New High efficiency models (H) for generation of synthetic time series of correlated wind speed (WS) and wind direction (WD) are proposed. They strongly reduce the dimension of a complete Markov Chain model (CM) preserving the number of classes used to discretize WS and WD without ignoring any possible single transition among classes; the states of the CM matrix columns are compacted into a reduced number of macro-states of the H matrix columns, each characterised by a transition probability obtained summing the transition probabilities of the corresponding compacted CM states. The computational burden and accuracy of the proposed models are compared with those of the CM and of the two simplified models proposed by the authors in previous papers, through numerical experiments based on field data.

This paper presents an extension of the iterative harmonic analysis (IHA) method to assess the propagation of conducted disturbances up to 150 kHz in multi-device systems. This includes a review of IHA and the implications and challenges associated with obtaining accurate network solutions in the 2-150 kHz frequency range. Numerical simulations confirm the applicability of the IHA method to cases of practical interest.

The paper reports on the latest developments associated with the issues and challenges behind the choice of feasible interharmonic limits in distribution networks to be included in future International Standards as discussed within the interharmonic distortion task force (IHD-TF), which is formed in the framework of the Harmonics WG (519) of the IEEE PES T&D Committee.

Electrical power quality is a vital aspect when designing or assessing the operation of all modern power systems and forms an important part of the ongoing energy transition to more efficient and multi-vector systems. However, the ongoing proliferation and changing functionality of power electronic devices, coupled with new grid operating paradigms, such as renewable energy sources integration, microgrids, low-voltage dc distribution networks, and the large-scale integration of electric vehicles, present unique opportunities and challenges for grid operators the world over and require new assessment methods and fresh perspectives on the role of power quality.

The ongoing integration of new power electronic interfaces is increasing emissions in the frequency range between 2 and 150 kHz. This paper considers the emission assessment from 0 to 150 kHz of the switch-mode power factor correction converter topologies widely utilised in modern single-phase loads. First, experimental analysis of a load constituted by a variable switching frequency converter is performed to introduce modelling considerations and proposals for the extended frequency range. Then, a full circuit time domain model of the considered load is developed. Following this, a fast and accurate hybrid modelling technique which simultaneously models the low frequency (f < 2 kHz) and high frequency (2 <= f < 150 kHz) emissions is presented. The proposed hybrid technique can be readily applied to a range of topologies and control algorithms and easily integrated in Iterative Harmonic Analysis for system level analysis of distortion up to 150 kHz.

Electrical power quality is a vital aspect when designing or assessing the operation of all modern power systems and forms an important part of the ongoing energy transition to more efficient and multi-vector systems. However, the ongoing proliferation and changing functionality of power electronic devices, coupled with new grid operating paradigms, such as renewable energy sources integration, microgrids, low-voltage dc distribution networks, and the large-scale integration of electric vehicles, present unique opportunities and challenges for grid operators the world over and require new assessment methods and fresh perspectives on the role of power quality.

This paper presents a power dependent frequency domain model (FDM) of an inverter-driven heat pump (Heating, Ventilation and Air-Conditioning) system for use in power system harmonic analysis. The FDM approach considered is the frequency coupling matrix (FCM) technique. Starting from a previously presented and experimentally validated time domain model (TDM), a detailed study on the impact of the operating power on the input current produces a set of FCMs. It is shown that the power dependent changes in the FCM elements can be accurately approximated using a polynomial function. As a consequence of this result, the power dependent changes are incorporated into the FDM using two different implementations - a (discretized) look-up table and simple (continuous) analytical functions - and compared. Monte Carlo Simulations confirm the ability of the power dependent FDMs to reproduce the input current characteristics of the TDM.

In this paper, a new accurate and comprehensive analytical model of harmonic and interharmonic distortion produced by a single-phase AC/DC diode bridge rectifier (DBR) is presented.Its main and new characteristic is the ability to consider the presence of interharmonics in addition to harmonics in the voltage at the terminals of DBR due to the background distortion.Analytical expressions able to predict DC voltage and AC current either in time or frequency domains are obtained.Several numerical and experimental tests have been performed showing very accurate results.The proposed model presents all the advantages of analytical models (e.g., fastness); therefore, it can be easily integrated with iterative harmonic and interharmonic analysis procedures.Subsequent applications are the possibility to perform parametric analyses and probabilistic studies, to derive harmonically and interharmonically coupled admittance matrices, to help in introducing standard limits for interharmonics.

