Search

PowerDynamics.jl is a Julia package for time-domain modeling of power grids that is specifically designed for the stability analysis of systems with high shares of renewable energies. It makes use of Julia's state-of-the-art differential equation solvers and is highly performant even for systems with a large number of components. Further, it is compatible with Julia's machine learning libraries and allows for the utilization of these methods for dynamical optimization and parameter fitting. The package comes with a number of predefined models for synchronous machines, transmission lines and inverter systems. However, the strict open-source approach and a macro-based user-interface also allows for an easy implementation of custom-built models which makes it especially interesting for the design and testing of new control strategies for distributed generation units. This paper presents how the modeling concept, implemented component models and fault scenarios have been experimentally tested against measurements in the microgrid lab of TECNALIA.

PowerDynamics.jl is an Open-Source library for dynamic power grid modeling built in the latest scientific programming language, Julia. It provides all the tools necessary to analyze the dynamical stability of power grids with high share of renewable energy. In contrast to conventional tools, it makes full use of the simplicity and generality that Julia combines with highly-optimized just-in-time compiled Code. Additionally, its ecosystem provides DifferentialEquations.jl, a high-performance library for solving differential equations with built-in solvers and interfaces to industrial grade solvers like Sundials. PowerDynamics.jl provides a multitude of dynamics for different node/bus-types, e.g. rotating masses, droop-control in inverters, and is able to explicitly model time delays of inverters. Furthermore, it includes realistic models of fluctuations from renewable energy sources. In this paper, we demonstrate how to use PowerDynamics.jl for the IEEE 14-bus distribution grid feeder.

A challenge for renewable and hybrid power systems is the dynamically stable integration of Renewable Energy Sources (RES). This paper specifically investigates the influence of intermittent RES and measurement delays from power electronic resources on frequency stability. In addition it presents an Open-Source framework to undertake dynamic RES modeling. First, for local intermittent fluctuations in lossy distribution grids I find a remarkable and subtle but robust interplay of dynamical and topological properties, which is largely absent for lossless grids. Second, I show how delays may induce resonance catastrophes and how the existence of critical delays sets an upper limit for measurement times. Further, I investigate whether centralized vs. decentralized power production, for different grid topologies, changes this behavior. Third, the code used for producing the above results is in the process of being published as an open-source Software framework called PowerDynamics.jl being developed in the programming language Julia. It will cover the rich novel dynamics caused by the integration of RES with the implementation of Differential Algebraic (DAEs), Delayed Differential (DDEs) and Stochastic Differential Algebraic Equations (SDAEs). Altogether, this paper investigates the stability of future power grids moving towards integrating more aspects of renewable energy dynamics and presents an adequate modeling framework for RES integration studies., Comment: arXiv admin note: text overlap with arXiv:1702.08707

We study the spreading of renewable power fluctuations through grids with Ohmic losses on the lines. By formulating a network adapted linear response theory, we find that vulnerability patterns are linked to the left Laplacian eigenvectors of the overdamped eigenmodes. We show that for tree-like networks fluctuations are amplified in the opposite direction of the power flow. This novel mechanism explains vulnerability patterns that were observed in previous numerical simulations of renewable micro-grids. While exact mathematical derivations are only possible for tree like networks with homogeneous response, we show that the mechanisms discovered also explain vulnerability patterns in realistic heterogeneous meshed grids by studying the IEEE RTS-1996 test system.

A major challenge for power grids with a high share of renewable energy systems (RES), such as island grids, is to provide frequency stability in the face of renewable fluctuations. In this work we evaluate the ability of electric vehicles (EV) to provide distributed primary control and to eliminate frequency peaks. To do so we for the first time explicitly model the network structure and incorporate non-Gaussian, strongly intermittent fluctuations typical for RES. We show that EVs can completely eliminate frequency peaks. Using threshold randomization we further demonstrate that demand synchronization effects and battery stresses can be greatly reduced. In contrast, explicit frequency averaging has a strong destabilizing effect, suggesting that the role of delays in distributed control schemes requires further studies. Overall we find that distributed control outperforms central one. The results are robust against a further increase in renewable power production and fluctuations.

Power generation in Germany is currently transitioning from a system based on large, central, thermal power plants to one that heavily relies on small, decentral, mostly renewable power generators. This development poses the question how transmission grids' reactive power demand for voltage management, covered by central power plants today, can be supplied in the future. In this work, we estimate the future technical potential of such an approach for the whole of Germany. For a 100% renewable electricity scenario we set the possible reactive power supply in comparison with the reactive power requirements that are needed to realize the simulated future transmission grid power flows. Since an exact calculation of distribution grids' reactive power potential is difficult due to the unavailability of detailed grid models on such scale, we optimistically estimate the potential by assuming a scaled, averaged distribution grid model connected to each of the transmission grid nodes. We find that for all except a few transmission grid nodes, the required reactive power can be fully supplied from the modeled distribution grids. This implies that - even if our estimate is overly optimistic - distributed reactive power provisioning will be a technical solution for many future reactive power challenges.

