Agenda

Stability in Power Grids and Influences of Climate Extremes

by Jürgen Kurths

Power grids, the human brain, arrays of coupled lasers, genetic networks, or the Amazon rainforest are all characterized by multistability. For power grids, the strongly ongoing transition to distributed renewable energy sources leads to a proliferation of dynamical actors. The desynchronization of a few or even one of those would likely result in a substantial blackout. Thus, the dynamical stability of the synchronous state has become a leading topic in power grid research. Here we claim that the traditional linearization-based approach to stability is in several cases too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. Remarkably, when taking physical losses in the network into account, the back-reaction of the network induces new exotic solitary states in the individual actors, and the stability characteristics of the synchronous state are dramatically altered. These novel effects will have to be explicitly taken into account in the design of future power grids, and their existence poses a challenge for control. Considering the vulnerability of power grids against extreme wind loads and, consequently, increasing its robustness to withstand these events is of great importance. Here, we combine a detailed model of the climatic drivers of extreme events, and a cascadable model of the transmission network to provide a holistic co-evolution model to consider wind-induced failures of transmission lines in the Texan electrical network.

Complexity and the Grid

by Frank Hellmann

I discuss how methods from complexity science can help to understand the self-organizing processes happening in todays and future power grids. The focus will be on analyzing models using probabilistic methods and on validate complex systems style modeling of power grids from first principles.

Voltage angle and frequency wave propagation through high-voltage power grid

by Philippe Jacquod

Decarbonization in the energy sector has been accompanied by an increased penetration of new renewable energy sources in electric power systems. Such sources differ from traditional productions in that, first, they induce larger, undispatchable fluctuations in power generation and second, they lack inertia. Therefore, substituting new renewables for traditional generation induces stronger and more frequent disturbances and modifies the way disturbances propagate across AC electric power grids. In this talk I will discuss issues of utmost importance relative to the dynamics of present and future high voltage power grids. I will focus on how faults propagate depending on their characteristic time scales, their location, their magnitude and the distribution of rotational inertia and damping in the grid. With this knowledge in hand, I will then discuss how to preserve the robustness of future power-grids. In particular, I will construct an optimization procedure to distribute dynamical resources to render the grid more robust to disturbances.

Fluctuation-induced stationary responses in power grids

by Moritz Thuemler

Increasing renewable energy supply and digitization of most aspects of our daily lives massively transform electric power grids and their dynamics. Increasingly strong and distributed power fluctuations are induced by wind and photovoltaic sources, as well as by the increasing and increasingly volatile customer demand. Yet, how fluctuations drive collective grid responses is far from fully understood to date. Here, we advance previous research and analyze the simultaneous and distributed frequency and voltage responses of a class of dynamic power grid models. Interestingly, fluctuation-driven pure frequency response dynamics strongly deviate from those with frequency & voltage dynamics. We demonstrate that pure voltage instabilities do not exist for physical reasons, in contrast to previous claims in the literature. Moreover, we uncover a nonlinear operating offset of the voltage variables and present a novel theoretical framework to predict the offset and potentially tipping point crossings induced by fluctuations.

Control of synchronization and cascading failures in multi-layer power grids

by Simona Olmi

The existing power grid was developed using a centralistic approach, therefore we have a few very high-power ac plants operating at 50 or 60 Hz interconnected by ac or dc transmission systems operating at very high voltages (e.g., 400 kV) and many substations, where the high voltage is transformed to the distribution level (e.g., 20 kV). In order to distribute the power in a capillary way, a huge number of distribution lines is present, supplying the loads directly (in the case of high-power loads) or after voltage transformation in the case of residential or low-power industrial loads (e.g., 400 V in Europe). Due to the design of the current power grid as a centralized system, the control is concentrated in central locations and only partially in substations, while remote ends, like loads, are almost or totally passive. Therefore it is necessary to design new systems that provide more effective and widely distributed intelligent control embedded in local electricity production, two-way electricity and information flows, thus achieving flexible, efficient, economic, and secure power delivery. Here we consider a multi-layer network in a full dynamic description. It consists of a power grid layer and two control layers, which provides the integral and proportional control for the power grid respectively. Each layer is governed by its own dynamics, which is dependent upon the state of the other layer. In particular the physical topology that relates the interconnection of distributed generators and loads is described by coupled Kuramoto phase oscillators with inertia, while the first control layer (integral control or communication layer), which describes the information flow of the power system control measurements, depends on the information of the neighbours of each node. Moreover, in the second control layer we introduce distributed control to prevent dynamically-induced cascading failures in power grids, which relies on the same topology of the physical layer. We restrict our analysis to cascades of line failures, i.e., failures due to power flows exceeding the maximum capacity of a line, which are induced by local perturbations in the physical grid (e.g. disconnecting a generator) and we validate our results, analysing the Italian high voltage (380kV) power grid.

