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

Quantifying fluctuations for dynamical power systems with stochastic excitations: A power spectral density-based method

Fluctuations of state variables play a pivotal role in analyzing small signal stability of the power system due to the integration of renewable energy sources. This paper develops a theoretical analysis methodology by using the power spectral density (PSD) for capturing the frequency and amplitude of state variable fluctuations in heterogeneous power systems with stochastic excitations. The fluctuations in generation and consumption occurring simultaneously are modeled by stochastic Ornstein-Uhlenbeck processes. The PSDs of the state variable fluctuations can be analytically calculated. PSD-based quantities have been proposed to evaluate angle and frequency deviations. Moreover, a global performance metric has been presented to measure the synchronization stability and calculated using the PSDs of frequency deviations. The underlying mathematical relationship between the metric and the primary control effort mimicking the H2-norm performance is explained in detail. Finally, the proposed analysis methodology is numerically illustrated on the IEEE RTS-96 test case. We investigate the impact of auto-correlations of stochastic processes on stability. Our results show the metric can be an alternative quantitative index of stability. We further find that the inertia allocation does not provide significant grid stability gain under small stochastic power fluctuations.

Small-Signal Stability of Multi-Converter Infeed Power Grids with Symmetry

Traditional power systems have been gradually shifting to power-electronic-based ones, with more power electronic devices (including converters) incorporated recently. Faced with much more complicated dynamics, it is a great challenge to uncover its physical mechanisms for system stability and/or instability (oscillation). In this paper, we first establish a nonlinear model of a multi-converter power system within the DC-link voltage timescale, from the first principle. Then, we obtain a linearized model with the associated characteristic matrix, whose eigenvalues determine the system stability, and finally get independent subsystems by using symmetry approximation conditions under the assumptions that all converters’ parameters and their susceptance to the infinite bus (Bg) are identical. Based on these mathematical analyses, we find that the whole system can be decomposed into several equivalent single-converter systems and its small-signal stability is solely determined by a simple converter system connected to an infinite bus under the same susceptance Bg. These results of large-scale multi-converter analysis help to understand the power-electronic-based power system dynamics, such as renewable energy integration. As well, they are expected to stimulate broad interests among researchers in the fields of network dynamics theory and applications.

Open database analysis of scaling and spatio-temporal properties of power grid frequencies

The electrical energy system has attracted much attention from an increasingly diverse research community. Many theoretical predictions have been made, from scaling laws of fluctuations to propagation velocities of disturbances. However, to validate any theory, empirical data from large-scale power systems are necessary but are rarely shared openly. Here, we analyse an open database of measurements of electric power grid frequencies across 17 locations in 12 synchronous areas on three continents. The power grid frequency is of particular interest, as it indicates the balance of supply and demand and carries information on deterministic, stochastic, and control influences. We perform a broad analysis of the recorded data, compare different synchronous areas and validate a previously conjectured scaling law. Furthermore, we show how fluctuations change from local independent oscillations to a homogeneous bulk behaviour. Overall, the presented open database and analyses constitute a step towards more shared, collaborative energy research.

Power grid frequencies mirror the state of the grid. Here, Rydin Gorjão et al. analyse measurements of power grid frequencies across areas and continents and uncover scaling laws of their fluctuations and spatio-temporal dynamics, which could aid the design, operation and control of power systems.

Time delay effects in the control of synchronous electricity grids

The expansion of inverter-connected generation facilities (i.e., wind and photovoltaics) and the removal of conventional power plants is necessary to mitigate the impacts of climate change, whereas conventional generation with large rotating generator masses provides stabilizing inertia, inverter-connected generation does not. Since the underlying power system and the control mechanisms that keep it close to a desired reference state were not designed for such a low inertia system, this might make the system vulnerable to disturbances. In this paper, we will investigate whether the currently used control mechanisms are able to keep a low inertia system stable and how this is affected by the time delay between a frequency deviation and the onset of the control action. We integrate the control mechanisms used in Continental Europe into a model of coupled oscillators which resembles the second order Kuramoto model. This model is then used to investigate how the interplay of changing inertia, network topology, and delayed control affects the stability of the interconnected power system. To identify regions in the parameter space that make stable grid operation possible, the linearized system is analyzed to create the system's stability chart. We show that lower and distributed inertia could have a beneficial effect on the stability of the desired synchronous state.