In this study, we develop a theoretical model of strategic equilibrium bidding and price-setting behaviour by heterogeneous and boundedly rational electricity producers and a grid operator in a single electricity market under uncertain information about production capabilities and electricity demand. We compare eight different market design variants and several levels of centralized electricity production that influence the spatial distribution of producers in the grid, their unit production and curtailment costs, and the mean and standard deviation of their production capabilities. Our market design variants differ in three aspects. Producers are either paid their individual bid price ("pay as bid") or the (higher) market price set by the grid operator ("uniform pricing"). They are either paid for their bid quantity ("pay requested") or for their actual supply ("pay supplied") which may differ due to production uncertainty. Finally, excess production is either required to be curtailed or may be supplied to the grid. Overall, we find the combination of uniform pricing, paying for requested amounts, and required curtailment to perform best or second best in many respects, and to provide the best compromise between the goals of low economic costs, low consumer costs, positive profits, low balancing, low workload, and honest bidding behaviour., Comment: 15 pages, 4 figures

80% of all Renewable Energy Power in Germany is installed in tree-like distribution grids. Intermittent power fluctuations from such sources introduce new dynamics into the lower grid layers. At the same time, distributed resources will have to contribute to stabilize the grid against these fluctuations in the future. In this paper, we model a system of distributed resources as oscillators on a tree-like, lossy power grid and its ability to withstand desynchronization from localized intermittent renewable infeed. We find a remarkable interplay of network structure and the position of the node at which the fluctuations are fed in. An important precondition for our findings is the presence of losses in distribution grids. Then, the most network central node splits the network into branches with different influence on network stability. Troublemakers, i.e. nodes at which fluctuations are especially exciting the grid, tend to be downstream branches with high net power outflow. For low coupling strength, we also find branches of nodes vulnerable to fluctuations anywhere in the network. These network regions can be predicted at high confidence using an eigenvector based network measure taking the turbulent nature of perturbations into account. While we focus here on tree-like networks, the observed effects also appear, albeit less pronounced, for weakly meshed grids. On the other hand the observed effects disappear for lossless power grids often studied in the complex systems literature.

Extreme events represent a challenge to natural as well as man-made systems. For critical infrastructure like power grids, we need to understand their resilience against large disturbances. Recently, new measures of the resilience of dynamical systems have been developed in the complex system literature. Basin stability and survivability respectively assess the asymptotic and transient behavior of a system when subjected to arbitrary, localized but large perturbations. To employ these methods to assess the resilience of power grids, we need to choose a model of the power grid. So far the most popular model that has been studied is the classical swing equation model for the frequency response of generators and motors. In this paper we study a more sophisticated model of synchronous machines that also takes voltage dynamics into account, and compare it to the previously studied model. This model has been found to give an accurate picture of the long term evolution of synchronous machines in the engineering literature for post fault studies. We find evidence that some stable fix points of the swing equation become unstable when we add voltage dynamics. If this occurs the asymptotic behavior of the system can be dramatically altered, and basin stability estimates obtained with the swing equation can be dramatically wrong. We also find that the survivability does not change significantly when taking the voltage dynamics into account. Further, the limit cycle type asymptotic behaviour is strongly correlated with transient voltages that violate typical operational voltage bounds. Thus, transient voltage bounds are dominated by transient frequency bounds and play no large role for realistic parameters.

Renewables will soon dominate energy production in our electric power system. And yet, how to integrate renewable energy into the grid and the market is still a subject of major debate. Decentral Smart Grid Control (DSGC) was recently proposed as a robust and decentralized approach to balance supply and demand and to guarantee a grid operation that is both economically and dynamically feasible. Here, we analyze the impact of network topology by assessing the stability of essential network motifs using both linear stability analysis and basin volume for delay systems. Our results indicate that if frequency measurements are averaged over sufficiently large time intervals, DSGC enhances the stability of extended power grid systems. We further investigate whether DSGC supports centralized and/or decentralized power production and find it to be applicable to both. However, our results on cycle-like systems suggest that DSGC favors systems with decentralized production. Here, lower line capacities and lower averaging times are required compared to those with centralized production., Comment: 21 pages, 6 figures This is a pre-print of a manuscript submitted to The European Physical Journal. The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2015-50136-y