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We apply a dynamic stochastic control (DSC) approach based on an open-loop linear feedback policy to a classical asset-liability management problem as the one faced by a defined-benefit pension fund (PF) manager. We assume a PF manager seeking an optimal investment policy under random market returns and liability costs as well as stochastic PF members’ survival rates. The objective function is formulated as a risk-reward trade-off function resulting in a quadratic programming problem. The proposed methodology combines a stochastic control approach, due to Primbs and Sung (IEEE Trans Autom Control 54(2):221–230, 2009), with a chance constraint on the PF funding ratio (FR) and it is applied for the first time to this class of long-term financial planning problems characterized by stochastic asset and liabilities. Thanks to the DSC formulation, we preserve the underlying risk factors continuous distributions and avoid any state space discretization as is typically the case in multistage stochastic programs (MSP). By distinguishing between a long-term PF liability projection horizon and a shorter investment horizon for the FR control, we avoid the curse-of-dimensionality, in-sample instability and approximation errors that typically characterize MSP formulations. Through an extended computational study, we present in- and out-of-sample results which allows us to validate the proposed methodology. The collected evidences confirm the potential of this approach when applied to a stylized but sufficiently realistic long-term PF problem.

We investigate the use of a P-spline generalized additive hedonic model (GAM) for real estate prices in large U.S. cities, contrasting their predictive efficiency against commonly used linear and polynomial-based generalized linear models (GLM). Using intrinsic and extrinsic factors available from Redfin, we show that the GAM model is capable of describing 84% to 92% of the variance in the expected ln(sales price), based upon 2021 data. In contrast, a strictly linear GLM accounted for 65% to 78% of the variance, while polynomial-based GLMs accounted for 82% to 88%. As climate change is becoming increasingly important, we utilized the GAM model to examine the significance of environmental factors in two urban centers on the northwest coast. While the results indicate city-dependent differences in the significance of environmental factors, we find that inclusion of the environmental factors increases the adjusted R2 of the GAM model by less than 1%. Thirdly, our results indicate that the importance of sex offender residence proximity as a pricing factor is strongly influenced by state sex offender residence regulations.

This article deals with the parameters’ measurement of interarea oscillations, which are low-frequency damped oscillations that affect the high-voltage transmission lines when an unbalance between the power demand and the generated power occurs. The authors propose a method that processes the samples provided by the phasor measurement unit (PMU) and performs the online estimation of the parameters that characterize the interarea oscillations. The method takes advantage of the speed of a heuristic algorithm, such as the particle swarm optimization (PSO), but performs an enhancement on the results to increase the reliability. The tests carried out for the method assessment prove that the proposed method is characterized by a fast response, high accuracy, and excellent reliability, regardless of the type of oscillation that is considered.

È proposta una strategia di controllo per la partecipazione flessibile dei collegamenti HVDC alla regolazione di frequenza basata sulla variazione adattativa della potenza sincronizzante e versatile rispetto alle condizioni di carico del sistema.

Intra-hour photovoltaic power forecasting provides essential information for real time optimal control of microgrids. At this purpose, a critical issue is the selection of the forecasting method. The choice of a forecasting method depends on many factors such as the availability of historical data, the time horizon, the lag period, and the time available for the forecast. Persistence based methods are particularly tailored for real time forecasting which require fast information and are typically a good trade-off choice when dealing with real time operation of microgrids. Their accuracy, however, could be not satisfactory in some cases such as when it appears critical to consider the trend of the power output in the last few minutes rather than only the last measured value. Derivatives help reach this goal, but fractional derivatives seem to be a more accurate choice in order to take into account the history of the variable to be forecasted as they are a promising tool for describing memory phenomena. In this paper, a novel intra-hour forecasting method is proposed based on the Caputo derivative. Numerical applications are carried out to show the efficacy of the proposed approach. Also, the accuracy of the proposed approach is tested through comparison with three models namely, persistence, derivative-persistence and auto regressive moving average models. The strength of the proposed forecasting tool is strictly related to its low computational burden without compromising accuracy. This makes of it an interesting means for real time grid operation strategies and can be of interest for the grid operators especially in vision of the changes distribution grids are witnessing with the transition to the smart grid paradigm.

