An optimal real-time pricing algorithm under load uncertainty and user number variation in smart grid

The progress of real‐time communication systems for smart grid has led to the importance of real‐time pricing becoming more highlighted. There are many investigations that have already been done. Real‐time pricing frameworks have proposed an implemented distributed algorithm with or without consideration of effect of load uncertainty. In some existing literature the effect of different types of load uncertainty models on average consumption and generated capacity is considered. However, the number of users is considered to be constant. In this paper, it is assumed that the number of users is varying independently and randomly. In this case the effect of variation of number of users on the basis of Poisson process and uniform distribution is compared with results from previous works, when bounded uncertainty model was applied for added noise to the consumption. Simulation results indicate that when users vary on the basis of Poisson distribution, the waste of energy decreases and the welfare increases.