Probabilistic correlation of renewable energies within energy hubs for cooperative games in integrated energy markets

Utilizing renewable energy sources like wind turbines and solar panels is increasing annually due to environ-mental and economic opportunities. Wind speed and solar irradiation depend on the time of day and the location of the site. The correlation of renewable energies with load and consequently with price in an energy market yields a more accurate estimation of energy optimization and consumption patterns. This problem will be more complicated when energy hubs choose to play in the integrated energy markets based on their coalitions with other energy hubs. An energy hub may join another energy hub to cooperate in an energy market or play self-autonomous to maximize its profit. This paper proposes a spatiotemporal correlation of wind speed, solar irra-diation, and price responsive loads considering cooperative and non-cooperative modes of energy hubs based on a game-theoretic approach in an integrated energy market. This paper applies mathematical programming with equilibrium constraints to solve the highly competitive behavior of the energy hubs in this market considering loss. Two comparative and comprehensive case studies demonstrate the strategic actions of the energy hubs in these complicated conditions.