The paper proposes an analytical approach to evaluate the effects of series compensation of an overhead transmission line (OHL) concerning the increase of (1) loadability and (2) practical loading of the line. The first part of the paper focuses only on the line characteristics, and proposes an analytical approach to determine the loadability curves of the line as a function of the compensating capacitive reactance. In the second part of the paper, the perspective shifts to examine the power loading of the selected OHL in a meshed electrical network. The target is to evaluate the compensation degree required to achieve a desired power flow increase in the line. To this purpose a fast analytical method, based on the compensation theorem, is presented. Preserving the linearity of the network model, the proposed method allows computation of the needed compensation degree by means of a closed form equation. Numerical applications performed on two simple test networks allow to compare the method with an ad hoc implemented classical optimal power flow. The results validate the method and highlight its effectiveness as a simple and useful tool to support power system planners and designers.

The forced switching converters are the kernel of the modern paradigm of VSC-HVDC system. It is widely recognized that appropriate control laws make these converters more advantageous than the traditional line commutated ones. They can play a versatile role by properly controlling active and reactive powers between electrical networks, improving the dynamic performances of the whole system. Besides this is more and more motivated by the wide spreading penetration of renewable resources. In this paper after a few references to basic concepts, a possible control strategy of VSC-HVDC transmission system is discussed. With respect to a two-area system with AC-DC link, a combined control law is investigated for improving inertial and primary frequency response. The control law is based upon the equivalent HVDC tie link synchronization coefficient which allows determining the reference value of the AC voltage reference angles of the converters. A damping action is further added for improving the power swings damping. The simulations performed with a simple but quite general case study permit to confirm the validity and the goodness of the proposed control strategy.

This paper deals with the problem of the optimal rating of mineral-oil-immersed transformers in large wind farms. The optimal rating is derived based on the probabilistic analyses of wind power generation through the Ornstein–Uhlenbeck stochastic process and on thermal model of the transformer through the integration of stochastic differential equations. These analyses allow the stochastic characterization of lifetime reduction of the transformer and then its optimal rating through a simple closed form. The numerical application highlights the effectiveness and easy applicability of the proposed methodology. The proposed methodology allows deriving the rating of transformers which better fits the specific peculiarities of wind power generation. Compared to the conventional approaches, the proposed method can better adapt the transformer size to the intermittence and variability of the power generated by wind farms, thus overcoming the often-recognized reduced lifetime.

This paper deals with the inertia estimation of power systems in presence of significant contribution provided by renewable energy sources. The efforts to decommission conventional power plants and replace them with renewable resources could affect the robust and reliable operation of future power systems. The main issue related to the integration of renewable-based generation in the networks deals with the substitution of conventional synchronous generators connected to the grid and equipped by rotating masses, with converter-based generator which have not rotating masses, or they are decoupled by the grid due to the presence of interfacing power converters. Since the system inertia is the inherent ability of the online synchronous machines to oppose sudden changes in generation or load, the increasing share of renewable generators, such as wind and solar, the overall system inertia could decrease. This leading network operators to introduce new tools for monitoring the system inertia values, to contain them within admissible values, and to better prepare for different kinds of operational scenarios with undesired reduction of the system inertia. At this purpose, in this paper a tool for the analysis and prediction of inertia is proposed. The proposed method is based on a minimum variance harmonic finite impulse response and can consider the actual penetration of renewable energy sources. The proposed approach is tailored for online monitoring and exploits the real time measurements of relevant features of the network. The method is tested with actual data of the Italian Transmission Network and its effectiveness is studied by comparisons with some popular and well-established method of analysis and prediction.

The paper deals with the design and control of a fast charger circuit for Energy Storage Systems based on supercapacitor. The proposed solution finds natural application in the recharge stations of electrical vehicles (e.g., electrical buses, forklift, etc.) typically alternating short runs to periodic stops. It performs the charge migration from a module to supercapacitors to another, following a constant current profile to minimize the charging time. The control law, designed to be implemented in a commercial microcontroller, exploits a sliding mode technique properly modified to operate in PWM mode. Numerical simulations in MATLAB/SIMULINK environment with SimScape have been performed to prove the effectiveness of the proposed control.

