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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.

Photovoltaic systems (PVSs) are among the most diffuse Distributed Generators based on renewable energy sources. PVSs contribute to the short-circuit currents during a fault, modifying the short-circuit capacity of the distribution systems. Then, the contribution of PVSs to the fault current must be adequately modeled to extend the traditional short-circuit analysis to distribution networks with PVSs. In this paper an analytical model based on the phase-coordinates approach is proposed to evaluate the fault contributions of three-phase PVSs connected to unbalanced distribution networks in presence of symmetrical and asymmetrical shunt short-circuits, with and without fault impedance. The model of the PVS takes into account the environmental conditions, the inverter control system, the maximum current that can flow through the inverter switching devices, the filter, the interface transformer and the self-protections imposed by the Standard IEEE 1547. Both a first cycles and a steady-state model of the PVS are developed accounting for inverter control systems equipped with VAr or LVRT control schemes or inverter control system without reactive power regulation. The model of the PVS is applied to a typical North American MV network and the results of the proposed approach are compared with time-domain simulations.

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.

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.

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.

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.

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.

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.

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.

In this paper the authors are to be commended for the significant contribution in the area of wind power prediction. The methodology presented allows the power production calculation through a two-step procedure: in the first step, the wind direction and velocity are predicted some minutes ahead, and then, in the second step, the power output is calculated using power curves direction-dependent. The authors comments on a method for short-term wind power prediction with multiple observation points are appreciated.

This paper proposes a novel scheme that jointly employs a sliding-window ESPRIT and DFT for estimating harmonic and interharmonic components in power system disturbance data. In the proposed scheme, separate stages are utilized to estimate the voltage fundamental component, harmonics and interharmonics. This includes the estimation of the fundamental component from lowpass filtered data using a sliding-window ESPRIT, of harmonics from a sliding-window DFT with a synchronized window, and of interharmonics from the residuals by applying the sliding-window ESPRIT. Main advantages of the approach include high resolution and accuracy in parameter estimation and significantly reduced computational cost. Experiments and comparisons are made on both synthetic and measurement data. Results have shown the effectiveness and efficiency of the proposed scheme.

The problem of developing a definition that adequately assesses power-quality (PQ) levels in the presence of distributed generation (DG) is addressed by using proper probabilistic indices for distribution networks. In the planning of new DG installations, these indices take the variation of PQ level into account and use weighting functions properly. They are useful in quantifying the impact of the installation of DG units because they can consider several PQ disturbances simultaneously. Also, they indicate how each PQ disturbance may affect the decision concerning the installation of DG units. Several tests on real distribution networks were performed and discussed in order to show the usefulness of these indices in evidencing the impact of DG on PQ levels. The analysis of the electrical distribution systems on the basis of the considered indices is valuable also to help decide the best allocation and size of distributed generators.

The paper deals with energy storage systems applications in Smart Grids. Several services can be performed thanks to the energy storage systems use, with objectives aimed at meeting needs internal or external to the Smart Grid. Optimal nonlinear constrained problems can be formulated and properly solved in order to perform the services in the best economical and technical way. In this paper, optimal control strategies are proposed in order to allow the Smart Grid to minimize internal losses and to sell energy and ancillary services during high power prices periods. The procedure involves the formulation of optimal power flow problems; proper objective functions and constraints are imposed to satisfying the services that have to be carried out. A numerical application on a 30-bus low voltage Smart Grid shows the effectiveness of the proposed procedure.

Distribution networks are undergoing radical changes due to the high level of penetration of dispersed generation. Dispersed generation systems require particular attention due to their incorporation of uncertain energy sources, such as wind farms, and due to the impacts that such sources have on the planning and operation of distribution networks. In particular, the foreseeable, extensive use of wind turbine generator units in the future requires that distribution system engineers properly account for their impacts on the system. Many new technical considerations must be addressed, including protection coordination, steady-state analysis, and power quality issues. This paper deals with the very short-term, steady-state analysis of a distribution system with wind farms, for which the time horizon of interest ranges from one hour to a few hours ahead. Several wind-forecasting methods are presented in order to obtain reliable input data for the steady-state analysis. Both deterministic and probabilistic methods were considered and used in performing deterministic and probabilistic load-flow analyses. Numerical applications on a 17-bus, medium-voltage, electrical distribution system with various wind farms connected at different busbars are presented and discussed.

