Three-phase Transformer Model Research Articles

Harmonic Nonlinear Transformer Modeling

This paper proposes a new saturated single-phase transformer model and a three-phase three-legged transformer model for their implementation in a harmonic load flow. The nonlinear magnetizing behavior of the transformer is represented in both models by a simple saturated reluctance function. The procedure for the nonlinear magnetizing current calculation is described. The model incorporation into the harmonic load flow is also analyzed. Simulations have been developed in order to show the performance of the proposed models, and have been compared with real measurements.

Analytical model of a T-connected three-phase transformer

Three-phase transformers usually consist of three sets of windings connected in W ye, delta or zigzag on three individual cores or on a single three-phase one. Two single-phase transformers can also be used in a less than well-known way called the T-connection. Depending on the actual connection, as in conventional three-phase transformers, secondary voltages are in phase or displaced by ±30°. Due to the reduced number of windings, the T-connected transformer can be economically produced. However, since it is an asymmetrical connection, the short-circuit impedances of the individual phases are not identical, leading to unbalanced load voltages and short-circuit currents. An analytical model of the T-connected transformer has been developed to evaluate the effects of the impedance unbalance. This model based on single-phase short-circuit tests can be used to determine voltage unbalances, active and reactive transformer losses and short-circuit impedances.

Measurement of /spl lambda/-i characteristics of asymmetric three-phase transformers and their applications

Modeling of three-phase transformers with three-limb cores is important, such units are very ubiquitous and are asymmetric due to the different lengths of the three limbs of the core. It is, therefore, important to devise a measuring procedure, where the (/spl lambda/-i) characteristics of the three limbs and the zero-sequence (/spl lambda//sub 0/-i/sub 0/) characteristic due to the tank can be determined. A simulation program is developed so that currents at no-load and symmetric or asymmetric loads can be computed. Measured currents are compared with computed results for 2.3-kVA and 45-kVA units.

Measurement of λ-1 characteristics of asymmetric three-phase transformers and their applications

Modeling of three-phase transformers with three-limb cores is important. Such units are very ubiquitous and are asymmetric due to the different lengths of the three limbs of the core. It is, therefore, important to devise a measuring procedure where the (λ-i) characteristics of the three limbs and the zero-sequence (λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -i <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> ) characteristic due to the tank can be determined. A simulation program is developed so that currents at no-load and symmetric or asymmetric loads can be computed. Measured currents are compared with computed results for 2.3 kVA and 45 kVA units.

Modeling and simulation of a cycloconverter drive system for harmonic studies

This paper discusses the steady-state harmonic modeling and simulation of a cycloconverter drive system (CDS). The operation and control of a cycloconverter drive and a synchronous motor load were modeled in the time domain. Based on the duality principle of electric and magnetic circuits, four types of three-phase transformer models with detailed nonlinear magnetizing characteristics were implemented. The harmonic behaviors of the entire system were studied under several worst operation conditions. The goal of this paper is to understand the harmonic problems associated with a CDS from an integrated system point of view, with special attention given to harmonic filtering and cancellation effect of converter coupling transformers.

Investigation of impacts of different three-phase transformer connections and load models on unbalance in power systems by optimization

This paper investigates the impacts of different three-phase transformer connections and load models on unbalance in power systems. New three-phase transformer models are presented. These models are derived from a new primitive impedance matrix incorporated with positive, negative and zero sequence elements. The constant power and constant impedance load models are discussed. The three-phase models are implemented in a general-purpose optimization software package. Two power systems are used to illustrate the test results. The test results provide assistance to engineers in understanding the effect of different connections on the transformers. This paper also emphasizes that a proper load model should be used; otherwise, an incorrect solution will be obtained.

A three-phase three-winding core-type transformer model for low-frequency transient studies

A topology-based and duality-derived three-phase, three-winding, core-type transformer model is presented. The model treats the leakage inductances and the coupling effects of the core in a straightforward and integrated way. The long-established positive- and zero-sequence star equivalent circuits of a three-phase three-winding transformer are derived from the original equivalent magnetic circuit of the transformer by applying duality. Formulations for determining the values of the leakage inductances and the core loss resistances from transformer open- and short-circuit test data are presented. A supporting routine is written to generate the /spl lambda/-i curves for each segment of the core and the other input data for EMTP. Since the duality-derived model consists of only RLC elements, no device-specific code to EMTP time-step code is needed. Winding capacitances are lumped to the terminals. The model is suitable for simulation of power system low-frequency transients such as inrush currents and ferroresonance, short circuits, and abnormalities including transformer winding faults.

Improved simulation of HVDC converter transformers in electromagnetic transient programs

In electromagnetic transient simulation HVDC converter transformers are normally represented as magnetically independent single-phase units. However, three-limb converter transformers are often used in HVDC schemes. Single-phase and three-limb three-phase transformer models are derived using a unified magnetic equivalent circuit concept. The new models are verified with laboratory and field data. Also, a comparison is made between the transient performance of HVDC converters with conventional and proposed transformer models.

Two-dimensional magnetic properties of a three-phase amorphous transformer core

The distribution of the rotational magnetic flux density and the rotational field strength in a three-phase amorphous transformer model core is investigated using a special sensor. The differences at various locations of the three-phase amorphous core can be compared with the results for a grain-oriented silicon steel sheet.

