This paper presents a review with a concise description and analysis of the fundamentals, characteristics, analytical details, merits, and drawbacks associated with existing methods in frequency and time domain for harmonic analysis in practical power networks. The description and analysis are centered on methods developed in the harmonic domain, hybrid frequency-time domain, and time domain, respectively. Validation of the reviewed methods for harmonic analysis, against one of the widely accepted digital simulators, such as EMTP, EMTDC, or MATLAB/SIMULINK, is reported in the cited individual contributions.

In this contribution, two voltage-source converter (VSC) models based on Fourier series and hyperbolic tangent function are proposed. The models are described in detail. The proposed models can be used for fast simulation in the time domain of power-electronic devices based on sinusoidal pulse-width modulation VSCs; the undesirable error introduced by the high rates in the commutation instants are removed; even though the harmonic distortion coming from the converter is taken into account. The switching instants in the Fourier model are approximated in a closed form, and an iterative algorithm based on the Newton-Raphson method is developed for the exact calculation of the switching instants. The hyperbolic tangent model does not need the calculation of the switching instants as in the case of the Fourier model. The proposed models are validated against the solution obtained with the power system blockset of Simulink and with PSCAD/EMTDC.

Averaged modeling is a commonly used approach used to obtain mathematical representations of VSC-based systems. However, essential characteristics mainly related to the modulation process and the harmonic distortion of the signals are not able to be accurately captured and analyzed. The extended harmonic domain (EHD) has recently been seen as an alternative modeling framework since it allows to consider the harmonic interaction explicitly. However, there is not a clearly established methodology to derive the EHD models in the presence of power electronic switches. This paper presents a generalized methodology based on the switching instants to obtain largesignal EHD models of VSC-based power systems. Three model order reduction approaches are also proposed to address the increased size of the resulting EHD models. Analytic formulas of three modulation techniques: sinusoidal pulse-width modulation (SPWM), third harmonic injection pulse-width modulation (THPWM) and space vector pulse-width modulation (SVPWM) are provided to obtain the open-loop large signal EHD models. A performance assessment of the proposed modeling approach in respect to model size, the computational time and the accuracy is presented based on simulations and experimental case studies. The obtained results show that the resulting EHD models are accurate and reliable, while the memory and computation time are improved with the proposed model order reductions.

Modern power systems face several problems at frequencies above the range of traditional stability studies due to the increasing penetration of power electronic devices. This phenomenon has been recently referred to as electromagnetic transient stability and is a common issue in systems with power electronic converters at any power and voltage level, such as FACTS, HVDC, power electronic interfaces for grid connection of renewable energies, custom power devices for power quality enhancement, among others. The study of power systems stability is usually carried out by simulation tools that represent the power system through phasor models. However, due to the faster dynamics of modern systems, the harmonic interaction among the controllers, the converters, and the electric power components, recent research results suggest that some stability analysis should be conducted with models suitable for wider frequency ranges, e.g., electromagnetic transient models. This paper reviews the use of frequency domain methods to analyze the influence of the modeling approach of passive power components on the results of electromagnetic transient stability studies.

High penetration of wind power plants may have an adverse impact on power systems’ stability by reducing the inertia, and problems like frequency stability could appear due to total inertia in the system being reduced, making the power system more vulnerable to disturbances. However, most recent grid codes include an emulation inertia requirement for wind power plants, because modern wind turbines are capable of providing virtual inertia through power electronic converter controls to improve frequency stability issues. Because of this, it is necessary that the inertia estimation analyze and quantify the impact of the inertia reduction in power systems. In this paper, an implementation of a methodology for the inertia estimation of wind power plants is presented. It is evaluated through synchrophasor measurements obtained from a Real-Time Digital Simulator (RTDS) implementation, using industrial Phasor Measurement Units (PMUs). This methodology is based on the swing equation. Furthermore, a comparison of the results obtained between two professional tools RSCAD and DIgSILENT PowerFactory is performed, in order to evaluate the accuracy and the robustness of the methodology. This methodology is applied for the inertia estimation of an equivalent of the southeast zone of the Mexican power system, where there is a large-scale penetration of wind power plants. The results demonstrate that this methodology can be applied in real power systems using PMUs.