An H<inf>∞</inf> design for dynamic pricing in the smart grid

An H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> design for dynamic pricing in the smart grid is proposed. This design jointly considers the operation of a distribution network operator and a market operator. In the design, a ratio of the regulated output energy to the disturbance energy is minimized to address the worst-case scenario. Linear matrix inequality approaches are used to formulate the design problem as a convex problem. Fuzzy interpolation techniques are integrated into the design procedure so that nonlinear grid dynamics can be addressed. In contrast with existing designs, the proposed design can yield a more reliable and practical pricing scheme as shown via simulations.