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We articulate the design imperatives for machine learning based digital twins for nonlinear dynamical systems, which can be used to monitor the “health” of the system and anticipate future collapse. The fundamental requirement for digital twins of nonlinear dynamical systems is dynamical evolution: the digital twin must be able to evolve its dynamical state at the present time to the next time step without further state input—a requirement that reservoir computing naturally meets. We conduct extensive tests using prototypical systems from optics, ecology, and climate, where the respective specific examples are a chaotic CO2 laser system, a model of phytoplankton subject to seasonality, and the Lorenz-96 climate network. We demonstrate that, with a single or parallel reservoir computer, the digital twins are capable of a variety of challenging forecasting and monitoring tasks. Our digital twin has the following capabilities: (1) extrapolating the dynamics of the target system to predict how it may respond to a changing dynamical environment, e.g., a driving signal that it has never experienced before, (2) making continual forecasting and monitoring with sparse real-time updates under non-stationary external driving, (3) inferring hidden variables in the target system and accurately reproducing/predicting their dynamical evolution, (4) adapting to external driving of different waveform, and (5) extrapolating the global bifurcation behaviors to network systems of different sizes. These features make our digital twins appealing in applications, such as monitoring the health of critical systems and forecasting their potential collapse induced by environmental changes or perturbations. Such systems can be an infrastructure, an ecosystem, or a regional climate system.

 

The widespread use of distributed energy sources (DERs) raises significant challenges for power system design, planning, and operation, leading to wide adaptation of tools on hosting capacity analysis (HCA). Traditional HCA methods conduct extensive power flow analysis. Due to the computation burden, these time-consuming methods fail to provide online hosting capacity (HC) in large distribution systems. To solve the problem, we first propose a deep learning-based problem formulation for HCA, which conducts offline training and determines HC in real time. The used learning model, long short-term memory (LSTM), implements historical time-series data to capture periodical patterns in distribution systems. However, directly applying LSTMs suffers from low accuracy due to the lack of consideration on spatial information, where location information like feeder topology is critical in nodal HCA. Therefore, we modify the forget gate function to dual forget gates, to capture the spatial correlation within the grid. Such a design turns the LSTM into the Spatial-Temporal LSTM (ST-LSTM). Moreover, as voltage violations are the most vital constraints in HCA, we design a voltage sensitivity gate to increase accuracy further. The results of LSTMs and ST-LSTMs on feeders, such as IEEE 34-, 123-bus feeders, and utility feeders, validate our designs. 

This paper describes how domain knowledge of power system operators can be integrated into reinforcement learning (RL) frameworks to effectively learn agents that control the grid's topology to prevent thermal cascading. Typical RL-based topology controllers fail to perform well due to the large search/optimization space. Here, we propose an actor-critic-based agent to address the problem's combinatorial nature and train the agent using the RL environment developed by RTE, the French TSO. To address the challenge of the large optimization space, a curriculum-based approach with reward tuning is incorporated into the training procedure by modifying the environment using network physics for enhanced agent learning. Further, a parallel training approach on multiple scenarios is employed to avoid biasing the agent to a few scenarios and make it robust to the natural variability in grid operations. Without these modifications to the training procedure, the RL agent failed for most test scenarios, illustrating the importance of properly integrating domain knowledge of physical systems for real-world RL learning. The agent was tested by RTE for the 2019 learning to run the power network challenge and was awarded the 2nd place in accuracy and 1st place in speed. The developed code is open-sourced for public use. Analysis of a simple system proves the enhancement in training RL-agents using the curriculum. 

The growing integration of distributed energy resources (DERs) in distribution grids raises various reliability issues due to DER's uncertain and complex behaviors. With large-scale DER penetration in distribution grids, traditional outage detection methods, which rely on customers report and smart meters' “last gasp” signals, will have poor performance, because renewable generators and storage and the mesh structure in urban distribution grids can continue supplying power after line outages. To address these challenges, we propose a data-driven outage monitoring approach based on the stochastic time series analysis with a theoretical guarantee. Specifically, we prove via power flow analysis that dependency of time-series voltage measurements exhibits significant statistical changes after line outages. This makes the theory on optimal change-point detection suitable to identify line outages. However, existing change point detection methods require post-outage voltage distribution, which are unknown in distribution systems. Therefore, we design a maximum likelihood estimator to directly learn distribution pa-rameters from voltage data. We prove the estimated parameters-based detection also achieves optimal performance, making it extremely useful for fast distribution grid outage identifications. Furthermore, since smart meters have been widely installed in distribution grids and advanced infrastructure (e.g., PMU) has not widely been available, our approach only requires voltage magnitude for quick outage identification. Simulation results show highly accurate outage identification in eight distribution grids with 17 configurations with and without DERs using smart meter data.