The tie-line bias control (TBC) method has been widely used in the load frequency control (LFC) of multi-area interconnected systems. However, it should be questioned whether the conventional TBC can still apply to LFC when considering the complication of structures of power systems. LFC, in essence, is to stabilize system frequency/tie-line power by controlling controlled outputs’ area control error (ACE). In this paper, relations between LFC control variables and controlled outputs are expressed as a system of equations, based on which an exemplary ring network is studied. Sufficient and necessary conditions for TBC applicability is presented, and a novel LFC mode is proposed for a general ring network where TBC cannot work. Finally, TBC applicability to multi-area systems with general topology is studied, and a general LFC mode is proposed for systems where TBC is not definitely applicable, thus rendering routines that may guide LFC design of future power systems with more complex topologies.