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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 paper deals with the probabilistic design of an end-user microgrid equipped with renewable energy generation and battery energy storage systems. The microgrid is connected to the distribution grid and is able to purchase energy under time of use tariff and to sell energy paid through feed-in tariff. The use of the battery is devoted at (i) increasing the self-consumption and (ii) reducing the cost for energy absorbed by shifting the load demand in the hours of lower energy price. An analytical tool is derived for the optimal sizing of battery energy storage systems accounting for minimization of the total costs incurred by the microgrid owner. The closed form expressions are included within a Monte Carlo simulation so considering uncertainties in load demand and renewable power generation. Though the proposed approach is quite general and can be easily extended to different case studies, the formulation and the results reported in this paper refer to the case of an industrial customer whose demand partially complies with the production of a photovoltaic system.

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.

Nowadays, the development of the hybrid microgrids is mainly addressed towards industrial applications, where different AC and DC typologies of distributed energy resources coexist. In a such context, the management of devices in the hybrid AC/DC microgrid becomes a not-obvious task, that has gained great interest in relevant literature. In this paper, the importance of the optimal management of both active and reactive powers in an hybrid AC/DC microgrid is analyzed, highlighting that, in these applications, the reactive power control is mandatory not only when the microgrid operates in islanding mode, but also in grid-connected mode. Specifically, a comparison between control strategies with and without reactive power management is performed in the hybrid AC/DC microgrid proposed for an actual industrial facility in the southern Italy. Numerical experiments demonstrate the need of utilizing the former strategy than the latter one.

In this paper, we address the problem of the probabilistic steady-state analysis of an electrical distribution system that includes wind and photovoltaic power plants. We propose a new method that takes into account the uncertainties due to the time variations of power load demands and the random nature of solar and wind energy. The new method extends a probabilistic approach proposed in the relevant literature for balanced electrical distribution systems to unbalanced electrical distribution systems, and it also takes into account the correlation among the random input variables. The method is based on Taguchi's orthogonal arrays. Numerical applications based on an IEEE test system provide evidence of the probabilistic performance of the proposed approach. The results obtained with the proposed method are compared with the results obtained using non-linear Monte Carlo simulation and the Point Estimate Method.

This paper deals with the optimal allocation (siting and sizing) of distributed electrical energy storage systems in unbalanced electrical distribution systems. This problem is formulated as a mixed, non-linear, constrained minimization problem, in which the objective function involves economic factors and constraints address the technical limitations of both network and distributed resources. The problem is cumbersome from the computational point of view due to the presence of both constraints of an intertemporal nature and a great number of state variables. In order to guarantee reasonable accuracy-although limiting the computational efforts-a new approach is proposed in this paper: it is based on a Simultaneous Perturbation Stochastic Approximation (SPSA) method and on an innovative inner algorithm, which allows it to quickly carry out the daily scheduling (charging/discharging) of the electrical energy storage systems. The proposed method is applied to a medium voltage (Institute of Electrical and Electronics Engineers) IEEE unbalanced test network, to demonstrate the effectiveness of the procedure in terms of computational effort while preserving the accuracy of the solution. The obtained results are also compared with the results of a Genetic Algorithm and of an exhaustive 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.

Waveform distortions are an important issue in distribution systems. In particular, the assessment of very wide spectra, that include also components in the 2–150 kHz range, has recently become an issue of great interest. This is due to the increasing presence of high-spectral emission devices like end-user devices and distributed generation systems. This study proposed a new sliding-window wavelet-modified estimation of signal parameters by rotational invariance technique (ESPRIT) method, particularly suitable for the spectral analysis of waveforms that have very wide spectra. The method is very accurate and requires reduced computational effort. It can be applied successfully to detect spectral components in the range of 0–150 kHz introduced both by distributed power plants, such as wind and photovoltaic generation systems, and by end-user equipment connected to grids through static converters, such as fluorescent lamps.

Excellence in the planning and operations of power systems largely relies on accurate forecasts of loads. Although load forecasting has been extensively studied over the past several decades, the scientific community has not yet paid much attention to industrial load forecasting. The electricity demand of factories depends on many factors, of which some are uncommon or not as important in the classical load forecasting models. For instance, the scheduled processes and work shifts are very important to forecasting short-term industrial loads. In this paper, we offer some insights into modeling industrial loads. We develop a set of multiple linear regression models for an Italian factory that manufactures transformers. The proposed models outperform two other benchmark models for forecasting industrial loads 24 hours in advance.

