Mean-field-type optimization for demand-supply management under operational constraints in smart grid

Abstract

The electricity business depends significantly on continuous, cost-effective sources of electricity, the efficient reaction to the demand and storage cost. But the increasing demands and alternative renewable energy sources on the power grid are causing instability and price volatility. Smart grid technology and programs are emerging to address these problems. In this paper we study demand-supply management under operational constraints and outage scheduling. We consider a model of an electricity market in which finite number of suppliers offer electricity. Each supplier has several power plants with different maximum capacity of production and different cost depending on the operational constraints. The response of the market to these offers is the quantities bought from the suppliers. The objective of the market is to satisfy the electricity demand at minimal cost. We develop a theoretical framework for cooperative production strategies between electricity producers. We formulate the problem as an optimal control problem under constraints. Using maximum principle techniques, we provide closed-form expressions of the joint production efforts between the electricity producers. Applying inf-convolution technique to the Hamiltonian we transform the multiple variable optimization problem into a single-variable optimization problem, reducing significantly the curse of dimensionality. In order to capture the random nature of most of the renewable energy sources, we introduce stochastic demand and stochastic production variabilities. We derive closed-form expressions using mean-field-type optimization techniques. The framework is shown to be flexible enough to include both risk-neutral and risk-sensitive behavior of a decision-maker when facing uncertainties. B Hamidou Tembine

A Survey and Taxonomy of Resource Allocation Methods in Wireless Networks

“…2) Cooperative Dynamic Incomplete Information RA (N > 1,C = 1, L = 1, I = 0): In order to minimize the mismatch between supply and demand under production, maintenance and refueling constraints, Tembine [80] formulates a dynamic cooperative game between the producers and between the generators in smart grid. By using this model, the smart grid market can satisfy the electricity demand at minimal cost.…”

Mean-Field-Type Games in Engineering

“…The rise of distributed power is also being driven by the ability of distributed power systems to overcome the energy need constraints, and transmission and distribution lines. Mean-field game theoretic applications to power grid can be found in [113,114,115,116,117,118,119,120,93,121,122,123,124]. A prosumer (producer-consumer) is a user that not only consumes electricity, but can also produce and store electricity.…”