Abner Ramirez

Implementation of the Numerical Laplace Transform: A Review Task Force on Frequency Domain Methods for EMT Studies, Working Group on Modeling and Analysis of System Transients Using Digital Simulation, General Systems Subcommittee, IEEE Power Engineering Society

In this paper a detailed description, an analysis, and an assessment of a frequency-domain technique highly applicable to power systems transient analysis (i.e., the numerical Laplace transform) are presented. The errors due to truncation and sampling when converting a frequency-domain signal to the time domain are analyzed. Additionally, the use of odd and regular sampling is discussed. Two major goals of the paper are the revival of the mentioned technique and its friendly description for power systems engineers. As an application, a transmission-line transient is presented.

The Modified Harmonic Domain: Interharmonics

This paper presents the basics of two techniques, named here as the modified harmonic domain and the modified dynamic harmonic domain, proposed for calculating steady and dynamic states, respectively. These techniques have their fundamental in the harmonic domain with a substantial improvement: the inclusion of interharmonics in either steady or dynamic state. This is performed through the use of the discrete Fourier transform which allows an arbitrary frequency-domain discretization, thus permitting the representation of interharmonics.

Dynamic Harmonic Domain Modeling of Transients in Three-Phase Transmission Lines

This paper presents a traveling wave based transmission line model which includes harmonics in transient state. The line model is interfaced with a nonlinear load and both are simulated through the dynamic harmonic domain technique. This technique permits the user to follow step-by-step the harmonics of the propagating waveforms during transient conditions. An illustrative example involving a transmission line network with nonlinear loads is presented and the proposed model is compared with its time domain counterpart.

Electromagnetic transients in overhead lines considering frequency dependence and corona effect via the method of characteristics

In order to take into account the frequency dependence of transmission line parameters, the propagation equations with transient parameters have to be solved. In this work these equations are integrated by means of the method of characteristics and a convolution procedure using synthesized rational functions. The effects of corona are included using voltage-dependent shunt capacitances and an iterative process in the finite difference solution of the line equations.

Harmonic domain characterization of the resonant interaction between generator and transmission line

It is known that an untransposed open-ended line causes a negative sequence component in the current and the generator reacts through third and higher harmonic voltages. The currents and voltages can be greatly amplified by resonance to any of these harmonics. The phenomenon of machine-line interaction has traditionally been explained as a sequence of interactive events between the line and the machine. This paper presents a unified noniterative mathematical representation of this interaction. The analysis is formulated in the harmonic domain abc-frame to detect resonance conditions and for the assessment of their stability.

Frequency-Domain Computation of Steady and Dynamic States Including Nonlinear Elements

This paper presents a Newton-type methodology to calculate the transient or periodic steady state of an electrical network including nonlinear elements. The basic idea is to decompose the complete network into linear and nonlinear subnetworks. On one hand, a nodal representation of the linear network is considered. On the other hand, a Jacobian corresponding to a nonlinear element is calculated numerically via input perturbations, with the terminal voltage being the input and the device current as being the output. The latter is calculated in the time domain, via a polynomial representation, and converted back into the frequency domain by numerical Laplace transform operations. Finally, the solutions corresponding to the linear and nonlinear subnetworks are included in a Newton-type iterative scheme having a current mismatch (at the point of coupling) as its basis. Two examples involving nonlinear loads in a network are presented for illustration of the aforementioned procedures.

Interfacing Techniques for Time-Domain and Frequency-Domain Simulation Methods

This paper reviews different methodologies for interfacing time-domain and frequency-domain simulation programs. The main objective for this interface is to obtain the steady-state or transient state of a power network containing linear and nonlinear loads, and the calculation of the corresponding harmonics and the foregoing values for different types of analyses in power systems.

Vector Fitting-Based Calculation of Frequency-Dependent Network Equivalents by Frequency Partitioning and Model-Order Reduction

This paper presents a methodology to identify a frequency-dependent network equivalent from a highly resonant frequency response and in a broad range of frequencies. Primarily, the identification process consists on dividing the complete frequency range into a number of subranges either uniformly spaced or by containing an equal number of resonance peaks. Vector fitting (VF) is then applied to each subrange, yielding an accurate local approximation. A refinement of the local set of partial fractions is made through model-order reduction to remove spurious (redundant) poles. The final equivalent comprises a reduced number of poles, keeping the computational load lower than when applying VF to the whole range of frequencies while giving a similar rms error. An illustrative example involving a transmission system is presented for validation of the procedures above.

Dynamic average modeling of line-commutated converters for power systems applications

Detailed switch-level models of high-pulse-count converters are relatively straightforward to implement using commonly available simulation packages used for digital time-domain simulations and studying of power systems transients. However, such models are computationally intensive due to switching, and could become the bottle-neck for system-level studies with large number of components and controllers. This paper describes approaches for developing dynamic average-value models, i.e., the analytical derivations and parametric modeling. The resulting approximate models do not represent switching but still capture the transient behavior of the original converter circuit. The paper presents the results for 3- and 6-phase rectifiers implemented in PSCAD/EMTDC and Matlab/Simulink and shows that dynamic average models can be very effective. The paper also shows that as the number of pulses/phases increases, so does the complexity of switching pattern that defines the operating modes.

Extended Harmonic Domain Model of a Wind Turbine Generator for Harmonic Transient Analysis

This paper presents an extended harmonic domain (EHD) model of a wind turbine generator (WTG) system based on a doubly fed induction generator. The proposed EHD WTG model includes both electrical and mechanical subsystems and permits monitoring step-by-step the harmonics time variation; this allows, among other applications, to detect contingency scenarios, such as resonance problems caused by a specific harmonic. Moreover, control efficiency can be improved by means of the power-quality indices which are instantaneously available by the EHD WTG model. The proposed model is capable of accounting for an arbitrary number of harmonics; however, the more harmonics that are included, the larger the system becomes. This affects the central-processing unit time by the transient simulation. An efficient heuristic remedy is proposed in this paper which consists of accounting for “high-impact” harmonics only, based on the converters frequency spectrum. The EHD WTG model is validated with the power system computer-aided design/electromagnetic transients including dc (PSCAD/EMTDC) software tool via a case study.