This paper details an approach for the optimal scheduling of microgrids, including different distributed resources such as datacenters, electric vehicles, and distributed generation units. Management of both loads and generation systems is considered to be a strategic approach to optimally operate the grid. At this purpose, a multi-objective strategy was formulated, including several objectives that are considered essential for the efficient grid operation. Numerical simulations were performed to test the effectiveness of the proposed approach and the results were compared with those obtained through uncontrolled scenarios.

This paper analyzes the influence of technology uncertainties on the sizing of battery systems. The sizing is based on the minimization of the costs incurred by the end customer and is performed considering demand response applications in the frame of time of use tariffs. The randomness of i) battery round trip efficiency, ii) life time duration, iii) unit costs related to battery capacity, power conversion system, operation and maintenance and replacement is taken into account in order to identify the most convenient solution from an economic and technical point of view. Based on the load requests of actual industrial and residential loads, numerical applications have been performed. The results provided useful information regarding the influence uncertainties have in the choice of a battery energy storage system.

Electric power systems are increasingly influenced by meteorological conditions due the wide penetration of renewable energy plants. In particular, wind speed plays a key role in transmission and distribution systems, as it determines wind power production and it influences line rating; also, extreme values of wind speed (EWS) affect mechanical reliability of wind towers and blades, causing loss of lifetime and damages. Several physical models provide EWS forecasts on global or local scales; however, such models require accurate initial and boundary conditions, and enormous computational effort. Statistical models are good alternatives to achieve accurate forecasts, but they require assumptions on the statistical distribution of EWS in parametric frameworks. This paper proposes an Inverse Burr - Inverse Weibull finite mixture distribution for EWS characterization and its Expectation-Maximization (EM) procedure for parameter estimation. The proposed mixture model is compared to commonly-used EWS distributions. Actual sites are considered to evaluate the goodness of fitting in different, real conditions; the EM procedure is compared to the maximum likelihood estimation. Sensitivity and error analyses are performed to individuate the main features of the proposed model; numerical results confirmed the suitability of the proposed model and of the EM estimation in the most of considered cases.

In the context of modern distribution systems, power quality is recognized as a crucial concern that requires advanced technical solutions in order to guarantee the correct operation of such complex systems. Among the power-quality disturbances, waveform distortions are one of the most important due to their impact on the equipment, and active filters are considered a useful technical solution to this disturbance even more significantly if they are optimally integrated into the grid. This paper addresses the problem of optimal siting and sizing of active filters in a multiconverter distribution systems by adopting a multiobjective approach. The proposed original formulation includes the control strategies of the active compensators among the decision variables and takes into account the various sources of uncertainties which characterize modern distribution systems. A heuristic simplified approach based on a trade-off/risk analysis is proposed to solve the multiobjective optimization problem under uncertainty with the aim of minimizing several conflicting objectives while meeting proper constraints.

In this paper, a comprehensive strategy for the scheduling of unbalanced microgrids is proposed. The microgrids are characterized by the presence of a variety of distributed resources, such as data centers, electric vehicles, and distributed generation systems. The operation strategy is based on the solution of a multi-objective optimization problem, whose objective functions are related to specific services and requirements of the microgrid, such as cost minimization, power quality improvements, and energy savings. Particular attention is paid to the unbalances presence in the microgrid with the aim to outline how the proposed strategy is able to significantly reduce them taking contemporaneously into account other important economic and technical objectives. An analysis of the objectives and the different operational perspectives also is proposed, which allows us to exploit the effectiveness of the multi-objective approach. The results of numerical applications are presented to show the effects of the considered strategy in terms of achievable advantages.

A high penetration of Photovoltaic (PV) systems into power networks can alter the fault currents and negatively impacts on the operation of the protection systems. In this paper, a new analytical model of the fault contribution of a three-phase PV system equipped with a voltage source converter is proposed. Such a model extends the classical steady-state short-circuit analysis to balanced active power networks including PV systems, with the aim to analyze their impact on the breaking capacity of the interrupting devices. The proposed model: (i) takes into account environmental conditions and VSC current limits; (ii) includes the effects of reactive power injections by a detailed representation of different type of VSC control systems; and (iii) can be easily integrated in a software package for power system analysis. The proposed approach is validated by comparing analytical results with time-domain simulations of the IEEE benchmark PV system. Furthermore, it is used to evaluate the impact of a large penetration of PV systems on the fault currents.

