This paper presents a state-space model-based control design for regulating line active-power flows in aC electric power systems using linear-quadratic-Gaussian (LQG) control. at its core, the proposed method relies on the linear mapping of nodal active- and reactive-power injections to active-power line flows. Building on this, we outline a combined linear-quadratic regulator and Kalman-filter design to optimally dispatch generators and controllable loads to maintain line flows while ensuring power balance. We demonstrate the utility of the proposed LQG controller with a representative congestion-management application.