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Electrical distribution networks are often inadequate to comply with the increasing load demand and to enable new installation of distributed energy resources. This inadequacy may result in upgrading existing transformers of in disconnecting the entire load during demand peaks, and into wasting a portion of the total renewable energy produced during favorable weather conditions. Increasing the capacity of electrical distribution network components is therefore mandatory in order to avoid these negative circumstances; however replacing lines and transformers is costly, and often the benefits are not worth the investments. Fortunately, the capacity of distribution networks can be unlocked by managing the electrical components by their dynamic ratings, allowing operating them even beyond their rated ampacity for a limited interval of time. This paper proposes a new risk-based procedure to manage distribution transformers by their dynamic rating. Probabilistic forecasts of loads and ambient temperatures are the inputs of the procedure, which are obtained in this paper from quantile regression forests. The procedure quantifies, in a probabilistic framework, the insulation thermal ageing due to the transformer (over)load in terms of the cost sustained for rewinding the transformer. The corresponding estimated risk is made available to the distribution system operator, who may therefore take a decision comparing it to an arbitrary level of risk coverage, favoring either the power delivery to customers or the reduction of the transformer ageing rate; this level is formulated in this paper having an intuitive physical meaning, thus enabling its setting also by non-expert operators. Comprehensive numerical experiments based on actual data are presented under different configurations and scenarios, in order to validate the proposal from an energetic and economic point of view.

Reactive power forecasting is essential for managing energy systems of factories and industrial plants. However, the scientific community has devoted scant attention to industrial load forecasting, and even less to reactive power forecasting. Many challenges in developing a short-term reactive power forecasting system for factories have rarely been studied. Industrial loads may depend on many factors, such as scheduled processes and work shifts, which are uncommon or unnecessary in classical load forecasting models. Moreover, the features of reactive power are significantly different from active power, so some commonly used variables in classical load forecasting models may become meaningless for forecasting reactive power. In this paper, we develop several models to forecast industrial reactive power. These models are constructed based on two forecasting techniques (e.g., multiple linear regression and support vector regression) and two variable selection methods (e.g., cross validation and least absolute shrinkage and selection operator). In the numerical applications based on real data collected from an Italian factory at both aggregate and individual load levels, the proposed models outperform four benchmark models in short forecast horizons.

Demand response (DR) is a useful tool for end users, since it allows noticeable reductions in the electricity bill. However, some customers have stringent constraints in terms of hourly active power, which makes DR attractive only when performed with the contemporaneous use of battery energy storage systems (BESSs). When this option is used, it is desirable to optimally size the BESSs, since their high investment costs could make their use impracticable for DR purposes. The uncertainties related to many of the inputs required by the BESS-sizing procedure make it necessary to use a probabilistic framework for sizing. In this paper, a probabilistic approach is proposed for the optimal sizing of BESSs when time-of-use (ToU) pricing is applied. The sizing procedure takes into account the uncertainties that unavoidably affect the evaluation of the total cost incurred by the customer such as load demand, energy prices, and economic factors.

The paper proposes a tool for the optimal sizing of an end user's battery energy storage system. The sizing is performed considering demand response applications with real time energy prices. The procedure, which takes into account also the battery degradation due to some stress factors, is performed based on uncertainties of generation, load, weather conditions, discount rate and energy price. Particularly, the sizing of the storage device is aimed at maximizing the economic benefit of the end user.

Scheduling the distributed energy resources in day-ahead scenarios requires the use of accurate forecasts of loads, generation, and energy prices. Forecasting errors may significantly influence the quality of the scheduling, resulting in overestimations or underestimations of the power required from the grid by a price-responsive customer. In this paper we provide an insight on the assessment of the impact of forecasting errors in a case study regarding an industrial customer who disposes of a photovoltaic system and of an electrical energy storage system. The day-ahead scheduling procedure, developed in previous works, is applied using forecasts obtained through random forests and through a benchmark model; the obtained results are compared with the ideal scenario, using the actual realizations of the unknown variables, in order to assess the responsiveness of the scheduling procedure to forecasting errors.