Bridging the gap between synchronization model studies and real power grid properties

by Bálint Hartmann

Power-law distributed cascade failures are well known in power-grid systems. The traditional electric swing equations, describing the power-flow among interconnected rotating generators and consumers (machines) is equivalent to a set of second-order Kuramoto equations. Our analysis has two parts, a thermalization regime, by which we create stable steady state conditions and a “line-cut” regime, where we allowed dynamical cascade failure events, by removing edges from the graph, whenever the power flows exceed certain threshold values. The talk focuses on the exploration of network heterogeneity effects, starting from homogeneous two-dimensional (2D) square lattices, possessing identical nodes and links, to a realistic electric power grid, exhibiting node dependent parameters. We show that too weak quenched heterogeneity, coming solely from the probabilistic self-frequencies of nodes, is not sufficient for finding power-law distributed cascades. On the other hand, too strong heterogeneity destroys the synchronization of the system.

Analyzing power systems via interpretable machine learning

by Benjamin Schäfer

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. To fully harness these data, advanced methods from machine learning must be used. In this talk, I present interpretable machine learning or explainable artificial intelligence (XAI) as a tool to quantify, predict, and explain essential aspects of power system operation and stability in three major European synchronous areas. I introduce the concept of XAI, and apply it to the power grid frequency, a central observable for control and balancing, as well as to control power. Combining XAI with domain knowledge, I identify main drivers and stability risks, advancing our understanding of complex energy systems.

What Adaptive Neuronal Networks Teach us About Power Grids

by Rico Berner

Power grids, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types of dynamical networks has attracted increasing attention over the last decade. This contribution provides a new perspective on power grids by demonstrating that they can be viewed as a special class of adaptive networks, where the coupling weights are continuously adapted by feedback of the dynamics, and both the local dynamics and the coupling weights evolve in time as co-evolutionary processes. Such adaptive networks are very common in neural networks with synaptic plasticity. In terms of power grids, the power flow into the network nodes from other nodes represent pseudo coupling weights. This modelling approach allows one to transfer methods and results from neural networks, in particular the emergence of multifrequency clusters, which may form in a hierarchical way and destabilize the desirable completely synchronized operating state of the power grid. In this work, the relation between these two types of networks, in particular the model of Kuramoto-Sakaguchi phase oscillators with inertia (swing equation for power grids) and the model of phase oscillators with adaptivity, is used to gain insights into the dynamical properties of multifrequency clusters in power grid networks. This relation holds even for more general classes of power grid models that include voltage dynamics. Moreover, the phenomenon of cascading line failure in power grids is translated into an adaptive neuronal network. Building on this relation between phase oscillators with inertia and adaptive networks, a new perspective on solitary states in power grid networks and their influence on network stability is provided and illustrated by the ultrahigh-voltage power grid of Germany.

Dynamic Virtual Power Plant Control

by Verena Häberle

This presentation addresses the problem of designing decentralized controllers for dynamic virtual power plants (DVPPs). The key idea is to design local feedback controllers for a collection of devices such that in aggregate they provide fast ancillary services including primary frequency and voltage control. First, a general overview of the DVPP control design as a coordinated model matching is presented, where the goal is to match the actual aggregate behavior as closely as possible to some desired dynamic behavior (by means of fully decentralized control) while at the same satisfying the local device limitations. To do so, the initial focus is refined to a DVPP with all devices at one common bus bar in the transmission grid. Moreover, the initial control setup considers a grid-following signal causality, where power injection is controlled as a function of a bus voltage measurement. A decentralized control design method is proposed to solve the control design problem at hand. It decomposes the problem into two steps: (i) disaggregating the desired dynamic behavior among the individual devices, and (ii) local model matching for each individual device. The theory behind this design approach is presented, and its excellent performance is demonstrated on modified IEEE 9 bus system illustrative examples. Finally, extensions of the initial control design method towards a grid-forming signal causality, as well as spatially distributed device arrangements are discussed.

Scalable control and observability of large-scale networks

by Adilson E. Motter

A major challenge in the current study of power grids and other large-scale networks is the lack of scalability of most existing control approaches. In this presentation, I will introduce a notion of network locality that can be exploited to make the control of networks scalable even when the dynamics are nonlinear. I will also present a graph-based theory and scalable computational approach for functional observability, the important scenario in which only a subset of state variables needs to be reconstructed. Example applications will include the control of synchronization dynamics and the detection of cyberattacks in power-grid networks. These results enhance our ability to explore otherwise inaccessible dynamical processes and show how large networks can be controlled with computation and communication costs comparable to those for small networks.

Program

Schedule: Playlist

Opening Remark (Video)

Stability in Power Grids and Influences of Climate Extremes (Video)

Complexity and the Grid (Video)

Meal break

Voltage angle and frequency wave propagation through high-voltage power grid (Video)

Fluctuation-induced stationary responses in power grids (Video)

Control of synchronization and cascading failures in multi-layer power grids (Video)

Bridging the gap between synchronization model studies and real power grid properties (Video)

Coffee break

Analyzing power systems via interpretable machine learning (Video)

What Adaptive Neuronal Networks Teach us About Power Grids (Video)

Dynamic Virtual Power Plant Control (Video)

Scalable control and observability of large-scale networks (Video)

Ending (Video)