Head-sensitive forbidden and restricted zones of large hydropower units are challenging the automatic generation control (AGC) as admissible operating zones are discontinuous and variational. This study focuses on the AGC of such a large hydropower plant to ensure the stability, security and timeliness of power grids. A methodology is developed to solve the unit commitment (UC) and load distribution in AGC. This methodology identifies in advance all feasible unit combinations under different water heads and determines admissible operating zones using combinatorial mathematics techniques. A fast strategy that includes the accurate estimation of varying water heads helps to eliminate infeasible unit combinations. Minimising the number of units working in restricted zones and times of unit output passing through forbidden zones is used to optimise the UC, where priority orders of units are introduced to evaluate UC schemes with the same objective value. Finally, a dynamic programming based model is formulated to solve an economic load distribution among operating units. The methodology is applied to the AGC of the Nuozhadu with nine 650 MW units of two different types. Three cases indicate that the number of units working in restricted zones and times of unit output passing through forbidden zones is significantly reduced.