Distributed generation (DG) produces many benefits for the distribution systems that are operated as active systems, even if they have been traditionally designed as passive networks. Then, new technical issues must be addressed, involving both normal and abnormal operating conditions such as short circuits. Photovoltaic systems (PVSs) are among the most diffuse DG and their contributions to the short-circuit operating conditions depend on several factors, such as environmental conditions, PVS inverter control characteristics, self-protection systems, and fault location and type. An analytical model that aims at quickly and accurately analyzing the three-phase short-circuit operating conditions in a distribution system in presence of PVSs is presented in this paper. The model is applied to a typical North American MV network characterized by large penetration of PVSs, investigating the influence of the aforementioned factors.

This chapter focuses on the optimal sizing of BESSs in end-user applications in the frame of time-varying energy pricing structures by adopting a probabilistic approach. More in detail, the proposed procedure focuses on one of the most used time-varying tariff structures (i.e. the ToU tariff) but it can be easily extended to other structures. In this chapter, starting from the procedure proposed, the probabilistic optimal sizing is performed applying the point estimate method (PEM), an algorithm that guarantees accuracy of the results with computational effort significantly lower than that implied by the Monte Carlo procedure.

In this paper, a probabilistic method is proposed to analyze the steady-state operating conditions of an active electrical distribution system with Wind (WD) and Photovoltaic (PV) generation plants. This method takes into account the uncertainties of power load demands and power production from renewable generation systems and combines Monte Carlo simulation techniques and multi-linearized power flow equations. The power flow equations include models of wind turbine and PV generation units and multi-linearization is accomplished by applying a criterion based on the total active power of the system. The method properly extends a probabilistic method proposed in the relevant literature for traditional passive electrical distribution systems to the field of an active electrical distribution system with WD and PV generation units. Numerical applications are presented and discussed with reference to a 17-bus test distribution system characterized by WD and PV systems connected at different busbars. The results obtained with the proposed algorithm are compared with the results obtained using a Monte Carlo simulation algorithm that included non-linear power flow equations.

A larger penetration of plug-in electric vehicle (EV) fleets and of data centres in the microgrids (µGs) is foreseeable in the near future. Their presence and the presence of distributed generation (DG) units represent a challenge for system operators in that they must identify approaches for using these distributed resources that allow them to operate the grid in a more efficient and economical way. With particular reference to EVs and data centres, it must be noted that they are equipped with storage devices that potentially could result in the modification of the daily load profile of µGs by shifting peak demand away from the high-cost periods. This study is focused on the use of data centres and EV aggregators as demand-response resources, and a new model for the operation of a µG that includes DG units, EV fleets and the data centre's storage systems has been proposed. The procedure is based on a non-linear, constrained, optimisation model with the aim of minimising the total cost of energy and simultaneously shaving peak power. The effectiveness of the proposed strategy was demonstrated by means of numerical applications to a low-voltage, test µG.

Demand response (DR) can be very useful for an industrial facility, since it allows noticeable reductions in the electricity bill due to the significant value of energy demand. Although most industrial processes have stringent constraints in terms of hourly active power, DR only becomes attractive when performed with the contemporaneous use of battery energy storage systems (BESSs). When this option is used, an optimal sizing of BESSs is desirable, because the investment costs can be significant. This paper deals with the optimal sizing of a BESS installed in an industrial facility to reduce electricity costs. A four-step procedure, based on Decision Theory, was used to obtain a good solution for the sizing problem, even when facing uncertainties; in fact, we think that the sizing procedure must properly take into account the unavoidable uncertainties introduced by the cost of electricity and the load demands of industrial facilities. Three approaches provided by Decision Theory were applied, and they were based on: (1) the minimization of expected cost; (2) the regret felt by the sizing engineer; and (3) a mix of (1) and (2). The numerical applications performed on an actual industrial facility provided evidence of the effectiveness of the proposed procedure.