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.

This paper deals with the numerical applications performed on real data to validate the short term active load power forecasting method proposed in the companion paper of the same title, Part I. The method proposed in Part I is a hybrid method based on the application of time series model and Bayesian inference on a dataset of load power measurements; it provides probabilistic forecasts for different time horizons and is particularly suitable for risk assessment associated to the management of smart grids. The numerical applications presented in this paper are performed using domestic load measurements taken from an Italian distribution system. The method was tested for different number of loads and time horizons of forecasts; in particular, 15-minutes and 24- to 48- hours lead times were considered. The performances of the proposed method are also evaluated by testing its reliability, sharpness and calibration.

Accurate short-term load forecasting is extremely important for the optimal management of smart grids allowing the increase of energy efficiency and enabling profitable demand response strategies. However, most of industrial and domestic loads are intrinsically affected by uncertainties due to many factors such as devices operational characteristics, time of use, weather conditions and other random effects. Therefore, probabilistic load forecasting is a challenging task and in relevant literature a great interest has been recently developed towards this topic. In this paper, the uncertainties related to the load demand are modeled through different probability density functions and a probabilistic method based on the Bayesian inference and stochastic time series is proposed for the shortterm forecasting of the probability density functions parameters. This paper shows the theoretical aspects of the proposed method and it is a companion paper to a paper of the same title, Part II, in which the numerical applications are reported.

In this paper an optimal strategy is proposed for the real time control of a hybrid microgrid (μG). Hybrid μGs are characterized by the presence of two sections operating in alternating current (AC μG) and in direct current (DC μG), respectively. They include dispatchable and non-dispatchable renewable generation units, battery energy storage systems and controllable loads. These different resources are connected to the AC or DC μGs through static converters that are optimally controlled for the simultaneous improvement of waveform distortions and minimization of the energy costs. In order to show the effectiveness and feasibility of the proposed approach, the control strategy was applied to a hybrid μG derived from the distribution system of an actual industrial facility.

Photovoltaic systems are expected to play a key role in the planning and operation of future distribution systems due to the benefits associated with their use. Unfortunately, a great problem is involved in photovoltaic power utilization, i.e., the unpredictability of the solar source. Thus, many forecasting methods have been developed in order to provide tools with adequate consistency, quality, and value. The methods can provide either deterministic or probabilistic forecasts; the latter seem to be the most appropriate for taking into account the unavoidable uncertainties of the solar source. In this paper, a new probabilistic method based on a competitive ensemble of different base predictors is proposed for the short-term forecasting of photovoltaic power. Three probabilistic methods were selected and trained as base predictors in order to obtain an ensemble of the predictive distribution with optimal characteristics of sharpness and reliability. Numerical applications based on actual data were performed to test the effectiveness of the proposed method with respect to single predictors and to a benchmark method.

The ability to forecast the production of power by photovoltaic(PV) systems accurately and reliably is of major importance for the appropriate management of future electrical distribution systems. Several forecasting methods have been proposed in the relevant literature, and many indices have been used to quantify the quality of the forecasts. The methods can provide either deterministic or probabilistic forecasts; the latter seem to be the most appropriate to take into account the unavoidable uncertainties of PV power production. Similarly, indices were used to quantify the quality of both deterministic and probabilistic forecasting methods, but they usually do not account for the economic consequences of forecasting errors. In this paper, two advanced probabilistic forecasting approaches based on the Bayesian inference method are applied to the short-term forecasting of PV power production. Moreover, new probabilistic indices were proposed with the aim of comparing the probabilistic forecasting methods in such way that the value of the forecast is not included only by the users in their decision-making process; instead, it is partially anticipated by the forecasters in their quality-assessment process. Numerical applications also are presented to provide evidence of the performances of the Bayesian-based approaches and the probabilistic indices that were considered.

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.

This chapter focuses on the optimal operation of plug-in vehicle fleets in a microgrid characterized by the presence of other distributed resources, such as distributed generation units. The possible services that vehicle aggregators can provide in the microgrid are discussed and the control actions to be performed in order to obtain such services while integrating the vehicle aggregator actions with those of the other distributed resources of the grid are outlined. The problems with optimal operation are formulated as single-objective and multi-objective optimization problems, specifying, in both cases, objective functions, equality and inequality constraints. The differences and criticisms of both approaches are extensively analyzed in the chapter, where the two approaches are also implemented and solved with reference to the practical cases.

