Guaranteed Conversion From Static Measurements Into Dynamic Ones Based on Manifold Feature Interpolation

The increasing penetration of renewable energy sources, coupled with the variability of loads such as Electric Vehicles (EVs), is leading to stability issues in power systems. Addressing this problem requires dynamic measurements. However, there may be a limited number of High-Resolution (HR) meters, such as Phasor Measurement Units (PMUs), especially in distribution grids. In contrast, there are extensive Low-Resolution (LR) meters. With multi-resolution sources, our objective is to develop methodologies for interpolating data. Existing interpolation methods arise from different domains, e.g., optimization, signal analysis, Machine Learning, etc. However, they generally face the following challenges. Firstly, they lack a principled design for complex dynamics. Secondly, they often overlook essential physical aspects and inherent constraints of power systems. Finally, these methods typically neglect uncertainties. To overcome these challenges, we combine Autoencoders (AE) with curvature regularization to propose an optimal design of interpolation first. Then, we integrate physical laws into our analysis using physics-informed neural networks (PINN) and address uncertainties with stochastic physics-informed neural networks (SPINN). Our proposed method is extensively verified within both transmission and distribution grids.