Nicola Chiesa

Transformer Model for Inrush Current Calculations: Simulations, Measurements and Sensitivity Analysis

The modeling of inrush currents that occur upon energization of a transformer is a challenge for Electromagnetic Transients Programs due to limitations in available transformer models and the ability to determine and specify initial flux. The estimation of transformer model parameters is also an issue. This paper presents a transformer model for low- and mid-frequency transient studies with a focus on the behavior in saturation and the estimation of residual fluxes. The comparison of the simulation results with analytical calculations and measurements proves the capability of the model to accurately represent energization and de-energization transients of a three-legged-core distribution transformer. A novel property is the ability of auto initialization after disconnection, made possible by the implementation of a hysteretic core model which properly simulates and remembers residual flux from the previous de-energization. Special attention is paid to parameter estimation. Detailed core and winding design data are not used as they are seldom available from the manufacturer. Sensitivity analysis is performed to verify the influence of each parameter on the inrush current envelope curve. It is observed that the parameter that most influences the current amplitude is the slope of the magnetization curve at extreme saturation.

Novel Approach for Reducing Transformer Inrush Currents: Laboratory Measurements, Analytical Interpretation and Simulation Studies

Transformer inrush currents can lead to a reduction of transformer lifetime and inadvertent tripping of relays. This paper investigates a novel approach for minimizing the inrush current with a potential application in circuit-breaker (CB) control strategies without independent-pole operation and residual flux estimation. For the analyzed transformer, the worst-case inrush current is halved compared to the rapid-closing switching strategy. Measurements of inrush current transients are performed on an unloaded 11-kV distribution transformer varying disconnection and connection instants systematically. This reveals a characteristic pattern in the extremal value of the inrush current as a function of switching times. The pattern is reproduced with simulations and extended to alternative winding configurations. A condition for minimum inrush currents, consistent for all phases and winding configurations, is identified and explained physically. The impact of the current chopping capability of the CB is important and is discussed in this paper.

Implementation of Inverse Hysteresis Model Into EMTP—Part II: Dynamic Model

The main features of a dynamic hysteresis model (DHM) and its implementation into the electromagnetic transient program (EMTP-ATP) are described. A method of fitting the DHM to catalog data is proposed. The implementation of the DHM within a transformer model is illustrated by transient calculations. Possible methods of fitting the DHM-based transformer model to a no-load test are outlined.The main features of the history-dependent inverse model of magnetic hysteresis are outlined. Its implementation into the Electromagnetic Transient Program-Alternative Transients Program (EMTP-ATP) is described, and the fitting of the model to catalog data is demonstrated. The abilities of the model are illustrated by its use in a single-phase transformer model.

Analytical Algorithm for the Calculation of Magnetization and Loss Curves of Delta-Connected Transformers

This paper proposes an analytical algorithm for the computation of the magnetization and loss curves for a transformer from standard no-load test report data. This is the input to standard transformer models for power system simulation. In the case of delta-coupled windings, the conversion from test-report root-mean-square line quantities to peak phase values requires processing of the triplen harmonics in the current. This is handled analytically in the paper with utilization of the concept of incremental inertance and conductance. The analysis shows that only the third harmonic needs to be treated to reach sufficient accuracy within the measurement errors. The test case with a 290-MVA generator stepup transformer shows an increase in the calculated current of above 10% at rated voltage with proper triplen harmonic handling. This difference will increase considerably with excitation voltage.

Practical Experience in Using a Topological Model of a Core-Type Three-Phase Transformer—No-Load and Inrush Conditions

This paper describes an experience in transformer modeling based on open-circuit test data obtained for a wide range of terminal voltages on the low-voltage side and inrush current measurements on the high-voltage side carried out for different residual fluxes of a 300-kVA transformer. The core-type transformer model is based on a dynamic hysteresis model, which is employed individually in the legs and yokes. We start with the case where the core geometry and winding turns are known when fitting the model. The method proposed is then extended to the case where only the nameplate data and the measured no-load losses and currents are available. For this latter case, an optimization model fitting is developed.

Calculation of off-core inductance in dual-circuit model of transformer

Zero sequence magnetic flux, generated in transformer core in different operation cases, is forced out of the core including the oil gap and the tank. These off-core flux paths can be represented by inductances in a duality transformation based electrical transformer model. These off-core inductances mainly determine the zero sequence impedance that is vital in analyzing a transformer subjected to the GIC event or unbalanced voltages. Estimation of these inductances is one of the challenges in identification of the electric equivalent circuit. The main contribution of this paper is to present an approach for calculation of the mentioned off-core inductances based on 2D-FEM. Since the transformer structure is not symmetric for off-core flux path, 3D-FE analysis is also used to evaluate and improve the presented method. The results calculated for a 3-leg 3-phase transformer have a good agreement with the values obtained from empirical equations typically adopted by manufacturer.

Duality Derived Transformer Models for Low-Frequency Electromagnetic Transients—Part I: Topological Models

The objective of this two-part paper is to provide clarity to physical concepts used in the field of transformer modeling, to dispel common misconceptions regarding numerical instabilities, and to present unified modeling techniques for low-frequency transients. This paper focuses on proper modeling of nonlinearities (magnetizing branches) since these components are critical to determine the low-frequency behavior. A good low-frequency model should properly represent: normal operation, inrush currents, open and short circuit, out-of-phase synchronization transient of step-up transformers, geomagnetic-induced currents, ferroresonance, and harmonics. This paper discusses the derivation of electrical dual models from the equivalent (magnetic) reluctance networks and the direct application of the principle of duality. It is shown that different dual models need to be derived for different transformer geometries and the advantages and disadvantages of each method are discussed. This paper also compares double-sided versus single-sided dual models, and shows that the double-sided model is a more general approach. The mathematical equivalency of several leakage models (negative inductance, mutual coupling, and BCTRAN) is demonstrated for three-winding transformers. It is also shown that contrary to common belief, a negative inductance is not the source of numerical oscillations, but they occur due to the use of noncorrect topological models for representing the core.

Duality-Derived Transformer Models for Low-Frequency Electromagnetic Transients—Part II: Complementary Modeling Guidelines

This two-part paper is intended to clarify definitions in dual transformer modeling that are vague, provide accurate modeling guidelines, clarify misconceptions about numerical instability, provide a unified dual model for a specific type of transformer, and introduce new paths of research to the power systems/electrical machinery community for low-frequency transients. Part I discussed the topology of duality-based models and some important issues, such as the most common approaches to derive dual models and their variety, the equivalence of negative inductance and mutual couplings to represent the leakage inductance of three-winding transformers, and the numerical oscillations caused by the use of nontopological models. This part of the paper discusses and compares white-, gray-, and black-box models. The paper also reviews hysteresis models (static and dynamic) and highlights the differences between the air-core inductance and saturation inductance. The available dual models for the representation of the transformer tank are then presented. A unified and accurate model of a three-phase core-type transformer adequate for all low-frequency transients is presented. Finally, concrete guidelines are presented for the appropriate selection of the model topology and parameters for different low-frequency transient studies.