Power quality (PQ) is an important issue due to the presence of an increasing number of perturbing and susceptible loads in modern power systems. In this context PQ evaluation requires advanced methods of signal processing that should be accurate and fast. In this paper, a new, advanced, parametric method is proposed that guarantees an accurate estimation of waveform distortions with reduced computational efforts. The method consists of a modified version of the well-known, parametric, high-resolution, sliding window estimation of signal parameters by rotational invariance technique (ESPRIT) method. The main benefit of the proposed scheme is that it significantly reduces the computational effort required to analyze waveforms by evaluating the frequencies and the damping factors of the spectral components one time or, at most, only a few times. Moreover, the waveform was appropriately sampled again to increase the accuracy of the results; the sampling frequency was chosen heuristically using information about the characteristics of the waveform of the power system. Experiments were conducted and the results were compared also in synthesis data. The results showed that the proposed scheme was effective and efficient.

Industrial systems are usually characterized by high energy consumption and presence of sensitive loads which require high levels of Power Quality. Based on the grid architecture of an actual Italian industrial facility, this paper proposes the installation of a hybrid AC/DC microgrid. The hybrid microgrid includes dispatchable and non-dispatchable renewable generation units, battery storage systems and controllable loads. An optimization model is formulated to solve the problem of the day-ahead optimal scheduling of the microgrid. The model aims to optimize the operation of dispatchable resources, controllable loads and storage systems minimizing the daily costs of the energy imported from the AC grid and the costs required by the dispatchable generators while satisfying operational constraints such as those related to the production process of the industry facility. Different case studies are investigated in order to show the feasibility and effectiveness of the proposed procedure. © 2015, European Association for the Development of Renewable Energy, Environment and Power Quality (EA4EPQ). All rights reserved.

Microgrids include distributed energy resources, controllable loads, and storage devices, and they can be classified into AC and DC types, depending on the characteristics of the supply voltage. In this paper, an optimal control strategy for a DC microgrid is proposed, and the strategy is aimed at minimizing the daily total energy costs. The DC micro grid can include non-dispatchable generation units (such as photovoltaic power generation) and dispatchable generation units, energy storage systems (batteries), and controllable/not controllable loads. The control strategy is based on a two-step procedure, i.e., (1) the implementation of one day-ahead scheduling and (2) a very short-time predictive control. The day-ahead scheduling is formulated using integer linear programming methodology and is aimed at achieving the optimal scheduling of controllable loads. The very short-time predictive control is based on the solution of a non-linear, multi-period, optimization problem and is aimed at achieving the real-time optimal charging/discharging profile of storage powers and the real-time optimal profile of powers of dispatchable generators thereby minimizing the cost of total daily energy. For both procedures, optimization models were formulated and solved, including technical constraints that guaranteed an adequate lifetime of the storage system. Case studies relative to a DC microgrid obtained by a modification of the actual structure of the electrical power plant of an Italian industrial facility were investigated in order to show the feasibility and the effectiveness of the proposed approach.

Voltage stability (VS) has become a fundamental issue in the new, liberalised 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 recently 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 analyse such conditions. This study deals with VS analysis in unbalanced power systems and proposes a new optimisation model to determine the critical point based on the use of complementarity constraints. In particular, the maximum stability margin is calculated by a single-stage or a multistage procedure that accounts for the relationship between the actual operating point and the maximum loading point. In addition, the multistage maximum stability margin problem is formulated also in a probabilistic framework to account for the uncertainties affecting the input data (e.g. load powers). An application is presented on a test system highlighting the feasibility and the goodness of the proposed technique.

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.

Modern distribution grids are rapidly evolving toward complex systems (Smart Grids) due to the increasing level of penetration of distributed energy systems and information and communication technologies. In this context, Power Quality (PQ) becomes an important concern and advanced technical solutions to PQ problems are needed. The waveform distortions are one of the most important PQ disturbances and active filters are considered an useful technical solution to this disturbance. This paper deals with multi-converter distribution systems and formulates the problem of siting and sizing of active filters as a multi-objective optimization problem. The problem includes also the control strategies of the active compensators among the problem variables. A heuristic simplified approach based on a trade-off analysis is proposed to solve the multi-objective optimization problem with the aim of minimizing several objectives while meeting proper equality and inequality constraints. The proposed approach is applied to a 17-busbars distribution test system giving evidence of its effectiveness

