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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.

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.

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.

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.

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.

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.

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.

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

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.

Plug-in Electric Vehicles (PEVs) could become remarkable resources for improving quality and reliability of future grids, if adequate control of their onboard storage systems is provided. Hence, the problem of PEVs optimal control strategies is a crucial topic of research in modern power system operation. This is particularly true in the Smart Grid (SG) context, where the presence of bi-directional communications among distributed energy resources and customers makes it possible to obtain an optimized operation of the grid. In this paper a critical overview of some of the most significant single-objective optimization methodologies proposed for the optimal operation of PEVs in electrical distribution networks is presented in order to verify their feasibility in the context of SGs. These methodologies allow the performance of several services, which aim to meet both needs internal to the SG (for example, the losses minimization or the minimization of average voltage deviations) and external to it (for example, ancillary services to the electrical system to whom the SG is interconnected). This paper reports the theoretical aspects of the optimization models, whereas the companion paper “Part II: numerical applications to vehicle fleets” proposes the results of the analysed models.

In recent years, modern distribution networks are rapidly evolving toward the new concept of Smart Grid (SG) due to the increasing level of penetration of distributed generation (DG) units, storage systems and information and communication technologies. In the framework of low voltage distribution systems, SGs based on either AC or DC grids have been proposed and compared in the technical literature, evidencing their advantages and drawbacks. Only recently, hybrid SGs that include both DC and AC grids have been proposed with the aim of optimizing the whole system behavior. In this paper, an innovative hybrid low voltage SG that includes properly controlled AC and DC grids is analyzed. The DC grids - including storage systems and interconnected to the AC grid through AC/DC PWM-controlled static converters - highly contribute to improve both quality and continuity of supply to AC and DC sensitive loads. The AC grid is optimally controlled to perform several system services (i.e., minimize power losses and optimize voltage profiles at fundamental frequency and at harmonic frequencies). Time domain simulations on a 30-node low voltage hybrid SG are presented and discussed to evidence the effectiveness of the considered solution.

In this paper, the point estimate method is applied to account for the uncertainties that affect the evaluation of the steady state operating conditions of an unbalanced three-phase power system in the presence of wind farms. The accuracy of the proposed technique is tested on the three-phase unbalanced IEEE 34-bus test system adequately modified to take into account the presence of wind farms; the results obtained by applying the Monte Carlo simulation are assumed as a reference. The main conclusion is that the point estimate method gives good solutions in terms of accuracy and computational efforts.

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.

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.

Discrete Fourier Transform (DFT) is recommended for waveform distortion assessment in IEC Standard framework. One of the most important problems for DFT application is the spectral leakage. It was shown in the literature that the most remarkable errors due to leakage problems in power system waveform assessment are mainly due to the errors in synchronizing fundamental and harmonics. In this paper, a new two-steps signal processing technique based on ESPRIT and DFT methods is proposed. This technique guarantees a fast and accurate synchronization of fundamental and harmonics; it also allows to obtain an accurate evaluation of the low frequency interharmonics. The proposed method is applied on test waveforms in order to demonstrate its effectiveness in terms of reduced computational efforts and accuracy of the results.

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.

The voltage continuity and quality are two different aspects of the quality on the electrical supply. Their regulation is of great importance due to the economical consequences associated with the presence of the disturbances in the electrical power systems. While voltage continuity has been regulated in several countries for his undouble importance, the voltage quality has only recently become an important concern for utilities, customers and consulting engineers. Actually, a fervid international debate is underway to find the best economic regulatory mechanism to improve the voltage quality. This paper illustrates some mechanisms of economic voltage quality regulation proposed in the most recent international literature.

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 stochastic prediction of voltage dips due to faults in transmission and distribution systems can be effected applying the Fault Position Method. Also assuming deterministic operating condition before the faults and pre-assigned failure rates of the faulted components, this method may require severe computational efforts in case of high dimension power systems. In the paper a Monte Carlo simulation procedure which properly include the Fault Position Method is proposed to evaluate the voltage dip indices taking into account also the randomness of the pre-fault conditions and the uncertainties that can characterize the failure rate values. To reduce the computational efforts, a complete matrix formulation of the Fault Position Method is used. Several numerical applications are presented and discussed with reference to a test system.

Probabilistic and time-frequency aspects of time varying waveforms in power systems are considered with reference to DC arc furnaces and adjustable speed drives using line commutated inverters. These loads are characterized by waveform whose spectral components are time-varying in amplitude and frequency. The problems of understanding and assessing their waveform distortion is taken into account. Some considerations on the most adequate techniques for the spectral component representation and calculation are effected

DC arc furnaces are more and more applied in large industrial power systems. They represent a source of perturbations for the feeding system, in dependence on the available short-circuit power at the point of common coupling and on the arc furnace rating. This paper deals with the problem of the compensation of perturbations due to DC arc furnaces behavior; in particular, the application of a new device, the decoupled compensator, is investigated. The study is performed with reference to a typical DC arc furnace and by using computer simulations developed by means of power system blockset, that is a tool of Matlab. Waveform distortions and voltage fluctuations indices are assessed in presence and in absence of the compensation device.

Some techniques are presented to obtain the probability density functions of phase-voltages in an unbalanced three-phase power system. The techniques are based on the Monte Carlo simulation applied to the non-linear and linear three-phase load flow equations, on convolution process and on the Pearson distributions. These methods are compared in terms of time execution and accuracy in the evaluation of phase-voltage and unbalance factor probability density functions and in particular regarding their 95/sup th/ percentiles, being these quantities the statistical measures of greatest interest in many international standards for power quality. Several numerical applications are presented and discussed with reference to the three phase unbalanced IEEE 13-bus distribution test system.

