A linear programming model for power distribution with demand response and variable renewable energy

A linear programming framework is proposed to model distribution network characteristics, and market clearing processes for flexible load and distributed energy resources providing reserve and reactive power compensation. One shows that the Nash equilibrium solution representing the interaction between utility and customers for demand response and distributed reserve transactions can be approximated by a linear program when the players (i.e. the customers) are numerous and tend to become infinitesimal. Then a linear program is shown to reveal the market prices, corresponding to the marginal cost for the utility. The goal in developing this model is to provide a new module for a regional long term model of development of smart energy systems. This module will then introduce in the modeling of energy transition, the new options and constraints that are provided by a penetration of renewables with the possibility of implementing distributed markets for demand response and system services permitted by the development of the cyber-physical layer. A case study of a potential smart urban distribution network in Europe is carried out and provides numerical results that illustrate the proposed framework.