There are many challenges associated with including interharmonic voltage and current limits in future versions of international Standards (e.g. new IEEE Standard 519). This paper introduces a new definition of interharmonic subgroups based on IEC concept and aimed at overcoming the difficulty of the existing definition in IEC 61000-4-7 in limiting interharmonic distortion. The new subgroups are better able to address the main problem caused by interharmonics, which is light flicker (LF) produced by modern lamp technologies (e.g. LEDs) that cannot be assessed by the IEC Flickermeter (IEC 61000-4-15). A numerical case study is presented to show the effectiveness of the new definitions and, additionally, to test their robustness versus both the desynchronization of the window width used to perform the DFT with system fundamental frequency, and the accuracy requirement of the voltage measurement chain contained in IEC 61000-4-7.

This paper analyzes interpolation and resampling accuracy in the processing of input data for short-term dispatching in large power systems. Simplified pre-processing techniques of different level of approximation are considered. A comprehensive problem definition in proper analytical terms is given together with the expression of different interpolation and resampling techniques. Some numerical experiments on real data, constituted by power demand relative to a part of the Italian electrical transmission system give a quantitative idea of the effects of different possible approximations that can be utilized.

This paper reports the issues and challenges behind the proposal to include interharmonic limits in the next revision of the IEEE Standard 519 as discussed within the interharmonic distortion sub-group formed in the framework of the Harmonics WG (519) of the IEEE PES Transmission & Distribution Committee.

This paper analyses importance of including wind direction (WD) as an additional explanatory variable to the wind speed (WS) for evaluating uncertainty in wind turbine (WT) power output (P-out). Using available measurements of an actual WT, the paper compares a 'two-dimensional' (2D) P-out-WS model with a 'three-dimensional' (3D) P-out-WS-WD model for two general cases: (a) for the specific input WS and WD values (i.e. WS and WD without uncertainties), and (b) for the forecasted input WS and WD values (i.e. WS and WD with uncertainties). In paper, 2D and 3D Gaussian mixture Copula model and vine Copula framework are combined with 2D and 3D Markov chain models, which are used to forecast input WS and WD data with uncertainties. The obtained results show that inclusion of WD will provide noticeable improvement for models with no uncertainties in input WS and WD data, while in the case of forecasted WS and WD data with uncertainties, WS is a much stronger contributor to the total WT P-out uncertainty than WD.

This paper proposes a methodology for improving the representation of component-based models intended for harmonic analysis of generic aggregate LED lamp loads by deriving pdfs of the parameter values. The methodology is illustrated using time-domain current waveform measurements of LED lamps with switch-mode driver circuits (without power factor correction). Following the model derivation, Monte Carlo simulations are used to synthesize generic aggregate LED lamp loads, which are compared against random aggregations of 51 measured lamps. It is demonstrated that a single model with mean values of the parameters, scaled by the total power demand, can be used to simplify the representation of generic aggregate LED lamp loads in large-scale emission assessment studies. Correction factors, which reduce the effect of this simplification in frequency domain applications, are also derived and discussed.

Light emitting diode (LED) lamps are now an established lighting technology, which is becoming prevalent in all load sectors. However, LED lamps are non-linear electrical loads, and their impact on distribution system voltage quality must be evaluated. This paper provides a detailed analysis of time domain and frequency domain approaches for developing and evaluating models suitable for use in large scale steady-state harmonic power flow analysis of the low frequency (LF) emission of LED lamps. The considered approaches are illustrated using four general categories of LED lamps, which have been shown to cover the vast majority of LED lamps currently available on the market. The aim is an in-depth assessment of the ability of commonly applied models to represent the specific design characteristics of different categories of LED lamps. The accuracy of the models is quantitatively evaluated by means of laboratory tests, numerical simulations, and statistical analyses. This provides an example, for each LED lamp category, of comprehensive information about the overall accuracy that can be achieved in the general framework of large scale LF harmonic penetration studies, particularly in the assessment of voltage quality in low voltage networks and their future evolution.

This paper presents a non-homogeneous Markov Chain (MC) model for generation of wind speed (WS) and wind direction (WD) synthetic time series taking into account their daily, monthly and seasonal characteristics. The bivariate nature of the wind process, represented by WS and WD, is modelled by means of an equivalent univariate random variable W, capable of taking into account the statistical dependency existing between WS and WD. A statistical characterization of the wind energy resource at the specific considered site demonstrates the time non-stationarity of the wind process over the year and over the seasons, so twelve monthly transition probability matrices of the variable W are developed. One thousand synthetic time series, each of three years length, are generated in a Monte Carlo framework, demonstrating the excellent performances and overall robustness of the presented model, also using new non-conventional metrics based on Markov transition matrices.

