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In the present paper, the process of estimating the important statistical properties of extreme wind loads on structures is investigated by considering the effect of large variability. In fact, for the safety design and operating conditions of structures such as the ones characterizing tall buildings, wind towers, and offshore structures, it is of interest to obtain the best possible estimates of extreme wind loads on structures, the recurrence frequency, the return periods, and other stochastic properties, given the available statistical data. In this paper, a Bayes estimation of extreme load values is investigated in the framework of structural safety analysis. The evaluation of extreme values of the wind loads on the structures is performed via a combined employment of a Poisson process model for the peak-over-threshold characterization and an adequate characterization of the parent distribution which generates the base wind load values. In particular, the present investigation is based upon a key parameter for assessing the safety of structures, i.e., a proper safety index referred to a given extreme value of wind speed. The attention is focused upon the estimation process, for which the presented procedure proposes an adequate Bayesian approach based upon prior assumptions regarding (1) the Weibull probability that wind speed is higher than a prefixed threshold value, and (2) the frequency of the Poisson process of gusts. In the last part of the investigation, a large set of numerical simulations is analyzed to evaluate the feasibility and efficiency of the above estimation method and with the objective to analyze and compare the presented approach with the classical Maximum Likelihood method. Moreover, the robustness of the proposed Bayes estimation is also investigated with successful results, both with respect to the assumed parameter prior distributions and with respect to the Weibull distribution of the wind speed values.

Rapid growth of the use of wind energy calls for a more careful representation of wind speed probability distribution, both for identification and estimation purposes. In particular, a key point of the above identification and estimation aspects is representing the extreme values of wind speed probability distributions, which are of great interest both for wind energy applications and structural tower reliability analysis. The paper reviews the most adopted probability distribution models and estimation methods. In particular, for reasons which are properly discussed, attention is focused on the evaluation of an opportune “safety index” related to extreme values of wind speeds or gusts. This topic has gained increasing attention in recent years in both wind energy generation assessment and also in risk and structural reliability and safety analysis. With regard to wind energy generation, there is great sensitivity in the relationship between wind speed extreme upper quantiles and the corresponding wind energy quantiles. Concerning the risk and reliability analysis of structures, extreme wind speed value characterization is useful for a proper understanding of the destructive wind forces that may affect structural tower reliability analysis and, consequently, the proper choice of the cut off wind speed value; therefore, the above two kinds of analyses are somewhat related to each other. The focus is on the applications of the Bayesian inference technique for estimating the above safety index due to its effectiveness and usefulness.

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.

Battery participation in the service of power system frequency regulation is universally recognized as a viable means for counteracting the dramatic impact of the increasing utilization of renewable energy sources. One of the most complex aspects, in both the planning and operation stage, is the adequate characterization of the dynamic variation of the state of charge of the battery in view of lifetime preservation as well as the adequate participation in the regulation task. Since the power system frequency, which is the input of the battery regulation service, is inherently of a stochastic nature, it is easy to argue that the most proper methodology for addressing this complex issue is that of the theory of stochastic processes. In the first part of the paper, a preliminary characterization of the power system frequency is presented by showing that with an optimal degree of approximation it can be regarded as an Ornstein–Uhlenbeck process. Some considerations for guaranteeing desirable performances of the control strategy are performed by assuming that the battery-regulating power depending on the frequency can be described by means of a Wiener process. In the second part of the paper, more realistically, the regulating power due to power system changes is described as an Ornstein–Uhlenbeck or an exponential shot noise process driven by a homogeneous Poisson process depending on the frequency response features requested of the battery. Because of that, the battery state of charge is modeled as the output of a dynamic filter having this exponential shot noise process as input and its characterization constitutes the central role for the correct characterization of the battery life. Numerical simulations are carried out for demonstrating the goodness and the applicability of the proposed probabilistic approach.

This paper proposes the Compound Inverse Rayleigh distribution as a proper model for the characterization of the probability distribution of extreme values of wind-speed. This topic is gaining interest in the field of renewable generation, from the viewpoint of assessing both wind power production and wind-tower mechanical reliability and safety. The first part of the paper illustrates such model starting from its origin as a generalization of the Inverse Rayleigh model by means of a continuous mixture generated by a Gamma distribution on the scale parameter, which gives rise to its name. Moreover, its validity for interpreting different field data is illustrated resorting to real wind speed data. Then, a novel Bayes approach for the estimation of such extreme wind-speed model is proposed. The method relies upon the assessment of prior information in a practical way, that should be easily available to system engineers. The results of a large set of numerical simulations—using typical values of wind-speed parameters—are reported to illustrate the efficiency and the accuracy of the proposed method. The validity of the approach is also verified in terms of its robustness with respect to significant differences compared to the assumed prior information.

Extreme Wind Speed modeling, i.e. the probabilistic characterization of extreme values of wind speed, is a key tool for properly understanding the destructive wind forces which may affect mechanical safety and reliability of wind power systems, but it is also extremely useful for the purpose of achieving accurate wind energy production estimations. Indeed, the need of more accurate wind estimations has been often highlighted in the literature, especially for Extreme Wind Speed, since classical adopted models, such as the Weibull distribution, behave poorly in the range of Extreme Wind Speed values. In the paper, a new model, generated by a proper mixture of the established Inverse Weibull distribution, is proposed and illustrated. The proposal is the “Inverse Log-logistic” distribution, whose adequacy in interpreting some sets of real Extreme Wind Speed data is shown after giving some hints to its identification. This study also develops a peculiar Bayesian statistical inference approach for the estimation of the above model from available data, using different prior distributions, i.e. the Lognormal, the Generalized Gamma and the Uniform distribution. Extensive numerical simulations confirm that the proposed estimation technique constitutes a very fast, efficient and robust method for the Extreme Wind Speed modeling.

Inverse Rayleigh probability distribution is shown in this paper to constitute a valid model for characterization and estimation of extreme values of wind speed, thus constituting a useful tool of wind power production evaluation and mechanical safety of installations. The first part of this paper illustrates such a model and its validity to interpret real wind speed field data. The inverse Rayleigh model is then adopted as the parent distribution for assessment of a dynamical “risk index” defined in terms of a stochastic Poisson process, based upon crossing a given value with part of the maximum value of wind speed on a certain time horizon. Then, a novel Bayes approach for the estimation of such an index under the above model is proposed. The method is based upon assessment of prior information in a novel way which should be easily feasible for a system engineer, being based upon a model quantile (e.g., the median value) or, alternatively, on the probability that the wind speed is greater than a given value. The results of a large set of numerical simulation—based upon typical values of wind-speed parameters—are reported to illustrate the efficiency and the precision of the proposed method, also with hints to its robustness. The validity of the approach is also verified with respect to the two different methods of assessing the prior information.

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.