The paper deals with design and control of a fault tolerant and reconfigurable photovoltaic converter integrating a Battery Energy Storage System as a standby backup energy resource. When a failure occurs, an appropriate control method makes the energy conversion system capable of operating in open-delta configuration in parallel with the grid as well as in islanded mode. In case network voltage is lacking due to heavy anomalies or maintenance reasons, the proposed control system is able to quickly disconnect the inverter from the grid while ensuring the energy continuity to the local load and the emergency fixtures by means of the integrated battery packs. In particular, the paper proposes a fast islanding detection method essential for the correct operation of the control system. This specific technique is based on the Hilbert transform of the voltage of the point of common coupling, and it identifies the utility lack in a period of time equal to half a grid cycle in the best case (i.e., 10 ms), thus resulting in good speed performance fully meeting the standard requirements. A thorough numerical investigation is carried out with reference to a representative case study in order to demonstrate the feasibility and the effectiveness of the proposed control strategy.

The paper deals with the analysis of inter-area oscillations. that originates from power transients occurred in high extension grids. The research activity is focused on the implementation of a method capable to provide the manager of the national transmission grid with a tool for real time and accurate monitoring of the power system stability. In particular, the authors present a signal-based algorithm which, starting from the values estimated by the Phasor Measurement Units (PMUs) on the grid, allows the online monitor of the parameters (damping and frequency) characterizing the inter-area oscillations. The proposed algorithm is based on the Particles Swarm Optimization (PSO) method, but the traditional PSO has been enhanced through the use of a Continuous Weighted Average (CWA) which, at each iteration step, filters the PSO outputs assuring the reliability of the estimates.

This paper presents a novel approach for the optimal design of the control system for battery energy storage systems adopted in power systems in the framework of the primary frequency control. The challenge issued by the use of batteries for frequency control in modern power systems is related to the need of the repeatedly deep charge and discharge phases. The presence of intermittent loads and generators, in fact, imposes very stressful power profiles to the battery which imply high rate of degradation to its lifetime. Based on the stress model of the battery, the proposed approach aims to design a control system which allows for containing the state of charge time variation within intervals able to match the requirements of frequency profile improvements and lifetime preservation. At this aim, the typical control scheme for batteries adopted for primary frequency control is analyzed and elaborated to address stable dynamic behavior of the regulator. Moreover, starting from the observation of the statistical nature of the power request for the pure frequency regulation service, a statistical study is conducted to perform an optimal design of the regulator in terms of both lifetime duration and primary frequency regulation service.

This paper focuses on very-short-term photovoltaic power forecasting based solely on power measurement. The approach proposed in the paper is tailored for real time operation of smart grids and microgrids, that deals with energy management and control of the various resources of the grid and, particularly, on those based on renewable energy sources. These resources are characterized by variable power production, thus constituting a challenge for the effectiveness of strategies and tools of management and control. This paper refers to photovoltaic power production and presents a new real time forecasting method which improves the classical persistence model. The proposed method is based on the idea of conveniently weighting information on past data by imposing continuity of the function, of its first derivative and of the second derivative so obtaining three estimates of the function in the forecast interval which are then opportunely weighted to provide the forecast. The effectiveness of the proposed approach is shown in the numerical application based on actual measured data. The accuracy of the proposed approach is also tested through comparisons with two models based on the persistence and auto regressive moving average models.

Large-scale penetration of renewable energy sources in power systems is essentially related to the need of reducing the environmental impact caused by the fossil-fuel. As well known, the interface between the power grid and this kind of energy resource is achieved by power converters, with a consequent dynamic behavior quite different from the synchronous generators. This matter involves negative impacts on the operating conditions of power systems. In this context, it is crucial to individuate estimation techniques able to predict promptly critical conditions which could, in extreme cases, compromise the stability of whole system. In this paper the authors employ an auto-regressive model which can describe the dynamic evolution of the power system inertia. The core of the procedure relies on an inertia model conceived as the sum of a periodic component and a noise stochastic process distributed according a Logistic model. The robustness of a novel estimation procedure, able to capture the dynamic evolution of the inertia, is investigated by testing two scenarios of Italian Transmission Network. The assumptions in terms of the obtained numerical results show the validity of the estimation technique and of the probabilistic characterization of the noise.

In setting a safe route for a ship, one of the problems to face is represented by excessive roll motions deriving from resonance phenomena in adverse weather conditions. An effective prediction of the roll motion amplification is related to a proper mathematical modelling of the ship motions. Linear models may result to be inadequate in case of large roll motions, where non-linear effects dominate. This paper investigates the roll response resonance in irregular waves. The developed method aims at demonstrating the influence of the non-linear immersed hull geometry, as already acknowledged in literature for regular seas. A 6-Dof non-linear model is applied for generating the time histories of ship roll motions in irregular waves. These are fed into an optimization routine, able of finding the linear system (focusing at its natural roll frequency) that better approximates the non-linear one at a certain mean roll amplitude. The outcomes of this research are meant to support the estimation of roll resonance period accounting for non-linearities of immersed hull geometry, allowing for a more reliable solution of weather routing problems.

