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Load pay back effect is the excess of load as a result of load curtailment, observed in direct load control programs related to thermostatically controlled appliances. In this paper, according to a stochastic difference equation, the load profile of an aggregation of customers without control will be attained. Then the assumption to consider load pay back as linear will be examined through simulations. Afterwards, based on a data structure gained from performing load curtailments at each interval, least-square method will be used to fit load pay back factors for each interval. It is notable that there are some significant differences between the results attained in this paper and what was assumed before.