Distribution networks are undergoing radical changes due to the high level of penetration of dispersed generation and storage systems. This trend is strongly modifying the structure as well as the management of distribution networks, which are progressively approaching the new concept of microgrids (MGs). Also, the level of penetration of storage systems for plug-in electric vehicles (PEVs) is increasing significantly due to the significant potential that PEVs have for reducing both emission levels and transportation costs. The inclusion of these vehicles in MGs leads to a series of challenges in grid operation, especially ensuring the provision of services that can improve the operation of distribution networks. This paper deals with MGs, including renewable generation plants and aggregators of PEV fleets connected to the grid through power electronic devices. A multi-objective optimization model is presented for obtaining optimal, coordinated operation of MGs. A multi-objective model was solved using two different methods, i.e., the exponential weighted criterion method and a compromise programming method. Both of these methods appeared to be particularly suitable when computational time is an important issue, as it is in the case of optimal control. The effectiveness of the multi-objective approach was demonstrated with numerical applications to a low-voltage microgrid; other multi-objective model-solving algorithms also were assessed in order to compare their programming complexity and the computational efforts required.

Capacitors and series voltage regulators are used extensively in distribution systems to reduce power losses and improve the voltage profile along the feeders. This paper deals with the problem of contemporaneously choosing optimal locations and sizes for both capacitors and series voltage regulators in three-phase, unbalanced distribution systems. This is a mixed, non-linear, constrained, multi-objective optimization problem that usually is solved in deterministic scenarios. However, distribution systems are stochastic in nature, which can lead to inaccurate deterministic solutions. To take into account the unavoidable uncertainties that affect the input data related to the problem, in this paper, we have formulated and solved the multi-objective optimization problem in probabilistic scenarios. To address the multi-objective optimization problem, algorithms were used in which all the objective functions were combined to form a single function. These algorithms allow us to transform the original multi-objective optimization problem into an equivalent, single-objective, optimization problem, an approach that appeared to be particularly suitable since computational time was an important issue. To further reduce the computational efforts, a linearized form of the equality constraints of the optimization model was used, and a micro-genetic algorithm-based procedure was applied in the solution method.

Several power system problems require solutions in an uncertain environment. According to the relevant literature, expected utility theory (EUT) has been used extensively to solve such problems. However, the application of Prospect Theory (PT) has demonstrated that people deviate from the expected utility maximization because their effective behaviors reflect loss aversion and risk-seeking, reflection effects. The aim of this paper was to compare and critically analyze EUT and PT with the goal of outlining the different behaviors of a “real” decision maker (DM) and an “ideal” DM, with the real DM operating in the frame of PT and the ideal DM operating as EUT describes. The results of using the two different theories were compared by solving three power-system problems in uncertain scenarios.

The ability to forecast photovoltaic (PV) power-production accurately and reliably is of primary importance for the appropriate management of the future distribution systems and for making decisions to satisfy the needs of all the stakeholders of the electricity energy market. Several forecasting methods have been proposed in the relevant literature and many indices have been used to quantify the accuracy of the forecasts. The majority of methods provides deterministic forecasts even though a great interest was recently dealt with probabilistic forecast methods. Similarly, the majority of indices that have been used to quantify the forecasting accuracy refers to deterministic forecasting and does not directly account for the economic consequences of forecasting errors in the framework of competitive electricity markets. In this paper, advanced, more accurate probabilistic indices are proposed: they account directly for the economic consequences of forecasting errors and the uncertainties that characterize the PV power-production. The improved capability of the proposed indices was verified on the PV power-production forecasted by using an advanced probabilistic forecasting method based on a Bayesian Inference approach. Numerical applications, that considered an actual PV plant, also are presented to provide evidence of the forecasting performances of both Bayesian-based approach and probabilistic indices that were considered.

Battery energy storage systems (BESSs) are considered a key device to be introduced to actuate the smart grid paradigm. However, the most critical aspect related to the use of such device is its economic feasibility as it is a still developing technology characterized by high costs and limited life duration. Particularly, the sizing of BESSs must be performed in an optimized way in order to maximize the benefits related to their use. This paper presents a simple and quick closed form procedure for the sizing of BESSs in residential and industrial applications when time-of-use tariff schemes are applied. A sensitivity analysis is also performed to consider different perspectives in terms of life span and future costs.

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.