Ivo Uglešić

Numerical calculations of three-phase transformer transients

A three-phase, two-winding transformer model is presented in this paper. Nonlinear magnetizing curves are piecewise linearized, while the input winding capacitances are lumped onto the transformer terminals. A stiff system of differential equations in a state space, describing the transformer transient behavior, is solved using the L-stable backward differentiation formulas (BDFs) numerical rule. It has been shown that using the BDF numerical rule has resulted in better stability properties than using the trapezoidal rule. A computer program has been developed for generation of variable-state waveforms. The developed program is suitable for simulations of low-frequency three-phase transformer transients such as inrush currents and ferroresonance. This computer program has proved to be numerically stable for the problems investigated in this paper. The results acquired in this way are compared to results obtained using MATLAB/Power System Blockset, as well as to results of laboratory measurements.

High-Frequency Model of the Power Transformer Based on Frequency-Response Measurements

In this paper, a new high-frequency black-box model of the power transformer is presented for the calculation of transferred lightning overvoltages. The model is based on frequency-response analysis measurements and the application of four-terminal network theory. The computational verification of the presented model was successfully performed on a white-box transformer model in Electromagnetic Transients Program-Restructured Version software. The experimental verification was carried out on 130-kVA and 36-MVA three-phase power transformers. The presented calculation and measurement results confirm the validity of the proposed model for full and chopped lightning impulse voltages.

Selection of Surge Protective Devices for Low-Voltage Systems Connected to Overhead Line

This paper presents a procedure of choosing an appropriate surge protective device for low-voltage systems connected to an overhead line. For a typical surge protection application, an appropriate Electromagnetic Transients Program model is devised. The energy overload is calculated for a surge protective device following a simulation of the lightning effect. This way, it is possible to determine the required class for the surge protective device in question. The procedure has been tested on some typical overhead low-voltage networks. The results of these calculations, as well as very good service experiences, demonstrate that the use of Class II surge protective devices seems to be appropriate for service entrances in buildings that have no lightning protection systems.

Simulations of Transformer Inrush Current by Using BDF-Based Numerical Methods

This paper describes three different ways of transformer modeling for inrush current simulations. The developed transformer models are not dependent on an integration step, thus they can be incorporated in a state-space form of stiff differential equation systems. The eigenvalue propagations during simulation time cause very stiff equation systems. The state-space equation systems are solved by using A- and L-stable numerical differentiation formulas (NDF2) method. This method suppresses spurious numerical oscillations in the transient simulations. The comparisons between measured and simulated inrush and steady-state transformer currents are done for all three of the proposed models. The realized nonlinear inductor, nonlinear resistor, and hysteresis model can be incorporated in the EMTP-type programs by using a combination of existing trapezoidal and proposed NDF2 methods.

Elimination of Overshooting Effects and Suppression of Numerical Oscillations in Transformer Transient Calculations

This paper presents an original method of modeling nonlinear elements, particularly acceptable in the calculation of low-frequency transformer transients. A way of generating the state matrix coefficients is described. An algorithm is developed for state variable calculations based on the hyper stable backward differentiation formulas (BDF) BDFp, p-th order. The advantages of developing an algorithm which enables elimination of overshooting effect, as well as the suppression of numerical oscillations in low-frequency transformer transient calculations, are presented. Also, the reasons for the existence of overshooting effects and numerical oscillations are identified when the transformer transients are calculated in a nodal formulation of equations based on the trapezoidal method. It is shown that an implemented equation conversion procedure and/or a stiff system equation are indeed causing numerical oscillations in transformer transient calculations.

Numerical calculations of three-phase transformer's transients

A three-phase, two-winding transformers model is presented in the paper. The triplex core configuration is assumed in the transformers model. Nonlinear magnetizing curves are piecewise linearized. Input winding capacitances can be lumped to the transformers terminals. A stiff differential system in state space, describing transformers transient behavior, is solved by the L-stable backward differentiation formulas numerical rule. BDF compared to trapezoidal rule shows better stability properties. A computer program is developed for generation of variable state waveforms. The developed program is suitable for simulations of low-frequency three-phase transformer transients such as inrush currents and ferroresonance. Results of the developed program are compared to MATLAB/power system blockset results.

Measurement, Modeling and Simulation of Capacitor Bank Switching Transients

Abstract This paper presents the results of experimental and simulated investigations of electromagnetic transient phenomena during energizing of industry capacitor banks. Experimental and simulated investigations based on the electrical network model having the nominal voltage of 6 kV are carried out. In addition, sensitive analyses of characteristic impact factors are performed. It is shown how capacitor banks switching transients influence a degradation of the power quality in electrical distribution system.

Overvoltages provoked by faults in the distribution electrical network

The study of the overvoltages generated by faults in the transmission distribution electrical network comprised over 500 live tests of a single phase-to-earth fault in a 10 kV network. The influence of the neutral point grounding resistance on overvoltages in the network is researched. Different values of the resistor were used. Moreover the networks with an insulated neutral point were tested. A computer model of the cable network and the supply station was additionally developed. Overvoltages are reduced to relatively low values, mostly below the value of a double phase peak voltage, if the neutral point of the network 10(20) kV is grounded through the resistor. This is under a condition that the nominal resistor current is three times greater than the earth fault capacity current.

Influence of cables on power transmission network frequency response

Harmonic resonance is an important factor to be considered in a power transmission networks during connection of remote generation units with high-voltage cables (e.g. wind or solar power plants etc.). It is known that cable characteristics differs from characteristics of conventional overhead lines. Cable capacitance is far higher than capacitance of an equivalent overhead line, what can potentially lead to the low resonant frequencies which may be triggered by various switching events, such as transformer or shunt reactor energization etc. In this paper, possible consequences of power plant connection to transmission network with long HVAC cable are analyzed, with regard to harmonic resonance and frequency response of the network. The research has been conducted on developed model of the power transmission network in the software for calculation of electromagnetic transients EMTP-RV.

Modelling of variable shunt reactor in transmission power system for simulation of switching transients

This paper describes a model of three-phase variable shunt reactor (VSR) for simulation of switching transients in EMTP-RV software. Inrush currents caused by VSR energization and overvoltages caused by de-energization are analysed. For this purpose, a model of VSR, substation equipment and electric arc in SF6 circuit breaker was developed in EMTP-RV software.