Accurate probabilistic forecasts of renewable generation are drivers for operational and management excellence in modern power systems and for the sustainable integration of green energy. The combination of forecasts provided by different individual models may allow increasing the accuracy of predictions; however, in contrast to point forecast combination, for which the simple weighted averaging is often a plausible solution, combining probabilistic forecasts is a much more challenging task. This paper aims at developing a new ensemble method for photovoltaic (PV) power forecasting, which combines the outcomes of three underlying probabilistic models (quantile k-nearest neighbors, quantile regression forests, and quantile regression) through a weighted quantile combination. Due to the challenges in combining probabilistic forecasts, the paper presents different combination strategies; the competing strategies are based on unconstrained, constrained, and regularized optimization problems for estimating the weights. The competing strategies are compared to individual forecasts and to several benchmarks, using the data published during the Global Energy Forecasting Competition 2014. Numerical experiments were run in MATLAB and R environments; the results suggest that unconstrained and Least Absolute Shrinkage and Selection Operator (LASSO)-regularized strategies exhibit the best performances for the datasets under study, outperforming the best competitors by 2.5 to 9% of the Pinball Score.

Energy storage is traditionally well established in the form of large scale pumped-hydro systems, but nowadays is finding increased attraction in medium and smaller scale systems. Such expansion is entirely complementary to the forecasted wider integration of intermittent renewable resources in future electrical distribution systems (Smart Grids). This paper is intended to offer a useful tool for analyzing potential advantages of distributed energy storages in Smart Grids with reference to both different possible conceivable regulatory schemes and services to be provided. The Smart Grid Operator is assumed to have the ownership and operation of the energy storage systems, and a new cost-based optimization strategy for their optimal placement, sizing and control is proposed. The need to quantify benefits of both the Smart Grid where the energy storage devices are included and the external interconnected grid is explored. Numerical applications to a Medium Voltage test Smart Grid show the advantages of using storage systems related to different options in terms of incentives and services to be provided.

A new short-term probabilistic forecasting method is proposed to predict the probability density function of the hourly active power generated by a photovoltaic system. Firstly, the probability density function of the hourly clearness index is forecasted making use of a Bayesian auto regressive time series model; the model takes into account the dependence of the solar radiation on some meteorological variables, such as the cloud cover and humidity. Then, a Monte Carlo simulation procedure is used to evaluate the predictive probability density function of the hourly active power by applying the photovoltaic system model to the random sampling of the clearness index distribution. A numerical application demonstrates the effectiveness and advantages of the proposed forecasting method.

The optimal allocation of capacitors in unbalanced distribution systems can be formulated as a mixed integer, non-linear, constrained optimisation problem. Fuzzy-based approaches, simulated annealing, tabu search and genetic algorithms are some of the techniques used for solving the problem in deterministic scenarios. However, distribution systems are probabilistic in nature, leading to inaccurate deterministic solutions. As a result, a probabilistic optimization model is required to take into account the unavoidable uncertainties affecting the problem input data, primarily the load demands. Of the various techniques for the solution of the problem, one of the most frequently used is the genetic algorithm. However, the application of simple genetic algorithms to solve the probabilistic optimization model involves tremendous computational effort. To reduce the computational effort, this paper proposes a new single-objective probabilistic approach based on the use of a micro-genetic algorithm. Two different techniques, one based on the linearised form of the equality constraints of the probabilistic optimisation model and one based on the point estimate method, were tested and compared. The proposed approaches were tested on the IEEE 34-node unbalanced distribution system to demonstrate the effectiveness of the procedures in generating reduced computational efforts and increased accuracy of the results.

