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In demand-side-management, the interruptible load management (ILM) plays an important role in constructing smart grid. One important issue is concentrate on how to determine the incentive payment for the ILM. The integration of consumers' willingness to curtail load in the ILM is helpful to the optimum allocation of the limited electricity resource. In order to design such kind of mechanisms, the consumers' type parameters are introduced to reflect the consumers' willingness to load interruption. In the meantime, the pay-as-you-go method and the pay-in-advance method are presented to the incentive payment. The results show that consumers with relatively large willingness to curtail load get more payments. The self disclosure of consumers' willingness is another merit of these methods. Simulation results certify the validity of the proposed methods on ILM.