Adaptive bayesian sparse polynomial chaos expansion for voltage balance of an isolated microgrid at peak load

Microgrids (MGs) are essential for ensuring a reliable and efficient power supply, particularly in isolated or islanded regions. One of the significant challenges faced is maintaining voltage balance during peak load periods, which is complicated by uncertainties in renewable energy availability, demand response, and system constraints. This paper introduces an Adaptive Bayesian Sparse Polynomial Chaos Expansion (BSPCE) framework designed to tackle these challenges effectively. Unlike traditional BSPCE methods that utilize fixed sampling strategies, our adaptive approach dynamically modifies sampling locations in response to approximation errors or model sensitivities. This allows for a more efficient allocation of computational resources, enhancing approximation accuracy in areas of high uncertainty. The framework systematically quantifies uncertainties related to maximum loadability and operational constraints, while also accounting for the impacts of battery energy storage systems, electric vehicles, and demand response mechanisms. By applying this methodology to the IEEE-15 bus system, we provide a comprehensive assessment of voltage balance in isolated microgrids during peak load conditions. The proposed method is capable of dealing with a big number of inputs that are correlated and follow unrelated distributions. The simulation modeling is performed on the MATLAB platform. The numerical results from the IEEE 15 test feeders confirm that the approach is accurate and efficient at the same time.