J.R. Marti

A multiphase harmonic load flow solution technique

The operation of nonlinear devices under unbalanced load conditions may cause harmonic problems in power systems. A computer-based multiphase harmonic load flow solution technique for analyzing such problems is described. The harmonic load flows are obtained from iterations between the Norton equivalent circuits of the nonlinear elements and the linear network solutions at harmonic frequencies. Harmonics generated by static VAr compensators with thyristor-controlled reactors under unbalanced load conditions are used to illustrate the method. >

Real-time EMTP-based transients simulation

A computer program has been written for the simulation of power system transients in real time. The program is based on EMTP models and solution techniques optimized for maximum performance in superscalar computer architectures. Timings ranging from 38 to 107 /spl mu/s have been obtained for systems from 18 to 30 nodes using an IBM RISC System/6000 Model 560 workstation. These timings are considered adequate for real-time testing of protective relaying equipment. The program is compatible with existing EMTP data cases. >

Suppression of Numerical Oscillations in the EMTP

When compared to other possible integration schemes for the EMTP, the trapezoidal rule of integration presents very good overall characteristics in terms of accuracy, efficiency, and run-off stability. During certain system conditions, however, the solution with trapezoidal may present sustained numerical oscillations (Fig. 1(a)). These oscillations are related to the behaviour of trapezoidal as a differentiator after a discontinuity is encountered (e.g., after a switching operation). To solve this problem, two kinds of approaches have been proposed in the past. One approach has been to add artificial damping to the system either through the integration rule itself, using for instance backward Euler instead of trapezoidal, or by adding external resistances to provide damping. The main drawback of this approach is that distortion through damping is introduced not only on the discontinuity but also on the rest of the simulation. The other approach has been to use interpolation to correct the initial conditions after the disturbance. These type of techniques, however, are relatively complicated to implement. The technique presented in this paper solves the problem of trapezoidal as a differentiator by neutralizing the overshoot at the discontinuity (for instance, in the voltage ¿ = L di/dt after switching) within one time step.

Suppression of numerical oscillations in the EMTP power systems

The integration scheme in the electromagnetic transients program EMTP has been modified to solve the problem of sustained numerical oscillations that occur when the trapezoidal rule has to act as a differentiator. These oscillations appear, for instance, on the voltage across an inductance after current interruption. The technique presented prevents these oscillations by providing critical damping of the discontinuity within one Delta t of the simulation. The critical damping adjustment (CDA) is achieved by means of two Delta t/2 integration steps using the backward Euler rule. With the CDA scheme the trapezoidal rule can still be used throughout the entire simulation without the problem at discontinuities. The effectiveness of the scheme is illustrated with simulation results. >

A phase-domain synchronous generator model including saturation effects

This paper presents a synchronous machine model for power system transient system analysis derived directly in phase coordinates. Working directly in the physical phase domain, instead of the mathematical dqo domain, simplifies the interfacing of the machine model with the power system network, and allows the more accurate representation of internal machine phenomena, such as variable reluctance and saturation effects. It also permits the simulation of internal faults in the machine. The paper presents the basic equations of the phase-domain model and a technique to incorporate saturation effects along the actual direction of the resultant magnetomotive force in the machine air gap at each instant of the time-domain solution.

Guidelines for Modeling Power Electronics in Electric Power Engineering Applications

This paper presents a summary of guidelines for modeling power electronics in various power engineering applications. This document is designed for use by power engineers who need to simulate power electronic devices and sub-systems with digital computer programs. The guideline emphasizes the basic issues that are critical for successfully modeling power electronics devices and the interface between power electronics and the utility or industrial system. The modeling considerations addressed in this guideline are generic for all power electronics modeling independent of the computational tool. However, for the purposes of illustration, the simulation examples presented are based on the EMTP or EMTP type of programs. The procedures used to implement power electronics models in these examples are valuable for using other digital simulation tools.

Simplified three-phase transformer model for electromagnetic transient studies

This paper presents a simplified high-frequency model for three-phase, twoand three-winding transformers. The model is based on the classical 60 Hz equivalent circuit, extended to high frequencies by the addition of the winding capacitances and the synthesis of the frequency-dependent short-circuit branch by an RLC equivalent network. By retaining the T-form of the classical model, it is possible to separate the frequency-dependent series branch from the constant-valued shunt capacitances. Since the short-circuit branch can be synthesized by a minimum-phase-shift rational approximation, the mathematical complications of fitting mutual impedance or admittance functions are avoided and the model is guaranteed to be numerically absolutely stable. Experimental tests were performed on actual power transformers to determine the parameters of the model. EMTP simulation results are also presented. >

Direct phase-domain modelling of frequency-dependent overhead transmission lines

A new wideband transmission line model, based on synthesizing the line functions directly in the phase domain, is presented. It includes the complete frequency-dependent nature of untransposed overhead transmission lines by means of recursive convolutions over a wide frequency range. The model belongs to the class of time-domain models and is designed to be implemented in general electromagnetic transients programs such as the EMTP. Because the synthesis of the frequency-dependent modal transformation matrix is avoided, the method requires fewer convolutions at each time step than full frequency-dependent modal-domain models. Simulations have been performed comparing the proposed model with existing line models, with field recordings, and with calculations from a frequency-domain program. The new model provides accurate answers in both steady-state and transient conditions.

Apparatus for Online Power Transformer Winding Monitoring Using Bushing Tap Injection

Online transformer condition monitoring techniques based on transfer function methods, such as transmission-line diagnostics and swept frequency-response analysis, require the injection of a known test signal into the transformer. On larger power transformers, a practical method is to use the available bushing tap connection. In this paper, we will discuss a custom high-power signal generator that injects high-frequency signals on the bushing tap of the transformer under investigation, as well as a circuit to replace the bushing tap short and allow online operation of the system. Finally, the system is demonstrated on a 650 kV transformer.

Implementation of the CDA procedure in the EMTP

The application of the critical damping adjustment (CDA) technique to some of the main equipment models in the DCG/EPRI version of EMTP is presented. The CDA procedure eliminates the numerical oscillations that can occur in transients simulations that use the trapezoidal rule of integration. The details of this implementation for linear elements, nonlinear reactors, frequency-dependent transmission lines, and synchronous machines are described. Simulation results involving these components are presented, showing the effectiveness of the procedure. >