This paper focuses on the thermal modelling of power transformers using physics-informed neural networks (PINNs). PINNs are neural networks trained to consider the physical laws provided by the general nonlinear partial differential equations (PDEs). The PDE considered for the study of power transformer’s thermal behaviour is the heat diffusion equation provided with boundary conditions given by the ambient temperature at the bottom and the top-oil temperature at the top. The model is one dimensional along the transformer height. The top-oil temperature and the transformer’s temperature distribution are estimated using field measurements of ambient temperature, top-oil temperature and the load factor. The measurements from a real transformer provide more realistic solution, but also an additional challenge. The Finite Volume Method (FVM) is used to calculate the solution of the equation and further to benchmark the predictions obtained by PINNs. The results obtained by PINNs for estimating the top-oil temperature and the transformer’s thermal distribution show high accuracy and almost exactly mimic FVM solution.

The emerging methodology of Physics Informed Neural Networks (PINNs) promises to combine available data and physical knowledge to achieve high accuracy and fast evaluation. Dynamic thermal modelling of power transformers is an application specifically set to benefit from these characteristics. Data collected during typical operation is not representative of extreme loading scenarios and the number of thermal sensors is limited. The detailed geometry is often not known by the asset owner which creates high uncertainty for physics-based simulation models. In this study, the transformer is modeled by the one-dimensional heat diffusion equation. PINN is constructed with a loss function including both data-based and physics-based terms. A time-dependent source term from a time series of measurement is also part of the PINN. The result is compared with a finite volume solution demonstrating good agreement. The PINN approach will be useful for further development in thermal modelling for power transformers. Copyright

Physics-Informed Neural Networks (PINNs) are a novel approach to the integration of physical models into Neural Networks when solving supervised learning problems. PINNs have shown potential in mapping spatio-temporal input and the solution of a partial differential equation (PDE). However, despite their advantages for many applications, they often fail to train when target PDEs contain high frequencies or multiscale features. Thermal modelling of power transformers is fundamental for improving their efficiency and extending their lifetime. In this work, we investigate the performance of different PINN architectures applied to a 1D heat diffusion equation with a specific heat source representing the heat distribution inside a transformer. Measurements, which include the top-oil temperature, the ambient temperature and the load factor are taken from a transformer in service. We demonstrate the limitations of PINNs, propose possible remedies, and provide an overall assessment of the potential of using PINNs for transformer thermal modelling.

Insulation is an essential part of power transformers, which guarantees an efficient and reliable operational life. It mainly consists of mineral oil and insulation paper. Most of the major failures of power transformers originate from internal insulation failures. Monitoring aging and thermal behaviour of the transformer’s insulation paper is achieved by different techniques, which consider the Degree of Polymerization (DP) to evaluate the cellulose degradation and other chemical factors accumulated in mineral oil. Given the physical and chemical nature of the problem of degradation, we couple it with machine learning models to predict the desired parameters for considered equations. In particular, the equation used applies the Arrhenius relation, which comprises parameters like the pre-exponential factor, which depends on the cellulose’s contamination content, and the activation energy, which is connected to the temperature dependence; both of the factors need to be estimated for our problem. For this reason, Physics-Informed Neural Networks (PINNs) are considered for solving the data-driven discovery of the DP equation.

Cellulose nanofibrils (CNFs) can be used as building blocks for future sustainable materials including strong and stiff filaments. The goal of this paper is to introduce a data analysis of flow-induced birefringence experiments by means of unsupervised learning techniques. By reducing the dimensionality of the data with Principal Component Analysis (PCA) we are able to exploit information for the different cellulose materials at several concentrations and compare them to each other. Our approach aims at classifying the CNF materials at different concentrations by applying unsupervised machine learning algorithms, like k-means and Gaussian Mixture Models (GMMs). Finally, we analyze the autocorrelation function (ACF) and the partial autocorrelation function (PACF) of the first principal component, detecting seasonality in lower concentrations. The focus is given to the initial relaxation of birefringence after the flow is stopped to have a better understanding of the Brownian dynamics for the given materials and concentrations.

Our method can be used to distinguish the different materials at specific concentrations and could help to identify possible advantages and drawbacks of one material over the other.