Genetic algorithms (GAs) are widely used for optimal allocation of capacitors in distribution systems. When dealing with large-scale systems, such as in case of unbalanced multi-converter distribution systems, these algorithms can require significant computational efforts, which reduce their effectiveness. In order to reduce processing time for GAs and simultaneously maintain adequate levels of accuracy, methods based on the reduction of the search space of GAs or based on micro-genetic algorithms have been proposed. These methods generally guarantee good solutions with acceptable levels of computational effort. In this paper, some fast, GA-based methods are compared and applied for solving the problem of optimal sizing and siting of capacitors in unbalanced multi-converter distribution systems. The algorithms have been implemented and tested on the unbalanced IEEE 34-bus test distribution system, and their performances have been compared with the performance of the simple genetic algorithm technique.

This paper applies the point estimate method to account for the uncertainties that affect the evaluation of the steady state operating condition of an unbalanced three-phase power system. Moreover, since the point estimate method requires that the input random variables are uncorrelated, a suitable adjustment to take into account the correlation is applied. Different point estimate schemes (2m, 2m + 1 and 4m + 1 schemes) are presented and tested. The accuracy of the proposed techniques is tested on a three-phase unbalanced IEEE 34-bus test system; the results obtained applying the Monte Carlo simulation are assumed as reference . Both correlated and uncorrelated input random variables are considered, and multimodal probability density functions are tested. The conclusion is that the 2m + 1 scheme gives the best solution in terms of accuracy and computational efforts; in the case of correlated input random variables, an adequate procedure to take into account the correlation must be applied.

– An electrical distribution system with several dispersed generation (DG) units interconnected to the AC grid through PWM static converters is considered. The DG units can provide both energy and system ancillary services (e.g. voltage regulation, voltage harmonic distortion and unbalance compensation). The DG unit converters are coordinated through a centralized control system that provides in real time the reference signals to the control systems of the DG static converters allowing them to provide the aforementioned services. The centralized control system calculates the reference signals using an optimization procedure whose inputs are measurements from the distribution network busbars and whose outputs are the reference signals; thus, the compensation action is depending on the unavoidable time delays introduced in the whole process by data acquisition, digital processing and data communication. With particular reference to the waveform distortion compensation, the paper proposes a new procedure to compensate them. Time domain simulations on an actual distribution system are reported in order to analyze the delay effects and show the effectiveness of the proposed compensation procedure.

The presence of the new liberalized markets has increased the interest in power-quality (PQ) disturbances due to their economic effect. In particular, in the case of disturbances caused by a single event (such as a capacitor switching or voltage sag), the waveform assessment can be difficult due to the rapid variations in waveform spectral component characteristics; these difficulties require a suitable choice of signal-processing techniques for spectral analysis and, in particular, the resort to time-frequency representations. In this paper, the adaptive Prony method is proposed to calculate PQ indices based on a time-frequency analysis of waveforms. Numerical applications on a simulated transient due to capacitor switching, a measured voltage sag, and a test waveform are also presented and discussed in order to investigate the validity of the proposed method.

The increasing penetration of dispersed generation (DG) influences the power quality (PQ) levels in the distribution networks. Then, an accurate assessment of PQ disturbances in presence of DG is needed and adequate probabilistic indices should be adopted to properly quantify the random nature of the disturbances. In this paper, a tool for the calculation of slow voltage variations, waveform distortions, unbalances, voltage fluctuations and voltage sag probabilistic indices has been developed by using DigSilent Power Factory software. Numerical applications are performed on a 120-bus distribution network whose DG units are wind generators and gas turbine units.

Electrical power system robustness is defined as the intrinsic capacity of an electrical power system to maintain assigned disturbance levels when external conditions change. This paper compares two methods for estimating voltage dip severity: the critical distance method and the fault position method. Their differences are not linked to the type of network but to the type of results which we are searching for. This paper proposes a graphical color visualization of the during fault voltage matrices that immediately correlates dip severity with colors defined by a proper scale. New robustness indices are also proposed to synthesize bus performance in terms of affected and exposed areas. Numerical applications refer to real transmission and real distribution systems.

