Competitive equilibrium pricing and cooperation in smart grids with energy storage

In this paper, we propose to model smart grid households equipped with energy storage systems in a local neighbourhood as a divisible two-good exchange economy market. Households or users cooperate to trade these goods, in this case, their real-time energy supplied by utility company and their stored energy in order to minimize consumption cost. Difference in pricing mechanisms adopted by utility companies that serve the locality gives incentive for users to trade real-time energy. Households schedule their storage devices to be charged during low-price off-peak hours and sell the surplus stored energy to neighbours during peak hours to generate additional income. This creates a trading environment or a market where users exchange real-time energy and stored energy at certain prices. Preference relations of users capture how energy is valued in an economy by each user. We model these preferences as a utility that is a continuous, monotonic, quasi-convex function of energy. Given a set of endowments, consumption profiles and energy prices in the market for each user, we show that a market is created where real-time energy and stored energy are exchanged between users and such an exchange takes place at the competitive equilibrium. We analyze a simple two-user two-good exchange economy market to illustrate the concepts discussed above and prove that the trading prices of the goods in the market regulate themselves in such a way that trading results in reduced costs for both users.