Three-phase electric vehicle (EV) battery chargers are expected to not impact the unbalance of distribution networks; moreover, using active power factor correction topologies they are expected to behave like resistive loads not affecting the system harmonic distortion. In this study, unexpected unbalance characteristics of fundamental and harmonic currents of three-phase EV battery chargers are analysed by means of experimental tests performed on two EV cars of different technology. In order to quantify unbalance and harmonic distortion, proper comprehensive indices, in part developed in this study with specific reference to currents, are utilised. The unbalanced current absorbed even under ideal voltage balanced supply conditions by one of the two EV tested is shown and quantified constituting a real-life case study of endogenous unbalance. Then, the influence of voltage unbalance supply conditions on fundamental and harmonic currents is evaluated by means of a proposed testing procedure, obtaining case studies of exogenous unbalance. The experimental results obtained for the two EVs should be extended to a larger set of cars; anyway, they show the need, before moving forward to full grid EV connection, for utilities and for designers to improve the current standard certification process and the control performances of three-phase battery chargers.

An important operational aspect of modern grids is implementation of a continuous assessment of low-order harmonic emissions from customer installations. While this problem was previously considered in MV systems by the same authors, this paper focuses on the interface between the HV grid and MV distribution systems. The voltage harmonic vector (VHV) approach is utilized to interpret quantities measured at the point of common coupling (PCC), either to check specific assigned emission limits, or to assess customers' installations contributions to the total harmonic distortion. An HV/MV test system is proposed, combining the HV test system previously proposed by CIGRE/CIRED JWG C4/B4.3S with the MV IEEE benchmark test system previously proposed by the IEEE PES TF on “Harmonic Modeling, Simulation and Assessment”. The analysis is conducted by means of iterative harmonic analysis, in order to manage large number of MV-HV components, as well as to deal with the resonances. The presented results illustrate differences when actual and reference impedances of HV system and MV customer installations are used for the analysis, confirming the overall good performance of the VHV approach when applied at the interface between HV and MV systems.

This paper analyses importance of correlating wind speed (WS) and wind direction (WD) for a more confident evaluation of uncertainty in wind turbine (WT) power output (P-out). Using the available measurements of actual WTs, the paper first presents a new model for the analysis of the P-out-WS-WD correlations, based on Gaussian mixture Copula model (GMCM) and vine Copula (i.e., vine-GMCM framework). Afterwards, the paper compares results of a two-dimensional P-out-WS model, previously proposed by some of the authors, with the cross-correlated three-dimensional P-out-WS-WD model, demonstrating that the ranges of variations of P-out can be better modelled by considering not only wind speed, but also wind direction.

This paper is the first part of a two-part series on aggregate load models of residential customers for application in harmonic studies. Part 1 paper builds on the previous work on component-based time-domain models (TDMs) of main types and categories of loads found in residential load sector and presents two aggregate TDMs. The first is based on a detailed modelling of individual loads in the aggregate load mix, where types, numbers and power demands of considered loads are obtained from the available energy consumption statistics, while mean values, ranges and distributions of circuit parameters are determined from the generic TDMs. The second model is based on a much simpler representation of the aggregate load mix, where main load categories and sub-categories are modelled with the corresponding "single-equivalent TDMs", for which circuit parameters are determined by scaling-up generic TDMs to represent power demand of all loads in the same category/subcategory. Particular attention is paid to the harmonic cancellation effects (diversity factors) between loads in the same (sub)category and loads from different (sub)categories, which are evaluated by probabilistic Monte Carlo approach and validated with available network measurements. In Part 2 paper, the presented TDMs are converted in corresponding frequency-domain models, which are expressed in the form of coupled harmonic admittance matrices.

The paper reports an experimental evaluation of LED lamps in terms of admittance Frequency Coupling Matrices (FCM) for harmonic modelling needs. After recalling the FCM approach, a description of the experimental setup used and an LED lamp classification previously proposed by the authors is presented. For each of the four lamp types identified, some harmonic fingerprint plots are shown to introduce the admittance characteristics. More detailed analysis of the characteristics is performed using the tensor representation of the FCM, which compares characteristics between the different lamp types and also between different lamps of the same type. It is shown that this approach can identify characteristics of different types of lamps for modelling purposes.