A Learning Automaton-Based Scheme for Scheduling Domestic Shiftable Loads in Smart Grids

In this paper, we consider the problem of scheduling shiftable loads, over multiple users, in smart electrical grids. We approach the problem, which is becoming increasingly pertinent in our present energy-thirsty society, using a novel distributed game-theoretic framework. In our specific instantiation, we consider the scenario when the power system has a local-area Smart Grid subnet comprising of a single power source and multiple customers. The objective of the exercise is to tacitly control the total power consumption of the customers' shiftable loads, so to approach the rigid power budget determined by the power source, but to simultaneously not exceed this threshold. As opposed to the "traditional" paradigm that utilizes a central controller to achieve the load scheduling, we seek to achieve this by pursuing a distributed approach that allows the users1 to make individual decisions by invoking negotiations with other customers. The decisions are essentially of the sort, where the individual users can choose whether they want to be supplied or not. From a modeling perspective, the distributed scheduling problem is formulated as a game, and in particular, a so-called "Potential" game. This game has at least one pure strategy Nash equilibrium (NE), and we demonstrate that the NE point is a global optimal point. The solution that we propose, which utilizes the theory of learning automata (LA), permits the total supplied loads to approach the power budget of the subnet once the algorithm has converged to the NE point. The scheduling is achieved by attaching a LA to each customer. The paper discusses the applicability of three different LA schemes, and in particular, the recently-introduced Bayesian learning automata. Numerical results, obtained from testing the schemes on numerous simulated data sets, demonstrate the speed and the accuracy of proposed algorithms in terms of their convergence to the game's NE point.