This paper deals with hybrid energy storage system (HESS) management strategies, optimized for urban road electric vehicle applications. These new control strategies aim to extend battery pack durability by reducing charging/discharging current peaks by means of supercapacitors. The optimization is carried out with reference to the case study of a HESS composed of a high power unit, i.e. supercapacitor module plus a high energy unit, i.e. a battery pack, based on nickel-chloride ZEBRA (ZEolite Battery Research Africa) technology. On-board integration of the two storage devices is obtained through a DC/DC bidirectional power converter, as this configuration is particularly convenient for many kinds of urban vehicle operations. The novelty of this work consists in an analytical methodology, based on non-linear programming and calculus of variations theory, to evaluate management strategies characterized by high effectiveness in reducing battery current transients. The identification and optimization of these strategies are initially performed on the basis of a vehicle model, built in the Matlab-Simulink simulation environment. To this purpose, the experimental characterization of the supercapacitor module is obtained with reference to three different models, whose selection depends on the required fitting performance and computational effort indexes, as evaluated in the paper. The energy management strategies identified show promising results in the simulation environment, followed by experimental activities carried out by means of a dedicated 1:1 scale laboratory test bench. The various experimental results presented in this manuscript highlight that the identified λ-control strategy presents effectiveness values up to 57%, close to the ideal results obtained in the simulation environment. In fact, the methodology proposed in this paper, validated by laboratory experiments, definitely reduces the negative consequences of power peaks on the HESS, indicating the real possibility of using these results in the design and control of urban road vehicles.

This paper describes a novel Energy Management Strategy (EMS) for hybrid energy storage systems, when used to supply urban electric vehicles. A preliminary off-line procedure, based on nonlinear programming, is performed in order to optimize the battery current profile for fixed working cycles. Hence, a suitable control strategy, which is based on a constrained minimization problem, is tailored for real-time applications. This control strategy exploits the off-line solution of a proper isoperimetric problem and aims to dynamically optimize the battery durability by reducing peak charging/discharging current values. The main advantage of the analysed EMS consists in the easy on-board implementation through the use of one single parameter, which can be quickly identified through a simple off-line numerical procedure. The proposed strategy is evaluated in simulation environment, through the use of a Matlab-Simulink model, for the case study of an urban electric vehicle running on a ECE 15 driving cycles. Simulation results have confirmed the good performance of the above strategy in reducing the battery peak charging/discharging current through the proper management of the hybrid energy storage system.

The study presents a significant development of an advanced control strategy for stand-alone three-phase induction generators. The system under study consists of a squirrel-cage induction generator driven mechanically by an internal combustion engine and electrically by a fault-tolerant converter coupled with a LC filter. As a novelty, in this study three low-cost electrical contactors are introduced in order to re-arrange the converter topology after a fault occurrence and a proper re-starting procedure is developed, allowing the converter to operate with only two legs. The control architecture is mainly described with respect to this last operating condition, evidencing its intrinsic robustness. The study focuses on the composite control of the converter and the prime mover in order to improve the dynamic assessment of the whole system. The converter control is designed around the sliding mode technique, due to its attractive performance, especially as far as parameter uncertainties are concerned. In order to validate the theoretical framework, this study presents the first ever made experimental tests of this system with reference to a generation unit of about 10 kVA. The results confirm the high capability of the proposed system in regulating voltage and frequency with very good dynamic features.

This paper describes the feasibility analysis of a methodology based on the Hilbert transform in order to detect the gear rattle phenomenon of automotive transmissions. The technique adopts the Hilbert transform to analyze experimental signals of the relative angular motion of gears starting from high-resolution optical encoder measurements. By this procedure it is possible to evaluate the severity of impacts occurring between the teeth of unloaded gears, by examining the root mean square value of the signal. The Hilbert transform is largely adopted in the detection of gear defects, such as tooth cracks, but it has not yet been used to detect gear rattle. This feasibility study highlights the capability in discriminating between impacts occurring on the two different sides of the tooth. The method puts in evidence the influence of oil lubricant between the teeth in reducing the severity of the impacts, by comparing many experimental tests performed with two different oils for transmission gears. Moreover, in order to evaluate the reliability of the proposed methodology some comparisons are conducted with a metric based on the fast Fourier transform, often adopted in this field, to highlight the goodness and simplicity of the technique based on the Hilbert transform.

