Physics-Informed Neural Networks for Power System Dynamics

The idea behind mathematical modelling is the representation of observations in a form that becomes useful for analysing, controlling, and predicting the underlying system. In the power system, modelling enables the operation of the power grid that aims for steady, secure, affordable, and carbon-neutral electricity supply. Achieving these objectives relies on having useful and tractable models. While the ongoing energy transition is a requirement to decarbonise the energy system, it, at the same time, poses a significant challenge for the existing modelling approaches and, hence, the operation of the grid. The need to consider more generation units, increased uncertainty, and more intricate dynamic behaviour calls for the development of complementary modelling approaches to better meet the operational objectives.

A key tool in power system operation is the solution of differential equations that govern the dynamic behaviour of the system. As their solution incurs a large computational cost and will increase in light of the energy transition, their acceleration is crucial for future operation. In this work, we investigate a recently suggested approach to solving these differential equations based on Machine Learning (ML), a method known as Physics-Informed Neural Networks (PINNs). We learn the solution and once it is learned, the evaluation can be several times faster than with a conventional numerical integration scheme. The question is if and how this approach can be applied to a realistic system size, i.e., are PINNs scalable?

We begin by providing a thorough investigation of the methodological proposition that PINNs offer in the context of a small dynamical system, i.e., a single machine. The introduction of a concept from the numerical analysis of dynamical systems, called flow, contributes to a better interpretation of the learned solution. On this basis, we demonstrate several techniques for improving the learned solution and to induce desirable numerical properties. To this end, we propose an additional loss term (dt-loss) and an extension to the architecture of PINNs (IRK-PINNs). The adoption of a probabilistic viewpoint of PINNs in the context of estimating the system parameters further enhances the understanding of PINNs as a modelling approach for dynamical systems.

Looking beyond a single machine system, the scalability to realistic sizes of the power grid with multiple machines proves to be challenging. While we show that it is possible to learn selected dynamics of a 39-bus system, the increasing complexity of the learning process becomes a practical barrier for the scalability of PINNs. Based on this analysis, we propose a simulator called PINNSim that combines the benefits of PINNs for small systems with the flexibility and scalability of a conventional numerical method. In PINNSim, the dynamics of each component are represented by a component-specific PINN, and we determine their interaction with a conventional root-finding algorithm. PINNSim allows for larger and hence fewer time steps as we demonstrate on a 9-bus system. It is conceptually scalable and enables a modular integration of PINNs.

Due to the safety critical nature of the power system, the adoption of ML-based modelling, such as PINNs, requires building trust on the grid operator’s side. We reflect on this challenge and suggest a classification of ML-based methods based on the benefits they could provide for different tasks.