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The widespread use of distributed energy resources in the future electric distribution systems represents both a challenge and an opportunity for all the Smart Grid operators. Among these resources, plug-in electric vehicles are expected to play a significant role not only for the economic and environmental benefits they involve but also for the ancillary services they can provide to the supplying grid. This chapter deals with real-time operation of unbalanced microgrids including plug-in electric vehicles. The operation is achieved by means of an optimal control strategy aimed at minimizing the costs sustained for the energy provision while meeting various technical constraints. Among the technical constraints, the optimal control allows guaranteeing the satisfaction of power quality requirements such as the containment of slow voltage variations and the unbalance factors. Case studies are investigated in order to show the feasibility and the effectiveness of the proposed approach.

This paper deals with the use of distributed energy storage systems in microgrids, and proposes a planning method which accounts for the uncertainties of load and distributed generation. Objectives of the planning method are the reduction of the energy costs, while providing the supply of ancillary services as a technical support to the network. The energy costs are evaluated considering a hourly varying pricing scheme and optimizing the storage systems charging/discharging stages. The technical support is devoted to the restraint of bus voltage amplitudes, and of network components' currents/powers within admissible ranges. The input data uncertainties are managed through three decision theory criteria (i.e., the minimization of expected costs; an approach based on the weighted regret felt by the design engineer; and a stability area criterion), which allow considering the multiple design alternatives and futures (i.e., possible values of uncertain input data) in an accurate and feasible way. The design alternatives refer to the size and location of the distributed storage systems, while each future is associated with a different level of load demand and power production of distributed generation over the whole planning period. The results of numerical applications are reported and discussed with reference to a Cigré test network.

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.

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.

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.

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.

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 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.

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.

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.

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

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.