Large-scale deployment of renewable energy sources in power systems is basically motivated by two universally recognized challenges: the need to reduce as far as possible the environmental impact of the massive increase of energy request and the dependency on fossil-fuel. Renewable energy sources are interfaced to the network by means of interfacing power converters which inherently exhibit zero inertia differently from the conventional synchronous generators. This matter jointly to the high level of time variability of the renewable resources involve dramatically frequency changes, recurrent frequency oscillations and high variability of frequency profile in general. The need of a fast estimation of time variability of the power system inertia arises at the aim of predicting critical conditions. Based on the analysis of some actual data of the Italian Transmission Network, in this paper the authors propose an autoregressive model which is able to describe the dynamic evolution of the power system inertia. More specifically, the inertia is modeled as the sum of a periodic component and a noise stochastic process distributed according a non-Gaussian model. The numerical results reported in the last part of the paper, demonstrating the efficiency and precision of estimation of inertia, allow justifying the assumptions of the above modeling.

This study tackles the issue of electromechanical modes identification through a measurement‐based methodology employing a novel signal decomposition theorem based upon the Hilbert transform. The methodology aims to answer in a simpler and more pragmatic manner to the main weaknesses of the Hilbert–Huang transform with respect to the major refinements in the relevant literature. These weak points are discussed with sufficient detailed degree in the study. The main contribution of this study consists in combining a recent signal decomposition theorem for separating an assigned signal into elemental ones, each of them characterised by a single frequency component and a robust preliminary non‐linear spectral analyser, named L _p periodogram. This procedure's results are very appropriate for analysing some critical cases of electromechanical oscillations, because of the L _p periodogram robustness against heavy‐tailed noise and also its intrinsic ability in estimating closely spaced frequency components. The proposed approach is found to be inherently simple, reliable and consistent in performance as well as characterised by low computational burden. Some numerical applications validate the methodology and assess its own performance on synthetic signals, near real‐life signals acquired by IEEE test networks and on a real measured signal from a wide‐area monitoring system currently in operation.

This paper discusses some common reliability architectures, such as “parallel” and “k out of n” systems, adopted to add redundancy in many modern industrial systems, such as parallel-inverter systems. The focus is on some crucial properties of the failure rate (FR) of such systems, motivated by the fact that, in applied literature, the system FR is often simply evaluated as the reciprocal of the “Mean Time To Failure” of the system. However, this relationship is valid if, and only if, the system has a “series” reliability architecture. This is indeed the only case in which also the system has a constant FR, i.e., an Exponential lifetime distribution. Instead, the system FR of redundant systems is a function of time, which can never be constant. It is simply shown indeed that the FR of a parallel system with constant FR components is an increasing, or “first increasing, then decreasing” function of time, eventually reaching the value of the smallest FR. These results are extended to k out of n reliability systems, and also to more general reliability models with nonconstant FR, such as the Weibull or the “bathtub” model.

An increasing share of renewable energy sources in power systems requires ad-hoc tools to guarantee the closeness of the system’s frequency to its rated value. At present, the use of new technologies, such as battery energy storage systems, is widely debated for its participation in the service of frequency containment. Since battery installation costs are still high, the estimation of their lifetime appears crucial in both the planning and operations of power systems’ regulation service. As the frequency response of batteries is strongly dependent on the stochastic nature of the various contingencies which can occur on power systems, the estimation of the battery lifetime is a very complex issue. In the present paper, the stochastic process which better represents the power system frequency is analyzed first; then the battery lifetime is properly estimated on the basis of realistic dynamic modeling including the state of the charge control strategy. The dynamic evolution of the state of charge is then used in combination with the celebrated rain-flow procedure with the aim of evaluating the number of charging/discharging cycles whose knowledge allows estimating the battery damage. Numerical simulations are carried out in the last part of the paper, highlighting the resulting lifetime probabilistic expectation and the impact of the state of the charge control strategy on the battery lifetime. The main findings of the present work are the proposed autoregressive model, which allows creating accurate pseudo-samples of frequency patterns and the analysis of the incidence of the control law on the battery lifetime. The numerical applications clearly show the prominent importance of this last aspect since it has an opposing impact on the economic issue by influencing the battery lifetime and technical effects by modifying the availability of the frequency regulation service.