Inertia is a measure of a power system’s capability to counteract frequency disturbances: in conventional power networks, inertia is approximately constant over time, which contributes to network stability. However, as the share of renewable energy sources increases, the inertia associated to synchronous generators declines, which may pose a threat to the overall stability. Reliably estimating the inertia of power systems dominated by inverted-connected sources has therefore become of paramount importance. We develop a framework for the continuous estimation of the inertia in an electric power system, exploiting state-of-the-art artificial intelligence techniques. We perform an in-depth investigation based on power spectra analysis and input-output correlations to explain how the artificial neural network operates in this specific realm, thus shedding light on the input features necessary for proper neural-network training. We validate our approach on a heterogeneous power network comprising synchronous generators, static compensators and converter-interfaced generation: our results highlight how different devices are characterized by distinct spectral footprints - a feature that must be taken into account by transmission system operators when performing online network stability analyses.

This work presents a technique to estimate on-line the inertia of a power system based on ambient measurements. The proposed technique utilizes the covariance matrix of these measurements and solves an optimization problem that fits such measurements to the synchronous machine classical model. We show that the proposed technique is adequate to accurately estimate the actual inertia of synchronous machines and also the virtual inertia provided by the controllers of converter-interfaced generators that emulate the behavior of synchronous machines. We also show that the proposed approach is able to estimate the equivalent damping of the classical synchronous machine model. This feature is exploited to estimate the droop of grid-following converters, which has a similar effect of the swing equation equivalent damping. The technique is comprehensively tested on a modified version of the IEEE 39-bus system as well as on a dynamic 1479-bus model of the all-island Irish transmission system.

This paper proposes an area inertia estimator based on an iterative equation error (EE) system identification (SI) approach. The inertia value can be accurately extracted for areas of different compositions with different penetrations of converter-interfaced generators. Firstly, the internal frequency variation of the generator units is computed by means of a frequency divider-based estimator. Subsequently, these internal frequency variations are used to carry out a generator clustering, which provides groups of coherent generators to the proposed inertia estimator. Finally, the iterative EE SI approach provides a joint inertia estimation for each of these coherent groups. Numerical results on a properly modified version of both the IEEE 39-bus and the IEEE 118-bus test systems highlight the accuracy of the proposed method using both ambient measurements and ringdown signal measurements (power imbalance events). Furthermore, the proposed method presents a low computational burden that allows fast estimation updating times.

The frequency behavior of an electric power system right after a power imbalance is determined by its inertia constant. The current shift in generation mix towards renewable energy sources is leading to a smaller and more variable inertia, thereby compromising the frequency stability of modern grids. Therefore, real-time inertia estimation methods would be beneficial for grid operators, as their situational awareness would be enhanced. This paper focuses on an inertia estimation method specifically tailored for synchronous generators, based on the extended Kalman filter (EKF). Such a method should be started at the time of disturbance, which must be estimated accurately, otherwise additional errors could be introduced in the inertia estimation process. In this paper, the sensitivity of the EKF-based inertia estimation method to the assumed time of disturbance is analyzed. It is shown that such sensitivity is influenced by the initially assumed inertia constant, the use time of the filter and by the time required for primary frequency regulation to be activated.

This paper presents a unified power flow algorithm for large and complex mixed AC/DC power systems based on the partitioning of power grids, a version of the two-level Newton method, and the modified nodal analysis formulation. Partitioning significantly increases numerical efficiency without altering the accuracy of the power flow solution. This approach can be applied to any combination of multiple DC and possibly non-synchronized AC systems. It considers the steady-state interaction of AC and DC systems for a wide range of converter representations and control functions. Simplification of elements within the converter stations is not required. Both DC and AC-side converter losses are adequately accounted for by using a generalized converter loss model. The steady-state converter equations are derived in their most general form, with the AC and/or DC-side power exchange or voltages defined as controlled quantities.