A three-phase multi-legged transformer model in ATP using the directly-formed inverse inductance matrix

A new transformer model based on core topology is developed. The model simulates the transformer as a set of coupled inductances. Winding flux linkages are chosen as state variables and currents are computed from the flux linkages using the directly-formed inverse inductance matrix, the /spl Gamma/-matrix. Due to the strong magnetic coupling among the windings, the inductance matrix of a transformer is ill-conditioned. Directly forming the /spl Gamma/-matrix will not only speed up the computation but also make it more stable. Transformer core saturation is represented by its anhysteretic magnetization curve. Eddy current and hysteretic losses of the core, and stray losses of the transformer are accounted for by a resistive load on the secondary. Winding capacitances are lumped to the terminals, the model is thus accurate up to 5 kHz. A supporting routine is written to generate /spl lambda/-i curve data for each segment of the core and the other input data for EMTP. The model has been incorporated into the Alternative Transients Program (ATP), the BPA EMTP, for evaluation, and has passed the benchmark test of the GPU line energization test of 1973.

Distributions on localized iron loss of three-phase amorphous transformer model core by using two-dimensional magnetic sensor

In the past, we reported on the two-dimensional magnetic properties of the three-phase transformer model core with silicon iron. They are measured by using the two-dimensional magnetic sensor. In this paper, the silicon iron core results are compared with those of an amorphous power core. As the results, the differences between the two materials are made clear.

Three phase models of specially connected transformers

To reduce power system imbalance, various types of specially-connected power transformers have been adopted in Taiwan and abroad. Because three-phase transformer models are necessary for three-phase load flow simulation, specially-connected transformers which have been adopted so far are selected to derive three-phase models in this paper. These transformers include the single-phase connection, the V-V connection, the wye-delta connection, the Scott connection, the Le Blanc connection and the modified-Woodbridge connection. The three-phase models with the specially-connected transformers offered in this paper distinctly represent the HSR feeding system by means of the physical three-phase circuit and the symmetrical-component equivalent circuit. The three-phase model could be joined to the three-phase load flow program to exactly analyze the system imbalance in the future. The symmetrical-component equivalent circuit may also be used to derive the approximate unbalance-estimating formula.

Representation of hysteresis in three-phase transformer models for electromagnetic transients

An efficient algorithm for the implementation of hysteresis effect in three phase transformer models for electromagnetic transient studies is presented. It is based on a simplification of the well-known Preisach model requiring few data, easily available, while it provides results close to the experimental ones. The model is validated by comparing measured and calculated results obtained from tests on a magnetic material used for the construction of transformer cores and a laboratory three-phase transformer.

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. >

An improved magnetic field analysis in oriented steel sheet by finite element method considering tensor reluctivity

An improved magnetic field analysis by using tensor reluctivity is presented. The conventional numerical modeling of materials can not exactly express the phase difference between the magnetic flux density and the magnetic field intensity. We therefore define the magnetic tensor reluctivity under an alternating and rotating flux condition, and calculate it from measured data, which are obtained by using two-dimensional magnetic measuring apparatus. This method is applied to a three-phase transformer model core made of oriented steel. As a result, it is shown that our new method is applicable to the strong anisotropic problems and rotating magnetic field problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

モデル鉄心を用いた三相変圧器内の局所２次元磁気特性分布に関する検討

モデル鉄心を用いた三相変圧器内の局所２次元磁気特性分布に関する検討

Three phase transformer modelling for fast electromagnetic transient studies

In this paper the overvoltages produced by switching the primary side of reactor loaded transformers are simulated using the Electromagnetic Transients Program (EMTP). Attention is focused on transformer modelling. Five general three-phase transformer models are used and from the results obtained, and comparisons with field tests, positive conclusions concerning the reliability and the accuracy of these models in the study of switching fast electromagnetic transients are drawn.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Radial distribution test feeders

Many computer programs are available for the analysis of radial distribution feeders. In 1992 a paper was published that presented the complete data for three four-wire wye and one three-wire delta radial distribution test feeders. The purpose of publishing the data was to make available a common set of data that could be used by program developers and users to verify the correctness of their solutions. This paper presents an updated version of the same test feeders along with a simple system that can be used to test three-phase transformer models.

Three-phase cogenerator and transformer models for distribution system analysis

The authors present detailed three-phase cogenerator and transformer models for analyzing a large scale distribution system. The cogenerator model presented can represent the inherent generator phase imbalance due to distribution system imbalance. The cogenerators can be synchronous or induction and can be on either primary or secondary systems. The transformer models consider the copper and core losses, the winding connection, the phase-shifting between primary and secondary windings, and the off-nominal tapping. An individual phase, as opposed to a balanced three-phase, representation is employed. This approach is oriented toward applications in distribution system operational analysis rather than planning analysis. >

Three-dimensional model of three-phase transformer for leakage field calculation

The simplified model of a small transformer for simulation of space-distribution of leakage field is described. The authors suggest for calculation a well-known and perspicuous finite difference method with numerical procedures based on Fast Fourier Transform worked out in the National Center for Atmospheric Research Colorado USA. The simpli-field model may be used for numerical calculations of transformer system in which the eddy-currents in constructional elements (e.g. in the transformer tank), are ommitted.