The International Electrotechnical Commission (IEC) standards characterize the waveform distortions in power systems with the amplitudes of harmonic and interharmonic groups and subgroups. These groups/subgroups utilize the waveform spectral components obtained from a fixed frequency-resolution discrete Fourier transform (DFT). Using the IEC standards allows for a compromise among the different goals, such as the needs for accuracy, simplification, and unification. In some cases, however, the power-system waveforms are characterized by spectral components that the DFT cannot capture with enough accuracy due to the fixed frequency resolution and/or the spectral leakage phenomenon. This paper investigates the possibility of a group/subgroup evaluation using the following advanced spectrum estimation methods: adaptive Prony, estimation of signal parameters via rotational invariance techniques, and root multiple-signal classification (MUSIC). These adaptive methods use variable lengths of time windows of analysis to ensure the best fit of the waveforms; they are not characterized by the fixed frequency resolution and do not suffer from the spectral leakage phenomenon. This paper also presents the results of the applications of these methods to three test waveforms, to current and voltage waveforms obtained from simulations of a real DC arc-furnace plant, and to waveforms measured at the point of common coupling of the low-voltage network supplying a high-performance laser printer.

Several transmission and distribution systems are known to have unbalanced lines and line sections carrying a mixture of single, double, and three-phase loads; moreover, their steady-state conditions are affected by unavoidable uncertainties that require to analyze these systems with probabilistic approaches. In this article, a probabilistic three-phase load flow using a multi-linear simulation algorithm is proposed. The method properly extends to the field of unbalanced systems a probabilistic method proposed for balanced systems. Numerical examples on the three-phase unbalanced IEEE 13-bus and 34-bus distribution test systems are provided and discussed to illustrate the application of the proposed method. The results obtained with the proposed algorithm are compared with the ones obtained using a Monte Carlo simulation algorithm, which includes the non linear three-phase load flow equations. Copyright © 2006 John Wiley & Sons, Ltd.

A primary problem in waveform distortion assessment in power systems is to examine ways to reduce the effects of spectral leakage. In the framework of DFT approaches, line frequency synchronization techniques or algorithms to compensate for desynchronization are necessary; alternative approaches such as those based on the Prony and ESPRIT methods are not sensitive to desynchronization, but they often require significant computational burden. In this paper, the signal processing aspects of the problem are considered; different proposals by the same authors regarding DFT-, Prony-, and ESPRIT-based advanced methods are reviewed and compared in terms of their accuracy and computational efforts. The results of several numerical experiments are reported and analysed; some of them are in accordance with IEC Standards, while others use more open scenarios.

The method of fault position is useful for characterising power-system performance in the presence of voltage dips due to faults. It is based on short-circuit simulations repeated for all the system nodes and for many points along the system lines: fault voltages that are below a preset threshold are the required voltage dips. These dips are stored in so-called dip matrices which contain only the dips in all the system nodes when faults occur at points along the lines. The paper proposes a new compact analytical formulation of dip matrices for balanced and unbalanced faults in terms of bidimensional vector relations and for site- and system-voltage dip indexes. Compact formulations are very useful tools when several sensitivity analyses have to be conducted to estimate variation of site- and system-voltage dip indexes in relation to possible reinforcement and/or compensation devices. Graphical presentation of dip matrices is also proposed as a valuable tool to ascertain the critical area for system performance. Numerical applications to an actual transmission system are presented to demonstrate the easy applicability of the model.

Distribution System Operators have the duty of managing the distribution system safely and efficiently. Distribution revenues are generally based on asset value but revenue systems based to some extent on network performance (e.g. on the level of losses or reliability) are becoming common in many countries. Thus the distribution planner has to maximise the profit of the investments for the system development and to improve the performance of the system as well. In many case the goals are conflicting and multiobjective planning criteria may be adopted to reduce network costs and investments and to maximise some specific performance (e.g. network reliability). Furthermore, with multiobjective programming the distribution planner has the possibility of choosing a trade-off solution in a set of acceptable solutions by applying criteria to minimise risks in uncertain scenarios. These features are particularly useful whether, according to the EU directive EU/2003/54, Embedded Generation (EG) and DSM are considered as possible planning alternatives to be compared with more traditional development actions in the search for the best solution to planning problems. In this context, a methodology is presented based on multiobjective programming and decision theory which helps the decision maker to find the best development plan for the system by using the EG as a development option and by explicitly managing risks and uncertainties. In particular, the proposed methodology solves the problem of maximising the network performance by optimising some power quality indicators, like voltage quality and harmonic distortion, and by minimising the network costs (e.g. energy losses or upgrade investments) with an optimised use of EG. For this reason, the problem of the optimal sizing and siting of EG has been reformulated as a constrained, multiobjective, and nondifferentiable optimisation problem. The main idea is to apply a double trade-off procedure: the first trade-off, by means of a multiobjective /spl epsiv/-constrained technique, allows a wide family of good EG siting and sizing solutions for all the scenarios considered (e.g. associated to a different set of wind speed at all the possible locations); the second one allows isolating the most robust solutions. In this way the planner is completely free to drive the optimisation in a certain direction without loosing objectivity and generality. Simulation results obtained by using the proposed procedure on a test system demonstrate that alternatives disregarded by the decision theory application can result the most interesting ones.

