Approaching Prosumer Social Optimum via Energy Sharing with Proof of Convergence

The conventional power system operation approach has been proven to be effective and reliable for decades. Specially, at the demand side, customers are managed centrally by aggregators and usually not price-responsive. With the prevalence of distributed energy resources (DERs), traditional consumers are now endowed with the ability to produce energy, turning into so-called prosumers. Prosumers can tradeoff between supply and demand and participate in energy management proactively. At the same time, the intermittent and uncertain nature of DERs call for a stronger capability of dealing with real-time energy fluctuation. In this context, exploiting demand-side flexibility to support real-time energy balancing, which can reduce required generation reserves and save costs, is a promising direction for energy system modernization. However, the traditional centralized scheme fails to allow a prosumer to act upon its profit-maximizing philosophy, which reduces prosumer incentives and restricts demand-side flexibility. Therefore, a new prosumer-oriented approach is desired. The emerging sharing economy in recent years, such as Airbnb and Uber, is a successful business model to enhance resource utilization efficiency by encouraging exchanges of goods among customers. Inspired by this, it is natural to ask: can energy be shared similarly? That is, is it possible to motivate idle generation resources to help support real-time energy balancing instead of relying on additional reserves? In this paper, an energy sharing mechanism is presented to achieve this goal. The main contributions are three-fold: 1) Mechanism Design. An energy sharing mechanism is proposed to accommodate prosumers' strategic decision-making on their self-production and demand in the presence of capacity constraints. The relationship between sharing quantity and sharing price is described by a generic supply-demand function so that prosumers' market roles are endogenously determined. Under this setting, all prosumers constitute a generalized Nash game whose equilibrium is difficult to characterize. Moreover, the inequality capacity constraints will further complicate equilibrium analysis. 2) Equilibrium. Main properties of the proposed energy sharing game are proved. The generalized Nash equilibrium of the game always exists and is partially unique. No prosumer is worse off so that it always has the incentive to participate in energy sharing. The energy sharing game achieves a $1-O(1/I)$ price-of-anarchy (PoA, which is less than 1 because the net cost is negative in our setting). Besides, as the number of prosumers $I$ increases, both the total net cost and individual prosumer strategies are proved to converge to the social optimum under the centralized operation. 3) Algorithm. A bidding process is developed to achieve the desired equilibrium in a distributed manner. This paper provides guidance for selecting the market sensitivity parameter so that the bidding process is guaranteed to converge. Our bidding process tends to the generalized Lagrange multipliers method to solve the centralized social optimum problem as the number of prosumers increases.