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This article reviews different kinds of models for the electric power grid that can be used to understand the modern power system, the smart grid. From the physical network to abstract energy markets, we identify in the literature different…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
We introduce a model for the dynamic self-organization of the electric grid. The model is characterized by a conserved magnitude, energy, that can travel following the links of the network to satisfy nodes' load. The load fluctuates in time…
Market-based coordination of demand side assets has gained great interests in recent years. In spite of its efficiency, there is a risk that the interaction between the dynamic assets through the price signal could result in an unstable…
In this paper, we examine both stability and sustainability of a network-based model of natural resource consumption. Stability is studied from a dynamical systems perspective, though we argue that sustainability is a fundamentally…
Motter et al. derived a real-valued master stability function which determines whether and to what degree a given power grid is asymptotically stable. Stright and Edrington adopted certain uniformity assumptions on a grid's components and…
The Smart Grid is not just about the digitalization of the Power Grid. In its more visionary acceptation, it is a model of energy management in which the users are engaged in producing energy as well as consuming it, while having…
The energy mix of future power systems will include high shares of wind power and solar PV. These generation facilities are generally connected via power-electronic inverters. While conventional generation responds dynamically to the state…
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…
The stable operation of the electric power grid relies on a precisely synchronized state of all generators and machines. All machines rotate at exactly the same frequency with fixed phase differences, leading to steady power flows…
This paper focuses on the operation of an electricity market that accounts for participants that bid at a sub-minute timescale. To that end, we model the market-clearing process as a dynamical system, called market dynamics, which is…
Efficient control of power systems is becoming increasingly difficult as they gain in complexity and size. We propose an automatic control strategy that regulates the mechanical power output of the generators in a power grid based on…
Smart grid technological advances present a recent class of complex interdisciplinary modeling and increasingly difficult simulation problems to solve using traditional computational methods. To simulate a smart grid requires a systemic…
Electrical infrastructures provide services at the basis of a number of application sectors, several of which are critical from the perspective of human life, environment or financials. Following the increasing trend in electricity…
Dynamic stability is imperative for the operation of the electric power system. This article provides analytical results and effective stability criteria focusing on the interplay of network structures and the local dynamics of synchronous…
With the rapid development of renewable and distributed energies, the underlying dynamics of power systems are no longer dominated by large synchronous generators, but by numerous dynamic components with heterogeneous characteristics. In…
We consider the problem of stability analysis for distribution grids with droop-controlled inverters and dynamic distribution power lines. The inverters are modeled as voltage sources with controllable frequency and amplitude. This problem…
Minimizing both power fluctuations and energy waste in an electrical grid is a central challenge to energy policy. Any discrepancy between power production and loads may lead to inefficiencies and instability in the system. Right now, the…
As the amount of volatile, renewable energy sources in power distribution grids is increasing, the stability of the latter is a vital aspect for grid operators. Within the STABEEL project, the authors develop rules on how to parametrize the…
Recent work in the area of interdependent networks has focused on interactions between two systems of the same type. However, an important and ubiquitous class of systems are those involving monitoring and control, an example of…