In this paper, an analytical approach that deals with the optimal sizing of energy storage systems in direct current networks is proposed. In modern power systems, the widespread use of power electronics, storage devices, and automation is driving power engineers to focus on the use of direct current networks. This new focus requires specific tools for the optimal planning and operation of these networks in order to increase energy efficiency and reduce operating costs. This paper is focused on the improvements in the efficiencies of direct current networks, which are characterized by the presence of loads, units for the generation of renewable power, and storage devices. Based on the calculus of variations, an original matrix formulation which starts with the nodal representation of the direct current network is proposed. Two attractive closed-form solutions are presented for minimizing power losses, i.e., (1) a solution based on the approximation of considering the voltage constant at all the network’s busses and (2) a solution based on the linear approximation of the load flow. In both cases, the goal is to minimize losses over a given time horizon (e.g., the daily cycle). The formulation of the problem allows an analytical solution to be obtained that represents a suitable tool for the purpose of designing storage. In addition, the proposed approach can be applied and extended to the optimal sizing of storage systems. The proposed sizing procedure, which uses an analytical approach, is formulated in a general manner that can be used for various storage technologies. The results of numerical applications clearly have demonstrated both the feasibility and accuracy of the methodology to be used in the proposed design. We also propose an interesting parametric study in order to determine the optimal technology and the optimal size of the storage device.

Three-winding transformer model is widely utilized in High Voltage Direct Current (HVDC) system or railway power supply system. Coupled with a diode rectifier, the application of three winding transformers for power distribution is now increasing because of increased demand for reliable and available electrical supply. This paper analyzes the application of a three-winding transformer as a primary power distribution system instead of a standard two-winding transformer. Moreover, we present a fast calculation of short circuit current.

In this paper a deep investigation of supercapacitor device modeling is performed with specific reference to hybrid energy storage modules, suitable to support both all electric /hybrid propulsion and on board MVDC distribution marine systems. In those applications, the combination of batteries and supercapacitors in realizing energy storage hybrid devices overtakes the intrinsic disadvantages of single use of electrochemical batteries and supercapacitors. On the other hand, proper design and management strategies of hybrid architecture are required in order to achieve the best performance in terms of dynamic and life cycle assessment on load profile of marine applications. In this way, the main results presented in this paper consists in a simple quadratic mathematical model of supercapacitor, evaluated as a quadratic function of the ultra-capacitor voltage, which is validated experimentally on the base of operative-cycle-based loading profiles, representative of marine application. The results and comparison reported in this work confirm the validity of the proposed model for preliminary design of hybrid energy storage systems and management strategies evaluation on the electrification of ship power systems.

This paper deals with the design and control aspects of modern ship power systems within the paradigm of an all-electric ship. The widespread use of power electronic converters is central in this context due to the technological advances in automation systems and the integration of the electrical propulsion systems and other components, such as electrical energy storage systems and renewable energy sources. The issue to address in this scenario is related to the request of increased performances in dynamic operation while pursuing advantages in terms of energy savings and overall system security. In addition, the presence of large load changes requires providing robustness of the control in terms of system stability. This paper is focused on medium voltage direct current (MVDC) ship power systems and the design and control of coupled inductor DC&ndash, DC converters. The load is handled in terms of a constant power model, which generally is considered the most critical case for testing the stability of the system. The robustness of the design procedure, which is verified numerically against large and rapid load variations, allowed us to confirm the feasibility and the attractiveness of the design and the control proposal.

This study is devoted to a proper modeling and estimation method of battery capacity fading under the widely adopted exponential decay model, in view of an efficient lifetime assessment of battery. The method is based upon recursive online Bayes estimation of capacity fading. It is also shown how a degradation-based modeling of battery reliability can be adopted, leading to a Bernstein lifetime distribution. The performances of the proposed method are successfully evaluated by means of extensive Monte Carlo simulations based upon available literature and experimental data. A brief account is also given of a robustness analysis of the proposed methodology with respect to departures from the assumption of Gaussian noise.

