Stackelberg Game Coordination of Virtual Power Plants and Price-Based Demand Response Under Renewable Energy Uncertainty Using an Improved PSO

Abstract

Modern power systems face new challenges in maintaining stability and real-time balance with the large-scale integration of intermittent renewable energy. To address the persistent issue of insufficient participation in demand-side management, this study proposes a three-tier Stackelberg game coordination framework for Virtual Power Plants (VPPs) and Price-Based Demand Response (PBDR). To efficiently solve the high-dimensional nested multilevel optimization problem, a Hierarchical Nested Particle Swarm Optimization (HN-PSO) algorithm is developed. Theoretical analysis and simulation results demonstrate the existence and uniqueness of the global equilibrium in the proposed game model. A 24-hour simulation further shows that the VPP can mitigate price volatility while balancing internal dispatchable generation and external procurement. Therefore, the proposed approach can provide an efficient and practical computational method for decentralized market dispatch under renewable energy uncertainty.