Dynamic and efficient brokering of energy suppliers and consumers in a smart grid

One of the fundamental tasks of a smart-grid is achieving an optimal balance between the supplied and consumed energy in the grid. The optimal balance avoids underutilisation as well as overloading of energy sources; minimises the cost of energy transportation and storage; and reduces the price of energy. In this paper we propose a stochastic model for associating energy-suppliers with consumers having matching characteristics in a probabilistic sense. The optimal number of users a particular supplier can serve is described in terms of the probability density functions of its energy production and the demand of consumers. We shall demonstrate both analytically and numerically that an optimal balance can be achieved when the supplied energy, the demand for energy, and the number of users associated with a particular supplier, all, have a normally distributed probability distribution function (pdf).