This paper proposes a new methodological approach in the field of studies devoted to proper and accurate selection of a reliability model for battery systems. The study is performed with particular emphasis on the modeling and estimation of the Conditional Reliability Function, conceived as a key analytical tool in predicting the "Remaining useful life" of the battery, which is in turn an important information in order to identify the best maintenance strategy selection, or for inspection optimization, and also spare parts provision. Estimation of the Conditional Reliability Function is developed by means of a method based on the Inverse Gaussian Distribution and its Bayes Estimation. The performances of this estimation are developed and validated by means of extensive simulations and available experimental data. A brief account is reported of robustness analyses of the method with respect to the assumed prior Distribution.

The aim of this paper is the definition of a daily index representing the risk-return on investments in the American film industry. The index should be used to predict the riskiness and the expected return of movie projects at the level of the overall industry and then to determine a premium for insurance for such an investment. Such an index can inform the decision making in relation to risk but also timing. Though not currently legal in the United States, such an index may be relevant at some point in the future or in other countries for film production companies as well as venture capitalists interested in investing in one or a slate of motion picture productions or more broadly in the holdings of a media conglomerate, an exhibition chain, or some other aspect of the media landscape.

Four-phase transmission lines have been recently proposed and studied as an alternative to the traditional three-phase lines. The identification of the best transformer typology to link the three-phase and four-phase system sections is still an open problem, despite some specific solutions were proposed. However, these solutions were not included in a general framework yet. Resorting to the classic Parton's theory of phase transformation and to a rigorous mathematical approach, this study provides a general framework for the specific problem in study. After having recalled the underlying principles of the Parton's theory of phase transformation, by formulating proper optimisation problems and solving them using a rigorous mathematical procedure, this study derives several solutions for three-to-four phase transformation, some of which were never proposed yet. This way, both traditional solutions (T-connection, Leblanc connection, Scott connection) and more recent proposals are described together with the new solutions within one common framework.

This paper discusses the themes of optimal design and management strategies of hybrid energy storage system (HESS) for marine applications. This design and related strategy are aimed to improve battery pack durability, ensuring a smooth profile of the required current, through the complementary action of super-capacitors. A DC/DC bidirectional power converter allows for the integration of these devices and control of on-board power fluxes. The proposed methodology is based upon the solution of a constrained optimization problem. In order to overcome computational issues, proper formulation of the mathematical problem is based upon the Ritz method, which is one of the direct methods for solving problems related to calculus of variations. The solution of the optimization procedure, which is the key finding in this paper, permits to obtain battery voltage and current profile, which enables the designer to determine battery and super-capacitor sizes and also provides battery/super-capacitor reference current profiles to be tracked by the DC/DC bidirectional power converter. The procedure is evaluated with reference to the case study of a water-bus operating in the Venetian lagoon, whose operative cycle has been acquired during proper measurement campaigns. Then, the performance of energy management strategies are verified by means of laboratory experimentations on the hybrid energy storage system, which have been carried out by scaling operative cycles at single storage cell level. The obtained results show the potential advantages of proper design and energy management obtained through this new methodology, in terms of investment and maintenance costs for sustainable maritime transport.

HV cables have a significant role in linking power sources and loads in electrical grids. The focus of this paper is on studying the thermal processes acting in a HV XLPE power cable, by using a matrix approach and taking into account the whole cable system, with all its layers. The work defines an approach, which, in presence of uncertainty, can be used to characterize the heat transfers between the cable layers. The approach is used in this paper to examine the loading transient phase over an interval of 60 minutes. A sensitivity analysis involving the parameters of each cable layer is carried out. The model is validated by using the results of a laboratory test. The optimal parameter fitting is also carried out.

Battery energy storage systems are widely recognized as viable means for providing frequency regulation in electrical systems characterized by the massive deployment of renewable resources. In this case, the estimation of the battery lifetime is very complex since its response depends strongly on the stochastic nature of various contingencies. By starting from the characterization of the power system frequency in terms of the stochastic process, in this paper, tools needed for the battery lifetime estimation are detailed. On the basis of a realistic dynamic model, the state of charge profile requested to a battery providing primary frequency regulation is derived, with the aim of characterizing statistically its degradation. In this way, it is expected to obtain an efficient battery lifetime estimation compared to the heuristic methods. Numerical simulations are carried out in the last part of the paper, illustrating a simulation tool for the estimation of the battery working cycle. © 2018 IEEE.