Recent advances in power electronic technology for interfacing dispersed energy resources to distribution grids offer potential solutions to several technical and economical problems in distribution networks. In particular, Dispersed Generation (DG) can be used to provide the usual energy service as well as some ancillary services, such as load following, back-up service, and compensation of Power Quality disturbances. In this paper, a fuel cell-based DG system is proposed for providing energy and ancillary services. The novelty of the system is that it can operate with a ‘system strategy’ (aimed at compensating for the disturbances in the whole system or in some privileged areas of the network) thanks to a suitable control technique of the power electronic interfaces. In this way, the benefits of using the dispersed generation system are maximized. Computer simulations were performed on an actual distribution grid to demonstrate the effectiveness of the compensation actions.

This paper deals with the problem of optimal allocation (siting and sizing) of storage resources in unbalanced three-phase low voltage microgrids. The siting and sizing problem is formulated as a mixed, non-linear, constrained optimization problem whose objective function deals with economic issues and whose constraints involve technical limitations of both network and distributed resources. Emphasis is given to the power quality issue with particular attention to unbalance reduction and voltage profile improvement. Technological issues, such as those related to the preservation of batteries’ lifetime, were also taken into account. The planning problem is solved by means of a genetic algorithm which includes an inner algorithm based on sequential quadratic programming. In order to limit the processing time while maintaining reasonable accuracy, the genetic algorithm search space is significantly reduced identifying a subset of candidate buses for the siting of the storage resources. The Inherent Structure Theory of Networks and the Loading Constraints Criterion were used to identify the candidate buses. The proposed method has been applied to a low voltage test network demonstrating the effectiveness of the procedure in terms of computational burden while also preserving the accuracy of the solution.

Some of the most remarkable issues related to interharmonic theory and modeling are presented. Starting from the basic definitions and concepts, attention is first devoted to interharmonic sources. Then, the interharmonic assessment is considered with particular attention to the problem of the frequency resolution and of the computational burden associated with the analysis of periodic steady-state waveforms. Finally, modeling of different kinds of interharmonic sources and the extension of the classical models developed for power system harmonic analysis to include interharmonics are discussed. Numerical results for the issues presented are given with references to case studies constituted by popular schemes of adjustable speed drives.

The new electric system restructuring requires more and more restrictive power quality requirements to be satisfied. The problem of disturbances compensation therefore becomes of noticeable importance, both in terms of device allocation and control strategy. The paper deals with active compensators, whose utilization is rapidly growing in modern power system, whereas power electronic devices play a fundamental role in controlling system behavior. An optimal control strategy for active compensators, particularly useful for distribution companies in a deregulated framework, is proposed with the aim of improving power quality. The proposed strategy is based upon a frequency domain approach for solving a linear quadratic regulator problem, without exceeding compensator rating. The proposed procedure is able to properly consider the buses sensitivity to different power quality disturbances. The methodology relies upon a Kalman filter based estimation technique, which enables an accurate tracking of relevant network state variables, as well as of harmonic disturbances injected into the power system. In the last part of the paper a numerical application with reference to a 18-busbar distribution network is presented, showing the feasibility and the effectiveness of the proposed methodology.

The ac/dc/ac double-stage converter, frequently used nowadays to provide ac adjustable frequency and magnitude voltages in the adjustable-speed drives, consists of a voltage source inverter (VSI) fed by a three-phase diode bridge rectifier; this rectifier generates high line current harmonics in the supply system. This paper presents a complete modelling of the VSI-fed drives, when energized by nonsinusoidal supply voltages, based on the analytical form of the current harmonics injected in the supply system; the equations of the current harmonics are obtained for both the continuous and discontinuous current modes and are derived by Fourier analysis of steady-state current time evolution. The high accuracy of the proposed models is demonstrated by comparison with the results of time-domain simulation. The modelling is useful to study the effects of supply voltage distortions on current harmonics injected in the supply system, both in continuous and discontinuous mode, with a very short computing time.

