Air-conditioning systems have great potential to provide energy flexibility services to the power grids of high-renewable penetration, due to their high power consumption and inherent energy flexibilities. Direct load control by switching off some operating chillers is the simplest and effective means for air-conditioning systems in buildings to respond to urgent power reduction requests of power grids. However, the implementation of this approach in today's buildings, which widely adopt demand-based feedback controls, would result in serious problems including disordered cooling distribution and likely extra energy consumption. This study, therefore, proposes a reconfigurable control strategy to address these problems. This strategy consists of supply-based feedback control, incorporated with the conventional demand-based feedback control, a control loop reconfiguration scheme and a setpoint reset scheme, facilitating effective control under limited cooling supply and smooth transition between supply-based and demand-based feedback control modes. The proposed control strategy is deployed in a commonly-used digital controller to conduct hardware-in-the-loop control tests on an air-conditioning system involving six AHUs. Test results show that the reconfigurable control achieves commendable control performance. Proper chilled water distribution enables even thermal comfort control among the building zones during demand response and rebound periods. Temperature deviation of the building zones is controlled below 0.2 K most of the time. 11.6 % and 27 % of power demand reductions are achieved during demand response and rebound periods respectively, using the proposed reconfigurable control compared with that using conventional controls.