Stochastic Portfolio Planning for Virtual Power Plants Using Stratified Sampling

The rise of Virtual Power Plants represents a major shift in the energy sector, promoting decentralized and sustainable power systems. Virtual Power Plants integrate distributed energy resources such as energy storage systems, distributed generators, photovoltaic systems, and wind turbines. This integration improves system efficiency by enabling unified operational schedules, reducing the need to manage each resource separately. Allocating these resources efficiently is critical due to the growing use of renewable energy and the changing nature of electricity markets. To address challenges caused by variable renewable energy generation and market price fluctuations, this study proposes a scenario modeling method using Kernel Density Estimation combined with Stratified Sampling. Forecast errors are further modeled using a copula-based approach that captures spatial and temporal correlations. A two-stage mixed-integer programming method is employed to optimize resource allocation within Virtual Power Plants, aiming to increase revenue and reduce imbalance penalties. Numerical results show that the proposed method improves resource allocation under uncertainty, increases revenue from market prices and renewable energy credits, and lowers imbalance penalties while meeting operational constraints. Specifically, total revenue increased by 1.6%, with a 2.6% improvement in market price revenue and a 5.6% reduction in imbalance penalties.