One of the goals of ubiquitous power internet of things is to make the energy consumption cleaner and lower carbon. Under the ubiquitous power internet of things, a peak shaving model considering carbon emission restriction is proposed based on Virtual Power Plant (VPP), which is used as a management means of distributed energy. According to the principle of carbon emission quota system, three different scenarios of carbon emission restriction are established, and the peak shaving cost and environmental benefits of the system under three scenarios are analyzed by using membrane computing based on distribution estimation. The results show that the carbon emission restriction will lead to the change of the output of peak shaving system to reduce carbon emissions, but within a certain range, the carbon emissions of the system will not change with the change of the restriction, in other words, there is a certain free carbon emission restriction space. The level of carbon emission restriction will affect the cost of VPP peak shaving system and the allocation of carbon emission rights should follow the principle of fairness and efficiency. This work is supported by National Natural Science Foundation of China (No. 61703249).