DC arc furnaces are more and more applied in large industrial systems and represent one of the major sources of perturbations for the feeding system. This paper deals with the problem of the dc arc modeling using three well-known chaotic attractors (Ro/spl uml/ssler, Chua, and Lorenz attractors). A new tuning procedure is adopted to determine the most adequate parameters of the attractors to model the dc arc furnace. Waveform distortions and voltage fluctuations indexes are calculated from the simulation results of a whole existing plant and compared with measured data. The proposed models of dc arc furnace can be used to assess the impact in terms of power quality of the dc arc furnace when planning new plants or evaluating the performances of compensating devices.

In designing a distribution system, engineers have to choose optimal solutions under environmental uncertainty; in most cases, among the uncertainties the ones deriving from the presence of nonlinear loads must be included. Under these conditions, the Decision Theory appears to be a valuable tool for solving distribution design problems. This paper considers three approaches based on the Decision Theory for the economical sizing of medium voltage distribution electrical lines under uncertainty, paying particular attention to harmonics due to nonlinear load presence. In the last part of the paper the implementation and practical application of the sizing procedures are discussed and compared in some case studies.

There is an increasing interest in standards and technical literature on the probabilistic characterisation of voltage and current harmonics in multiconvertor power systems. Characterisation requires the expression of input data of the harmonic penetration modelling by random variables and application of probabilistic techniques of analysis. A probabilistic method is described for harmonic analysis of a multiconvertor power system which takes into account the interactions between the supply voltage distortions and the converter current harmonics. To reduce computational effort, the proposed method linearises around an expected value region the nonlinear equation describing the system steady-state behaviour. Consequently it offers a faster solution than the one based on probabilistic iterative methods which need Monte Carlo simulation procedures. Numerical applications to a test system are presented and discussed to demonstrate the accuracy and speed of the proposed method.

In actual systems unavoidable uncertainties affect the steady-state operating conditions of a power system: these uncertainties are mainly due to changes of load demands and of generation system. Taking into account the uncertainties, it is most useful to introduce random variable and to apply probabilistic techniques of analysis. Up to now probabilistic power flows neglect the unbalances of the loads and of the other components and consider adequate single-phase model of the whole power system. In this paper the probabilistic power flow is extended to the three-phase field to evaluate the uncertainties which affect the steady-state operating conditions of an unbalanced power system. Both Monte Carlo procedure and a linearized form are proposed. A numerical application to a test system is also discussed.

The most adequate way to take into account the uncertainties which affect the modelling of harmonic penetration is to express the input data by random variables and to apply probabilistic techniques of analysis. In this paper a probabilistic method is proposed for assessing harmonic distortion levels in power systems. This method transfers to the field of probabilistics a deterministic iterative procedure which is extremely useful for analysing multiconvertor systems. The proposed method, called the 'probabilistic iterative harmonic method', employs a Monte Carlo simulation technique. A numerical application to a test system is also discussed.

Battery storage plants can be interfaced to electric power systems by AC/DC line-commutated converters, whose behavior is strongly influenced by AC and DC side interactions, and which can work in nonideal conditions such as those arising from voltage harmonics and imbalances. Mathematical models of battery storage plants with conventionally and nonconventionally controlled line-commutated converters are presented. The aim is to carry out a complete harmonic analysis in steady-state nonideal conditions. The models, which include the DC side of the converter, can be directly employed in an iterative harmonic analysis of a power system with converters. Numerical simulation results are discussed. >

Harmonic bursts are short-duration waveform distortions which result from the sudden variations in nonlinear loads; they often cause damage to common power system components. A probabilistic model is proposed that describes these disturbances in terms of suitable stochastic processes. The use of this model results in indices that can be used to characterise the system state. The indices are based on appropriate mean values of random functions which measure the quality degradation in terms of the occurrence of disturbance levels higher than a fixed value. They are particularly suited to the characterisation of the risk related to the severe burst occurrences and can allow a suitable prediction of system behaviour over time. A numerical application is presented to illustrate the physical meaning of these indices. The key feature of the proposed model is that it can be used for both burst amplitude and duration characterisation.