In the last years there has been a considerable growing interest in connecting generation to distribution systems. Thus, Embedded Generation is predicted to play an increasing role in the future electric systems. For this reason, distribution system engineers should properly take into account its impact in the system studies. On the other hand, power quality has recently become an important concern for utility, facility and consulting engineers since the electric disturbances have significant economic consequences. In this paper a three step procedure, based on Genetic Algorithm and Decision Theory, is applied to obtain the best generation sizing and siting on a medium voltage distribution network, considering in the objective function and in the constraints the power quality disturbances and taking into account the unavoidable uncertainties that the Embedded Generation production introduces. A numerical application to a simple distribution test system gives evidence of the power quality and uncertainty influence.

Voltage stability has become a fundamental issue in the new, liberalized markets due to the fact that the new power systems are approaching more and more the stability limits. Then, several approaches were proposed in the relevant literature to find the critical conditions and the problem was faced also with reference to unbalanced three phase power systems. The unbalances, in fact, can be responsible of more critical stability conditions than in balanced power systems. Continuation power flow and optimal power flows were applied to analyze such conditions. In this paper a new three-phase optimal power flow is proposed that makes use of complementarity constraints to take into account the effect of reactive generation limits on voltage stability in unbalanced power systems. An application is presented on a test system highlighting the feasibility and the goodness of the proposed technique. Both load and line unbalances are taken into account to capture the dependence of voltage stability on the level of unbalances.

Electrical storage systems are a potential solution for some challenges that will face future Smart Grids due to the large number and variety of services they can perform. These services can be further enlarged if an optimal operation of the storage systems is guaranteed. This paper deals with the energy management of battery storage systems in the frame of real time pricing. An optimal control strategy is proposed in order to minimize the electricity bill costs of an industrial facility. Firstly, the optimization model is formulated considering a multi-battery system. Then, two algorithms are applied to solve the problem: the linear programming and the dynamic programming. Numerical applications to an actual industrial facility demonstrate the effectiveness of the proposed procedure and the differences obtained applying linear and dynamic programming algorithms.

Electrical energy storage systems can provide several benefits along the entire value chain of the electrical system. In this paper attention is paid to the end user point of view, with particular reference to industrial customers. An optimal operating strategy is proposed for energy storage systems with the aim of reducing the electricity bill costs sustained by an industrial customer and contemporaneously satisfying technical constraints for the maximization of the storage system efficiency and life cycle. The proposal, which is developed in this paper by means of computer simulations, will be realized in an industrial facility located in the South of Italy in the frame of the GREAT project, a research plan aimed at developing advanced methods and tools for micro-grid applications.

In this paper, we propose a novel scheme that jointly employs sliding-window (SW) Prony and the discrete Fourier transform (DFT) for estimating power-quality indices based on the time-frequency analysis of non-stationary waveforms in power-system disturbances. These indices, recently proposed in the relevant literature, require the separation of the waveform in two parts, i.e., the fundamental component and the disturbance waveform. In the proposed scheme, Prony’s method was applied to calculate only the fundamental component from low-pass, filtered data, while the disturbance waveform is obtained by using DFT. The application of Prony’s method only to the fundamental component reduces the computational effort required by this method significantly and allows the size of the window of the DFT to be set as an integer multiple of the estimated fundamental period, which minimizes the spectral leakage of the DFT. The main advantages of the proposed, new approach include high resolution and accuracy in the estimation of indices and significant reduction of the computational cost. Experiments were conducted and comparisons were made using both synthetic and measured data. The results confirmed the effectiveness and efficiency of the proposed scheme.

This is the companion paper to “Part I: theoretical aspects”. Part I reviews and critically analyses some of the most significant single-objective optimization methodologies proposed for the optimal operation of plug-in electric vehicles (PEVs) operating in Smart Grids. This Part II applies the models presented in Part I to a low voltage test Smart Grid. Analysis of the results highlights the behavior of the considered control strategies in terms of their compliance with both the objective functions and constraints. In the final part of this paper the results are summarized and compared in order to give an useful tool for understanding the more appropriate objectives and constraints to be taken into account for an optimal control of the Smart Grids.