Coordinating flexible loads via optimization in the majorization order

A key feature of the smart grid is the integration of a large group of flexible loads which, depending on their respective natures, are deferrable, and/or interruptible. To fully exploit such load flexibilities, the system operator attempts to make decisions towards an efficient coordination of flexible loads so as to achieve specifically aimed energy consumption patterns. One desirable consumption pattern, motivated by reducing generation costs and customer expenditures, is to make the total load profile as smooth as possible. To this end, we model the load coordination as an optimal zero-one matrix completion problem. In particular, we propose an optimization problem in the majorization order. Although such problem seems combinatorially hard at first sight, due to its nice structure, we show that it can be solved with low complexity. We firstly discuss the existence and uniqueness of the optimal solution. Then, a sequential algorithm is proposed to solve the optimization problem efficiently, even in the case of a large population of loads. Moreover, we address the connection between our work and the valley-filling behavior presented by a substantial number of works in the literature.