A Stackelberg Game Approach to Control the Overall Load Consumption of a Residential Neighborhood

TL;DR

This paper formulates a Stackelberg game between a coordination agent and participating homes to control the overall load consumption of a residential neighborhood and develops a distributed optimization framework based on gradient descent to attain a better price vector.

Abstract

This paper formulates a Stackelberg game between a coordination agent and participating homes to control the overall load consumption of a residential neighborhood. Each home optimizes a comfort-cost trade off to determine a load schedule of its available appliances in response to a price vector set by the coordination agent. The goal of the coordination agent is to find a price vector that will keep the overall load consumption of the neighborhood around some target value. After transforming the bilevel optimization problem into a single level optimization problem by using Karush-Kuhn-Tucker (KKT) conditions, we model how each home reacts to any change in the price vector by using the implicit function theorem. By using this information, we develop a distributed optimization framework based on gradient descent to attain a better price vector. We verify the load shaping capacity and the computational performance of the proposed optimization framework in a simulated environment establishing significant benefits over solving the centralized problem using commercial solvers.

Figures (2)

• Figure 1: The average ranks over attained objective value for all competing methods on 15 problems. Lower rank corresponds to a better performance. Bold horizontal lines shows the methods that are not different in a 5% significance level according to the Nemenyi test.
• Figure 2: The desirable and the optimal power consumption profiles of the community consisting of 100 homes.