Stochastic Optimization of Real-Time Dynamic Pricing for Microgrids with Renewable Energy and Demand Response

This paper presents a comprehensive framework for real-time energy management in microgrids integrating distributed renewable energy sources and demand response (DR) programs. To address the inherent uncertainties in key operational variables—such as load demand, wind speed, solar irradiance, and electricity market prices—this study employs a probabilistic modeling approach. A two-stage stochastic optimization method, combining mixed-integer linear programming and optimal power flow (OPF), is developed to minimize operational costs while ensuring efficient system operation. Real-time dynamic pricing mechanisms are incorporated to incentivize consumer load shifting and promote energy-efficient consumption patterns. Three microgrid scenarios are analyzed using one year of real historical data: (i) a grid-connected microgrid without DR, (ii) a grid-connected microgrid with 10% and 20% DR-based load shifting, and (iii) an islanded microgrid operating under incentive-based DR contracts. Results demonstrate that incorporating DR strategies significantly reduces both operating costs and reliance on grid imports, especially during peak demand periods. The islanded scenario, while autonomous, incurs higher costs and highlights the challenges of self-sufficiency under uncertainty. Overall, the proposed model illustrates how the integration of real-time pricing with stochastic optimization enhances the flexibility, resilience, and cost-effectiveness of smart microgrid operations, offering actionable insights for the development of future grid-interactive energy systems.