Optimal Demand Response and Supply Schedule Under Market-Driven Price: A Stackelberg Dynamic Game Approach

TL;DR

This paper models the interaction between energy providers and users in a dynamic market using a Stackelberg game, deriving optimal demand and supply schedules that balance demand and supply while setting reasonable prices.

Contribution

It introduces a novel two-layer optimization framework and characterizes the Stackelberg equilibrium for demand response and supply scheduling in dynamic markets.

Findings

Price is driven to a reasonable value.

Total demand and supply are balanced.

Closed-form Nash solution for demand response.

Abstract

In this work, we use a Stackelberg infinite discrete-time dynamic game model to study the optimal supply schedule and the optimal demand response under a market-driven dynamic price. A two-layer optimization framework is established. At the lower layer, for each user, different appliances are scheduled for energy consumption. For enegy provider, different generators are utilized for energy generation. At the upper level, with the supplier acting as a leader and the users acting as followers, a Stackelberg dynamic game is used to capture the interaction among the energy provider and the users where the energy provider and the users care only about their own cost. We analyze the one-leader-N-followers Stackelberg dynamic game and characterize the Stackelberg equilibrium. We provide a closed-form Nash solution of the optimal dynamic demand response problem when the supply is announced. A set of linear constraints is developed to characterize the Stackeberg equilibrium. Simulation results show that the price is driven to a reasonable value. Also, the total demand and the supply is balanced.