In the companion paper [1], the first part of this technical contribution, the way Renewable Energy Sources (wind turbines and photovoltaic units) affect power system's rotational inertia was thoroughly discussed. It is well understood that this relationship, becoming obviously more and more important in the last years, has implications for frequency dynamics and power system stability. Frequency dynamics are indeed faster in power systems with low rotational inertia, making frequency control and power system stability more challenging. In the first paper, after discussing the impact of low rotational inertia on power system stability, a new Bayesian statistical inference approach has been proposed for the on-line estimation of the “Renewable Energy Source Share” and thus the rotational inertia of a given system. This was discussed from the point of view of developing a theoretical methodological contribution. In this second part, extensive numerical simulations confirm that the proposed estimation technique constitutes a very fast, efficient and, especially, a robust method for an efficient assessment of rotational inertia.

The use of the micro-gas turbine devices is an important solution for distributed power generation and cogeneration. A cogenerating micro gas turbine of 30kW, operating with a recuperated thermal cycle, is examined under the point of view of the transient developments, induced by variations in electrical loads. The result is defined by the fuel supply law and by the response delay of the rotating and stationary components. In the paper, an optimization method in order to reduce the fuel consumption by varying load is presented. The control strategy adopted is able to determine the optimal reference value of the rotational speed and the ratio between the inlet air and fuel mass flow rate by a simple PI controller. Some results have been reported in terms of TIT temperature, global efficiency and outlet recuperator temperature to evaluate the respond time during a transient operation.

The growing diffusion of electric vehicles connected to distribution networks for charging purposes is an ongoing problem that utilities must deal with. Direct current networks and storage devices have emerged as a feasible means of satisfying the expected increases in the numbers of vehicles while preserving the effective operation of the network. In this paper, an innovative probabilistic methodology is proposed for the optimal sizing of electrical storage devices with the aim of maximizing the penetration of plug-in electric vehicles while preserving efficient and effective operation of the network. The proposed methodology is based on an analytical solution of the problem concerning the power losses minimization in distribution networks equipped with storage devices. The closed-form expression that was obtained is included in a Monte Carlo simulation procedure aimed at handling the uncertainties in loads and renewable generation units. The results of several numerical applications are reported and discussed to demonstrate the validity of the proposed solution. Also, different penetration levels of generation units were analyzed in order to focus on the importance of renewable generation.

In the last years, large-scale deployment of renewable energy sources has led to the use of significant shares of generation from intermittent sources. Renewable energy sources units are notably inverter-connected wind turbines and photovoltaic that as such do not provide rotational inertia: this has implications for frequency dynamics and power system stability and operation. Frequency dynamics are faster in case of systems with low rotational inertia, thus making frequency control and power system operation more challenging. While the impact of low rotational inertia on power system stability and operation have been widely investigated in the recent literature, in this paper a new Bayesian statistical inference approach is proposed for the on-line estimation of the rotational inertia of a given system. The need for estimation is based upon the observation that the amount of renewable energy affecting the system is a random process. The authors' researches of this paper is devoted to the Bayesian on-line recursive estimation of the amount of the so-called “Renewable Energy Source Share”. The numerical application reported in the companion paper [1] confirms that the proposed estimation technique constitutes a very fast, efficient and, especially, a robust method for ‘tracking’ the above share in view of an efficient assessment of rotational inertia.

This paper deals with the loadability characteristics of overhead transmission lines (OHLs). The target is to provide a general analytical formulation of the loadability characteristics of uncompensated OHLs. This is a completely new approach: no previously published work has adopted an analytical approach to characterize the different regions of the loadability curves. In order to allow a direct comparison with previous works, an application example concerns the 400 kV single circuit OHLs widely used in Western Europe.

This paper deals with the loadability of series-compensated lines. Aim of the paper is to provide loadability curves calculated considering various technical limits, namely the thermal limit, the voltage drop limit, the Joule losses limit, and the steady-state stability limit. These curves are evaluated with respect to single circuit 400-kV overhead transmission lines (OHLs) equipped with standard triple-core aluminium conductor steel-reinforced (ACSR) conductor bundles of $\pmb{3\times 585}\mathbf{mm}^{\pmb{2}}$ cross section. The paper describes the optimization procedure used to maximize the active power transported at the receiving-end of the line. The optimal level of series compensation is obtained as a result of the optimization problem constrained by all the technical limits listed above. The last part of the paper is devoted to an extensive numerical application that has the aim of demonstrating the feasibility and applicability of the nronosed annroach. This study highlights the loadability increase that can be obtained through series capacitors, and might support the decision-making for the investments required by series compensation.