Self-Organized Synchronization and Voltage Stability in Networks of Synchronous Machines

The integration of renewable energy sources in the course of the energy transition is accompanied by grid decentralization and fluctuating power feed-in characteristics. This raises new challenges for power system stability and design. We intend to investigate power system stability from the viewpoint of self-organized synchronization aspects. In this approach, the power grid is represented by a network of synchronous machines. We supplement the classical Kuramoto-like network model, which assumes constant voltages, with dynamical voltage equations, and thus obtain an extended version, that incorporates the coupled categories voltage stability and rotor angle synchronization. We compare disturbance scenarios in small systems simulated on the basis of both classical and extended model and we discuss resultant implications and possible applications to complex modern power grids.Comment: 9 pages, 9 figure

Bridging between Load-Flow and Kuramoto-like Power Grid Models: A Flexible Approach to Integrating Electrical Storage Units

In future power systems, electrical storage will be the key technology for balancing feed-in fluctuations. With increasing share of renewables and reduction of system inertia, the focus of research expands towards short-term grid dynamics and collective phenomena. Against this backdrop, Kuramoto-like power grids have been established as a sound mathematical modeling framework bridging between the simplified models from nonlinear dynamics and the more detailed models used in electrical engineering. However, they have a blind spot concerning grid components, which cannot be modeled by oscillator equations, and hence do not allow to investigate storage-related issues from scratch. We remove this shortcoming by bringing together Kuramoto-like and algebraic load-flow equations. This is a substantial extension of the current Kuramoto framework with arbitrary grid components. Based on this concept, we provide a solid starting point for the integration of flexible storage units enabling to address current problems like smart storage control, optimal siting and rough cost estimations. For demonstration purpose, we here consider a wind power application with realistic feed-in conditions. We show how to implement basic control strategies from electrical engineering, give insights into their potential with respect to frequency quality improvement and point out their limitations by maximum capacity and finite-time response.Comment: 12 pages, 6 figure

Heterogeneities in electricity grids strongly enhance non-Gaussian features of frequency fluctuations under stochastic power input

Stochastic feed-in of fluctuating renewable energies is steadily increasing in modern electricity grids and this becomes an important risk factor for maintaining power grid stability. Here we study the impact of wind power feed-in on the short-term frequency fluctuations in power grids based on an IEEE test grid structure, the swing equation for the dynamics of voltage phase angles, and a series of measured wind speed data. External control measures are accounted for by adjusting the grid state to the average power feed-in on a time scale of one minute. The wind power is injected at a single node by replacing one of the conventional generator nodes in the test grid by a wind farm. We determine histograms of local frequencies for a large number of one-minute wind speed sequences taken from the measured data and for different injection nodes. These histograms exhibit a common type of shape, which can be described by a Gaussian distribution for small frequencies and a nearly exponentially decaying tail part. Non-Gaussian features become particularly pronounced for wind power injection at locations, which are weakly connected to the main grid structure. This effect is only present when taking into account the heterogeneities in transmission line and node properties of the grid, while it disappears upon homogenizing of these features. The standard deviation of the frequency fluctuations increases linearly with the average injected wind power.Comment: 9 pages, 7 figure

The impact of turbulent renewable energy production on power grid stability and quality

Feed-in fluctuations induced by renewables are one of the key challenges to the stability and quality of electrical power grids. In particular short-term fluctuations disturb the system on a time scale, on which load balancing does not operate yet and the system is intrinsically governed by self-organized synchronization. Wind and solar power are known to be strongly non-Gaussian with intermittent increment statistics in these time scales. We investigate the impact of short-term wind fluctuations on the basis of a Kuramoto-like power grid model considering stability in terms of desynchronization and frequency and voltage quality aspects. We present a procedure to generate realistic feed-in fluctuations with temporal correlations, Kolmogorov power spectrum and intermittent increments. By comparison to correlated Gaussian noise of the same spectrum and Gaussian white noise, we found out that while the correlations are essential to capture the likelihood of severe outages, the intermittent nature of wind power has significant consequences on power quality: intermittency is directly transferred into frequency and voltage fluctuations yielding a novel type of fluctuations, which is beyond engineering status of knowledge

Heterogeneities in electricity grids strongly enhance non-Gaussian features of frequency fluctuations under stochastic power input

Stochastic feed-in of fluctuating renewable energies is steadily increasing in modern electricity grids, and this becomes an important risk factor for maintaining power grid stability. Here, we study the impact of wind power feed-in on the short-term frequency fluctuations in power grids based on an Institute of Electrical and Electronics Engineers test grid structure, the swing equation for the dynamics of voltage phase angles, and a series of measured wind speed data. External control measures are accounted for by adjusting the grid state to the average power feed-in on a time scale of 1 min. The wind power is injected at a single node by replacing one of the conventional generator nodes in the test grid by a wind farm. We determine histograms of local frequencies for a large number of 1-min wind speed sequences taken from the measured data and for different injection nodes. These histograms exhibit a common type of shape, which can be described by a Gaussian distribution for small frequencies and a nearly exponentially decaying tail part. Non-Gaussian features become particularly pronounced for wind power injection at locations, which are weakly connected to the main grid structure. This effect is only present when taking into account the heterogeneities in transmission line and node properties of the grid, while it disappears upon homogenizing of these features. The standard deviation of the frequency fluctuations increases linearly with the average injected wind power

Bridging between load-flow and Kuramoto-like power grid models: A flexible approach to integrating electrical storage units

In future power systems, electrical storage will be the key technology for balancing feed-in fluctuations. With increasing share of renewables and reduction of system inertia, the focus of research expands toward short-term grid dynamics and collective phenomena. Against this backdrop, Kuramoto-like power grids have been established as a sound mathematical modeling framework bridging between the simplified models from nonlinear dynamics and the more detailed models used in electrical engineering. However, they have a blind spot concerning grid components, which cannot be modeled by oscillator equations, and hence do not allow one to investigate storage-related issues from scratch. Our aim here is twofold: First, we remove this shortcoming by adopting a standard practice in electrical engineering and bring together Kuramoto-like and algebraic load-flow equations. This is a substantial extension of the current Kuramoto-like framework with arbitrary grid components. Second, we use this concept and demonstrate the implementation of a storage unit in a wind power application with realistic feed-in conditions. We show how to implement basic control strategies from electrical engineering, give insights into their potential with respect to frequency quality improvement, and point out their limitations by maximum capacity and finite-time response. With that, we provide a solid starting point for the integration of flexible storage units into Kuramoto-like grid models enabling to address current problems like smart storage control, optimal siting, and rough cost estimations