R.C. Degeneff

A method for constructing a reduced order transformer model for system studies from detailed lumped parameter models

All power transformer manufacturers maintain computer programs that compute the internal transient voltage distribution when the transformer is subjected to transient voltages. This information is used to design the insulation structure for the transformer. Utility engineers also need to represent the power transformer in some detail in their system studies since significantly higher failure rates on large EHV units suggest the transient voltage that the system places on the terminals of the transformer is in some measure a function of the impedance characteristic of the transformer. A reduction technique is presented which uses the detailed lumped parameter transformer model as a starting point and allows its reduction to any size specified by the user. The method is straightforward mathematically and while retaining the physical configuration of the transformer does not require any proprietary information from the transformer suppliers. The necessary mathematics are presented, and the method is illustrated using a 500 MVA auto-transformer. >

Nonlinear, lumped parameter transformer model reduction technique

The behavior of large power transformers under transient conditions is of significant interest to both transformer designers and power system engineers. The designer employs computer programs to construct detailed electrical models enabling him to compute the transformers internal transient voltage distribution. Using this information, and various other tools, the design engineer can develop a reliable and cost effective insulation structure. The power engineer requires a reduced model that accurately represents the transformers behavior to investigate the effects of power system transients. Reduced models are generally obtained either from detailed design models, or from measurements on fully constructed transformers. The latter technique has the major disadvantage that in the absence of an expensive prototype design, improvements cannot be made. Presently, both methods are subject to varying degrees of error. This paper presents a reduction technique that starts with the linear, detailed design model, and provides a reduced model of any specified size, while retaining the same computational accuracy as the original model. The method is mathematically exact, relatively straight-forward and compatible with time domain transient analysis programs. Application of the technique to the detailed model of a 765/345/34.5 kV, 500 MVA single phase autotransformer is provided. >

Determining the effect of thermal loading on the remaining useful life of a power transformer from its impedance versus frequency characteristic

It is well known that cellulose materials used to insulate transformer windings gradually degrade during service due to a combination of thermal, mechanical, and electrical stresses. As a result, the mechanical characteristics of the paper change during use and may affect the useful life of the transformer. It has generally been assumed that the electrical characteristics remain relatively constant throughout the aging process. If, however, thermal aging changes the electrical characteristics, it may be possible to gauge the thermal age of a transformer by externally monitoring these electrical characteristics over time. In this work, samples of oil impregnated thermally upgraded Kraft insulating paper are subjected to accelerated thermal aging. The relative dielectric constant and loss tangent are investigated by monitoring changes in capacitance and conductance as a function of frequency and thermal aging. This paper presents data showing that the thermal aging process produces changes in the electrical characteristics of the insulating system paper. An example is presented comparing the admittance versus frequency for a model of a 765 kV 500 MVA auto transformer. This demonstrates that the effect of aging can theoretically be observed from the terminals of the transformer.

Kron's reduction method applied to the time stepping finite element analysis of induction machines

The behavior of large induction motors during transient as well as steady state running conditions is of significant interest to the power industry. A variety of analytical predictive tools are employed to aid the design and predict their operation under transient and steady state conditions. This paper presents a strategy to reduce the required running time in order to make a parametric study of induction machines such as the assessment of different design options feasible. This is accomplished by reducing the number of finite element equations that must be solved while maintaining the same level of accuracy of solutions. This method is based on Krons network reduction work for linear systems and has successfully been applied to large lumped parameter model of transformers. This paper illustrates the reduction method by comparing the flux density in the air gap for a complete FEM model of an induction machine to that of the reduced model. The results are essentially identical with a reduction in computational time of approximately 71%.

Pipe-type cable ampacities in the presence of harmonics

This paper explores the effect of harmonics on high-pressure fluid filled pipe-type transmission cable ampacity. Industry currently calculates the current carrying capacity of underground power cable based on the assumption of a purely sinusoidal 60 Hz current. However, increasing levels of harmonics on power systems have raised concern about their effect on cable ampacities. The issue has already been addressed for distribution cables. This paper begins with a discussion of Neher and McGraths classic equations and some recent revisions, and develops a closed form composite equation accurately reflecting the effect of harmonics. The effect of frequency on the loss ratio is shown and supported by comparison with measured data at 60 Hz and a finite element analysis at a number of harmonic frequencies. The effect of specific harmonic scenarios is shown in light of the IEEE standard on harmonics. The results are used to develop a derating factor to compensate for current harmonics on transmission systems. >

Transformer model reduction using time and frequency domain sensitivity techniques

The paper investigates the use of sensitivity methods to identify the parameters of reduced transformer models. The reduced model retains the structure of the original model. The identification is performed in both the time domain and the frequency domain. The technique is applied to a lumped-linear model of an experimental coil, and the results are promising. >

Computing the internal transient voltage response of a transformer with a nonlinear core using Gear's method. Part 1: Theory

An EHV transformers insulation structure must be designed to withstand the internal stresses generated during transients. Computer models are employed for predetermination of these stresses. This paper develops a detailed transformer model and solution method which represent the nonlinear, saturable characteristic of the magnetic core during transients. The resulting set of stiff nonlinear differential algebraic equations are solved by application of Gears method. This paper describes the transformer model and the necessary set of equations based on linearization of the iron cores saturable magnetic characteristic at each time interval. >

Determination of the effect of harmonics on pipe-type power cable AC/DC resistance ratios

The authors present a closed-form expression for computing the AC/DC resistance ratio of high-pressure fluid-filled (HPFF) pipe-type cable in the presence of harmonics. Industry computes this factor with the assumption that the currents are purely sinusoidal at 60 Hz. However, as levels of harmonics increase on power systems, concern for the effect of harmonics on system ampacities rises. The authors develop a closed-form hybrid of the resistance ratio equations presented by J.H. Neher and M.H. McGrath (1957), and they compare the results with measured data at 60 Hz. No measured data are available for the resistance ratio at higher frequencies, so a two-dimensional finite element model is developed to view the effect of frequency on the resistance ratio. The effect of a specific harmonics scenario on the resistance ratio of a given system is discussed, and results are presented for some example systems. >

Computing the internal transient voltage response of a transformer with a nonlinear core using Gear's method. II. Verification

An EHV transformers insulation structure must be designed to withstand the internal electrical stresses generated during system transients. Computer models are employed for predetermination of these stresses. Part I of this paper developed a detailed transformer model and solution method representing the nonlinear, saturable characteristic of tire core during transients. The resulting set of stiff nonlinear differential algebraic equations are solved by application of Gears method. Part II presents the verification of this methodology. This is accomplished by comparing the computed and measured response of a 765/345/34.5 kV 500 MVA autotransformer during energization and transient excitation. >

Transient finite element analysis computational reduction technique

The finite element analysis of a large, complex region under transient magnetic field conditions often requires significant computational time; the solution of realistic problems may be rendered impractical by this computational burden. Often, however, the entire solution of the region being modelled is not of interest. For example, the area of interest of a system composed of magnetic material and air gaps subject to magnetic field transients is often limited to the conducting regions which support eddy currents. This paper presents a methodology which significantly reduces the computational time required for a transient finite element analysis of such problems by solving for only the pertinent regions with no effect on result accuracy. >