Incorporating renewable energy sources (RESs) into manufacturing systems has been an active research area in order to address many challenges originating from the unpredictable nature of RESs such as photovoltaics. In the energy-aware scheduling for manufacturing systems, the traditional off-line scheduling techniques cannot always work well due to their lack of robustness with respect to uncertainties coming from imprecise models or unexpected situations. On the other hand, on-line scheduling or rescheduling, which can improve the robustness by using the model and the latest measurements simultaneously, suffer from a high computational cost. This work proposes a hybrid scheduling framework, which combines the advantages of both off-line scheduling and on-line scheduling, to provide a balanced solution between robustness and computational cost. A novel concept of partially-dispatchable state is introduced. It can be treated as a constant in scheduling when the model works well. When the model does not work well, it is triggered as the variable to tune to improve the performance. Such an event-triggered structure can reduce the number of rescheduling and computational costs while achieving a reasonable performance and enhancing system robustness. Moreover, the choice of partially-dispatchable state also provides an extra design freedom in achieving green manufacturing. Simulation examples on a manufacturing system, which consists of a 100-kW solar photovoltaic system, a 10-machine flow shop production line, a 50-kWh energy storage system, a 100-kW gas turbine, and the grid for power supply, demonstrate the validity and applicability of this event-triggered hybrid scheduling (ETHS) framework.