A variational inequality approach to instantaneous load pricing based demand side management for future smart grid

In this paper, we investigate a new polynomial pricing function based demand side management scheme for future smart grid, where the consumers are charged based on their instantaneous load. A non-cooperative game is formulated, where each consumer aims to minimize their total energy cost based on the given pricing function. By casting this game in the variational inequality framework, we present sufficient conditions for the uniqueness of the optimal solution. We then propose a distributed and simultaneous algorithm to achieve the optimal solution. Sufficient conditions for the geometrical convergence of our algorithm are also provided and proved. Numerical results reveal that our proposed algorithm converges very quickly, and is effective in encouraging consumers to shift their energy usage from peak to non-peak times.