Optimal Sensor Placement in Power Transformers Using Physics-Informed Neural Networks

TL;DR

The paper tackles the problem of monitoring power transformers under sensor constraints by employing Physics-Informed Neural Networks (PINNs) to predict internal temperatures. It formulates the 2D heat diffusion dynamics with a PINN-based solver, exemplified by the equation $ \frac{\partial T}{\partial t} = \kappa \nabla^2 T + S $. By coupling PINNs with Mixed Integer Optimization Programming, it computes optimal sensor placements that enable accurate temperature reconstruction with a limited sensor budget. This approach offers a scalable, physics-driven solution for cost-effective transformer health monitoring, applicable to both 1D and 2D sensing configurations.

Abstract

Our work aims at simulating and predicting the temperature conditions inside a power transformer using Physics-Informed Neural Networks (PINNs). The predictions obtained are then used to determine the optimal placement for temperature sensors inside the transformer under the constraint of a limited number of sensors, enabling efficient performance monitoring. The method consists of combining PINNs with Mixed Integer Optimization Programming to obtain the optimal temperature reconstruction inside the transformer. First, we extend our PINN model for the thermal modeling of power transformers to solve the heat diffusion equation from 1D to 2D space. Finally, we construct an optimal sensor placement model inside the transformer that can be applied to problems in 1D and 2D.