The necessity for flexible electric systems, changing regulatory and economic scenarios, energy savings and environmental impact are providing impetus to the development of distributed generation, which is predicted to play an increasing role in the future electric power system; with so much new distributed generation (DG) being installed, it is critical that the power system impacts be assessed accurately so that DG can be applied in a manner that avoids causing degradation of power quality, reliability and control of the utility system. Considering that uncertainties on DG power production are very relevant and different scenarios have to be taken into consideration, traditional deterministic planning techniques should not be used to take the right decisions. In this paper a three step procedure, based on genetic algorithms and decision theory, is applied to establish the best distributed generation siting and sizing on an MV distribution network, considering technical constraints, like feeder capacity limits, feeder voltage profile and three-phase short circuit currents in the network nodes. In the last part of the paper the procedure is applied to an actual distribution network.

This paper describes a new probabilistic method for harmonic analysis of multiconverter power systems which allows the evaluation of the percentiles of the voltage and current harmonics, that are the probabilistic quantities of interest in the most recent international recommendations or standards. In order to reduce the computational efforts, the proposed method firstly linearizes the well known nonlinear equation system describing the steady state behavior of multiconverter power systems and then calculates the mean and other moments of the voltage and current harmonic probability density functions: finally, the percentiles of interest are obtained applying the Pearson distributions, which require the knowledge of only the first four moments of the probability density functions. Numerical applications to a test system are also presented and discussed to demonstrate accuracy and speed of the proposed method.

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.

The increasing presence of current and voltage harmonics in distribution and transmission systems is well known. The harmonics are due to the wide-spread use of nonlinear loads both for efficient energy utilization in residential, commercial and industrial areas and for increasing the flexibility of power systems; they can seriously damage the system components and operation. Over the past several years electric utilities have experienced and research groups have confirmed the nondeterministic nature of harmonics, due to continual changes in system configurations, in linear load demands and in operating modes of nonlinear loads. Taking into account the time-varying nature of harmonics, it is most useful to introduce random variables and to apply probabilistic techniques of analysis.

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. >

The deregulated market requires a great deal of attention to satisfy reliability, security and optimisation objectives. As is well known, the voltage stability problem may become more and more frequent in this new scenario. Various techniques have been proposed in order to incorporate voltage stability aspects into the classical analysis methods of power systems. However, some technical problems, such as unbalances typical of distribution or transmission systems, require suitable formulations in order to derive critical conditions and their dependence on interest parameters. Hence, a three-phase formulation arises in order to characterise properly the inability of unbalanced power systems to meet heavy load demand. More specifically, a three-phase constrained optimal power flow is proposed in which the load demand at the assigned bus is maximised, simultaneously satisfying power balance equations and various technical constraints. An application is presented with reference to the IEEE 13-bus test system, which highlights the feasibility and the goodness of the proposed technique. Sensitivity analyses are performed in order to capture the dependence of voltage stability on the level of unbalance.

Passive and active filters have traditionally been used to reduce harmonics in power systems. Only recently combined systems of shunt passive and active filters have been proposed in order to overcome the technical problems of passive filters and to reduce the costs of active ones. The paper tries to overcome some drawbacks of a combined filtering system (modified high-pass filter) which appeared in literature. In particular, improvements in the system structure and in the steady-state design methodology are proposed to obtain a filtering system with both satisfactory compensation characteristics and low costs. Finally, numerical applications are discussed considering a test case.

This is a companion paper to a paper of the same title, Part I, in which the theoretical aspects of some spectrum estimation methods for analysis of nonstationary voltages and currents in power systems with nonlinear loads are analysed. In particular, the Prony model and rootMusic method are taken into account. In this work, numerical applications of the methods presented in Part I are discussed, in order to illustrate their implementation problems and practical applications. To investigate the methods, several experiments were performed using nonstationary voltage and current waveforms in a supply system of a DC arc furnace. For comparison, similar experiments were repeated using the short-time Fourier transform. The comparison proved the effectiveness of the new methods; however, their computational efforts can be much more complex. Conclusions and recommendations are made concerning the framework of each method.

The problem of voltage disturbance compensation in an industrial power system is considered. Reference is made to a case-study where a transformer feeds an AC/DC boost power converter, a capacitor VAr compensator and a balanced AC load. The transformer supplying voltages are supposed to be affected by flicker, slow variations and unbalance. The proposed perturbation compensation consists in suitably controlling the boost power converter which so acts as both a rectifier and static VAr compensator. The power converter sizing is discussed and the controller design presented. The effectiveness of the proposed compensation is shown via simulations obtained by means of the SIMULINK implementation of the power system dynamic model.

The inherent structure theory of networks, already applied in the literature at the fundamental frequency to a variety of planning problems, is extended to the field of power system harmonics. In the context of this theory, the harmonic admittance matrices are reformulated in terms of their eigenvalues and eigenvectors, showing that these expansions can be useful to create a framework in which the power system response to harmonic disturbances can be better understood. After the presentation of the theoretical background, some power system harmonic problems are tackled to show possible applications of this theory. Numerical experiments on a 17-busbar distribution system give evidence of the significance of application to the field of power system harmonics.

Representation of signals in time and frequency domain has been of interest in power systems for many years, especially in the case of nonstationary signals. Standard tools of waveform distortion analysis are based on the Fourier transform while only recently the Prony and rootMusic methods were tested for this purpose. However, these methods show a strong sensitivity to the number of spectral components when applied to evaluate waveform distortion indices. This paper investigates this problem in order to evidence their optimal number. Numerical simulations on test waveforms and on DC arc furnace current waveforms allow to point out the most suitable choices.