Bruce A. Mork

Transformer modeling for low- and mid-frequency transients - a review

One of the weakest components of modern transient simulation software is the transformer model. Many opportunities exist to improve the simulation of its complicated behaviors, which include magnetic saturation of the core, frequency-dependency, capacitive coupling, and topologically correctness of core and coil structure. This paper presents a review of transformer models for simulation of low- and mid-frequency transients. Salient points of key references are presented and discussed in order to give an accessible overview of development, implementation and limitations of the most useful models proposed to date. Techniques for representation of the most important behaviors are examined, with the intent of providing the needed foundation for continued development and improvement of transformer models.

Application of nonlinear dynamics and chaos to ferroresonance in distribution systems

Ferroresonant overvoltages or undervoltages can occur in cable-fed power transformer installations when single phase switching or interrupting is practiced. This paper identifies the ferroresonant circuit as a nonlinear dynamical system. Analysis and classification methods are presented which provide new insight into the global behavior of ferroresonance. The concepts presented offer potential for progress in the areas of transformer model development and evaluation, analysis and prediction of ferroresonance, and distribution system design and operation. Measurements from a typical five-legged core transformer installation are used to illustrate the application of nonlinear dynamics and chaotic systems to the problem of ferroresonance. >

Hybrid Transformer Model for Transient Simulation—Part I: Development and Parameters

A new topologically correct hybrid transformer model is developed for low and midfrequency transient simulations. Power transformers have a conceptually simple design, but behaviors can be very complex. The selection of the most suitable representation for a given behavior depends on the type of transformer to be simulated, the frequency range, and other factors, such as the internal design of the transformer and available parameters or design data. Here, a modular model suitable for frequencies up to 3-5 kHz is developed, utilizing a duality-based lumped-parameter saturable core, matrix descriptions of leakage and capacitive effects, and frequency-dependent coil resistance. Implementation and testing of this model was done for 15-kVA 208Delta-120Y 3-legged and 150-kVA 12,470Y-208Y 5-legged transformers. The basis and development of the model is presented, along with a discussion of necessary parameters and the approaches for obtaining them

Five-legged wound-core transformer model: derivation, parameters, implementation and evaluation

The ability to predict or confirm ferroresonance and to evaluate its severity depends primarily on the correctness of the transformer model used in the computer simulation. An equivalent circuit is developed here for the widely used three-phase grounded-wye to grounded-wye five-legged wound-core distribution transformer. Recently developed equivalent circuits are generally correct, but cannot faithfully reproduce all of the ferroresonant modes possible in this transformer. This new equivalent circuit is derived using duality transformations. Core saturation and losses and coil capacitances are included in the model. Model parameters are obtained via measurement, obviating the need for proprietary manufacturer design information. The model is implemented in EMTP. Simulation results are presented and compared to measurements. A technique for predicting ferroresonance on a system level, based on the use of bifurcation diagrams and Poincare sections, is developed and implemented using EMTP. The model performs quite well, even though coil capacitances are not entirely included in the model. One of the key advancements is the development of a bifurcation simulation method to predict ferroresonant behaviors for a large range of capacitance values.

An All-DC Offshore Wind Farm With Series-Connected Turbines: An Alternative to the Classical Parallel AC Model?

In this paper, the concept of an all-dc wind park with series-connected turbines is investigated as an alternative to the classical ac parallel or radial wind park. This paper presents a literature overview of all-dc wind park concepts with series connection. A three-phase conversion system with permanent magnet machine, ac-ac converter, high-frequency transformer, and diode bridge rectifier is suggested in this paper for the series connection of dc turbines. The dc series park with the suggested conversion system is compared in terms of losses, cost, and reliability to the state-of-the-art park configuration which is the ac radial park with HVDC transmission. It is found that the dc series park becomes comparable with the ac radial design for high ratings of the dc turbines. Furthermore, the comparison shows that emphasis must be put on reducing the losses in the conversion system of the dc turbine and, particularly, the ac-ac converter. Therefore, the efficiency of the ac-ac converter is compared for three different topologies: the direct matrix converter, the indirect matrix converter, and the conventional back-to-back converter. The direct matrix converter is found to be the most efficient, suitable for the suggested conversion system.

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.

Hybrid Transformer Model for Transient Simulation—Part II: Laboratory Measurements and Benchmarking

The topological structure and basic approaches for parameter estimation for a new hybrid transformer model are presented in Part I of this two-paper set. Part II deals with the model benchmarking and also discusses additional methods for parameter estimation based on laboratory measurements. The simulation results confirm the validity of the model for the low- and medium-frequency range

Comparison of wind farm topologies for offshore applications

Increasing energy demand and environmental factors are driving the need for the green energy sources. The trend, in general, with respect to wind farms is to increase the number and the size of wind farms. The wind farms are also being located offshore with the prospect of more consistent and higher energy capture. The offshore wind farms are likely to move farther off from the shores to reduce visual impacts and increase the size. But, this has implications in terms of design of the collection grid and grid interconnection. Farms of 1 GW size and at distances of about 100 km are envisaged [1]. The design of collection system and turbine interconnection will become very important as the farms move farther offshore. Proper choice of collection system topology is important from the point of view of maximum energy capture while ensuring a high reliability of the design. Different collection system topologies have been proposed by researchers before, with the radial system being most popular. One of the key factors in selection would be the losses in the farm. In order to select the most suitable topology a comparison of different topologies with respect to losses, reliability and costs has to be done. Comparisons of calculations indicate that the DC series and series-parallel wind farm design may be options for future wind farm designs. The DC series and series-parallel design have lower reliability, but can be improved by providing redundancies. The designs have equipment costs almost equal to the AC wind farm costs. The losses in DC series-parallel wind farm are higher by about 12 % when compared to AC wind farms. The DC series design is also very attractive design, but has restrictions with respect to insulation. Also, the required turbine ratings may be significantly and unrealistically high when it comes to designing large wind farms. It can also be concluded that the novel designs require significant amount of work before these can be used in real wind farms.

Parameter Estimation Methods for Five-Limb Magnetic Core Model

The majority of transformer model realizations used for power system transient simulations have some significant deficiencies, particularly related to the transformer core implementation. They either do not include the multilimb topology of the iron core, come upon some numerical stability issues, have limited use for three-phase transformers, or lack a complete leakage representation. Detailed consideration of the saturation effects is essential for accurate transient simulation of ferroresonance, excitation, inrush currents, half-cycle saturation, and similar phenomena. A recently published topologically correct core model, valid for low- and mid-frequency ranges, addresses this need. This paper details the parameter estimation methods developed for the five-legged core of this model.

Improved Application of Surge Capacitors for TRV Reduction When Clearing Capacitor Bank Faults

Current-limiting reactors are placed in series with capacitor banks to limit the rate of rise of current to the values specified in the circuit breaker (CB) standards. But this arrangement has created capacitor bank failures when attempting to clear faults in between the reactor and the capacitor bank. After detailed analyses of failures, solutions have been proposed by researchers: 1) Add a surge capacitor to ground on the capacitor bank side of the breaker and 2) add a surge capacitor across the reactor. These surge capacitors are sized based on the stray capacitances of the bus, the reactor, the circuit breaker, and on the maximum-available fault current at the substation. This paper presents a simplified means of sizing the surge capacitors for method 2), based only on the CBs interrupting current rating and reactor size. This eliminates the need for and uncertainty of stray capacitance values. Also, the design does not need to be revisited when grid enhancements increase the available fault current at a substation. A standard surge protection package, which can also be applied to existing installations, is proposed. This new approach has been verified with studies using Electromagnetic Transients Program/Alternative Transients Program.