The increase in variable renewable energy sources has brought about significant changes in power system dynamics, mainly due to the widespread adoption of power electronics and nonlinear controllers. The resulting complex system dynamics and the unpredictable nature of disturbances pose substantial challenges for real-time dynamic security assessment (DSA). Machine learning (ML) methods offer advantages in terms of computational speed compared to numerical methods and simulators. Offline-trained ML models, however, are limited by their training domain; e.g., they cannot easily consider various grid topologies and data changes. Neural Ordinary Differential Equations (NODEs) leverage the integration of neural networks and ODE solvers to enable continuous-time dynamic trajectory predictions from time series data, resolving the limitation on topological and data changes. This paper introduces the Online Neural Dynamics Forecaster (ONDF) workflow, designed to monitor and assess system security in real-time using multiple NODEs trained solely with local post-fault measurements. Through several case studies, we compare the regression and DSA classification capabilities of ONDF with various ML models. Our findings demonstrate that ONDF provides a novel and scalable approach for system operators to make informed decisions and apply corrective control actions based on predicted dynamics.

The reader of the chapter will be able to connect techniques from machine learning (ML) and digital twins (DTs) to gain insights for monitoring and control of (dynamic) security for electrical power systems. DTs are validated and verified high-fidelity (hf) models providing high simulation accuracy. DTs can be used for simulation of the supervised process of system operation and are therefore able to provide synthetic studied data, where measurement data are scarce. However, for some real-time applications in monitoring and control, such high-fidelity simulation models are not appropriate due to the corresponding computational barrier. There, ML aims to create an application-specific, low-fidelity (lf) approximation of the digital twin. Such trained lf models are used in real-time applications where computational time is scarce and lf information is sufficient. The conceptual intersection of hf and lf models has been little explored and becomes increasingly complex. This chapter aims to provide a conceptual overview of how such hf and lf models can be combined. This chapter is split into two parts where the first part is to introduce ML, lf models, and digital twins, hf models, for power systems analysis, and the second chapter is to use these two types of models to form purpose-driven surrogate lf models, illustrated on the example of dynamic security assessment (DSA). In the first part, the concepts for using DTs as hf models for online power system studies and their corresponding tuning of model parameters are introduced. Subsequently, ML i.e., lf models, are introduced and their corresponding training frameworks.