The transition to a sustainable energy system is challenging for the operation and stability of electric power systems as power generation becomes increasingly uncertain, grid loads increase and their dynamical properties fundamentally change. At the same time, operational data are available at an unprecedented level of detail, enabling new methods of monitoring and control.

In this talk, how modelling, data science and interpretable machine learning may support our understanding of power systems. First, I present a case of Braess' paradox emerging in realistic power grids. Next, I will demonstrate how highly non-trivial statistics occur in household demand and the power balance of large islands. Finally, I will demonstrate how the impact of regulatory changes can be investigated with interpretable machine learning.

Recently, machine learning (ML) techniques have come into the spotlight for their ability to solve numerous problems while reducing computational time. In this talk, three machine learning algorithms (random forest, support vector machine, and artificial neural network) are tested using synthetic power grids with two different input-power distributions. The importance of network topology features and AC power dynamics features is tested for these ML algorithms. The results show that the models trained with heterogeneous input-power distributions improve their prediction of stability. Furthermore, the transferability of these machine learning algorithms to real-world power grids is demonstrated, suggesting the potential application of these techniques in power-grid studies.

To safely operate future power grids with large shares of renewable energies, a detailed understanding of their non-linear dynamical behavior is needed. However, dynamical models of power grids are highly complex and costly to simulate. Recent work shows that Machine Learning (ML), and in particular Graph Neural Networks (GNNs), are promising tools for more efficient dynamic stability assessment.

In the past decade, complex systems science investigated the considerable influence of the power grid's topology on its dynamical behavior, and identified several network measures that correlate with stability. But how do these insights compare to the performance of GNNs, when it comes to predicting stability outcomes? To push to the limits of the network science approach, we collect relevant network measures in an extensive literature review. In turn, we quantify their linear correlation with power grid stability, and employ them as inputs for various feature-based machine learning models such as Multi-layer Perceptrons and Gradient Boosted Trees. This allows us to capture their combined impact, which may be nonlinear in nature. We find that this combination of network science and ML delivers convincing results regarding prediction performance, interpretability and amount of data needed for the training. However, with sufficiently large amounts of training data, GNNs show the best performance, which indicates that they learn novel relations between topology and stability which are as of yet unknown to domain experts. Our study gives a detailed understanding of the advantages and disadvantages of either approach, and demonstrates the large potential of the combination of network science and machine learning for improving the stability assessment of future power grids.

The stable flow of energy on power grids requires a synchronized 50Hz alternating voltage and current on the networks nodes and links. The dynamics of this oscillating operating state has recently been recast using the concept of complex frequency. This can be seen as an extension of phase reduction to relevant amplitude dynamics while making an underlying system symmetry explicit, and provides us with a normal form for the dynamics of those actors in the grid tasked with stabilizing the operating state. I show that this approach enables us to recast the full dynamics of the AC Power Flow as adaptive network equations. I show some new results on stability of the dynamics and optimal control laws using this approach, as well as their use in training Graph Neural Networks for the task of identifying vulnerable locations in the power system.

The challenge of understanding stability in synchronized oscillator systems is often complex and compounded by computational difficulties. In our research, we propose an alternative perspective that emphasizes energy dynamics within these systems. Our approach involves approximating the system's energy function and observing the energy of perturbations applied to each node. This exploration allows us to identify the energy threshold necessary for maintaining synchronization, offering a fresh lens to examine the stability of these systems.

Additionally, we investigate the intriguing transition from synchronization to various limit cycles when these systems face substantial perturbations. By employing our energy-focused methodology, we uncover critical constraints these limit cycles abide by. This finding provides a novel way to understand the dynamic steady state of such systems. Although our approach deviates from conventional methods, it offers an accessible and promising foundation for further research, with the potential to enhance our understanding of stability analysis in synchronized oscillator systems.

The spatial distributions of diverse facilities are often understood in terms of the optimization of the commute distance or the economic profit. Incorporating more general objective functions into such optimization framework may be useful, helping the policy decisions to meet various social and economic demands. As an example, we consider how hospitals should be distributed to minimize the total fatalities of tuberculosis (TB). The empirical data of Korea shows that the fatality rate of TB in a district decreases with the areal density of hospitals, implying their correlation and the possibility of reducing the nationwide fatalities by adjusting the hospital distribution across districts. Approximating the fatality rate by the probability of a patient not to visit a hospital in her/his residential district for the duration period of TB and evaluating the latter probability in the random-walk framework, we obtain the fatality rate as an exponential function of the hospital density with a characteristic constant related to each district’s effective lattice constant estimable empirically. This leads us to the optimal hospital distribution which finds the hospital density in a district to be a logarithmic function of the rescaled patient density. The total fatalities is reduced by 13% with this optimum. This talk end with introducing the study very briefly to investigate the spatial effect of power generators. In this work, we systematically control the spatial uniformity of the geographical distribution of generators and conclude that the more uniformly generators are distributed, the more enhanced synchronization occurs. In the presence of temporal failures of power sources, we observe that spatial uniformity helps the power grid to recover stationarity in a shorter time.

The high dimensionality of power grids and other complex infrastructure networks directly limits our ability to fully control or monitor its states. Decentralized control strategies offer a viable alternative to circumvent the energy-intensive nature of full-state control in large-scale networks with limited actuators and sensors. However, the performance of such methods are dependent on resources, such as the position and number of control and sensor nodes, that directly define the size of the control neighborhood in the network. Here, we discuss the notions of target controllability and functional observability for the (decentralized) control and monitoring of power grids. Based on a graph-theoretical characterization of these notions, we establish a duality between functional observability and target controllability that enables the development of scalable algorithms for the optimal placement of both controllers and sensors in power grids. Our results lead to immediate applications in cyber-attack detection and decentralized optimal control in power grids.