Risk-based Stochastic Optimal Power Flow for AC/DC Grids Using Polynomial Chaos Expansion

Renewable energy sources (RES) are increasingly integrated into power systems, introducing operational uncertainties that challenge the way we manage the grid. These uncertainties necessitate strategies to address the risks in grid reliability and economic performance. This paper introduces a framework to simultaneously manage the risk associated with economic performance and grid reliability under non-Gaussian uncertainty. The framework utilizes Polynomial Chaos Expansion to solve the risk-based and chance-constrained Stochastic Optimal Power Flow for hybrid AC/DC grids. The risk associated with the costs is addressed by introducing the Value-at-Risk parameter, derived through moment-based calculations, to facilitate risk-averse decision-making. Numerical studies illustrate the impact of risk-neutral versus risk-averse decision-making on the probability distribution functions of RES curtailment and operational costs. Additionally, analyzing efficient frontiers for various confidence levels showcases the framework’s capability to construct a portfolio of strategies that effectively balance risk and operational costs under varying confidence levels of non-Gaussian uncertainty.