Three-phase Transformer Model Research Articles

Practical Experiments with a Ready-Made Strategy for Energizing a Suitable Pre-Magnetized Three-Column Three-Phase Dy Transformer in Unloaded State for Inrush Current Computations

This article presents the results of an experimental verification of three-phase Dy transformer dynamics under no-load conditions. This study is motivated by previous ferroresonance analyses where the occurrence of inrush currents has been observed. The measurements covered all available electrical quantities in a transient state (12 measured and 3 additionally computed waveforms) during the device’s start-up under no-load conditions, as well as in a long-term steady state. A detailed analytical analysis is carried out for the obtained comprehensive set of measurement results. As a result of the conducted research, the mathematical model of the pre-magnetized three-phase Dy transformer is modified. Particular attention is paid to the issue of residual magnetism of the transformer core and its consideration in further research. The original strategy for energizing a three-column three-phase Dy transformer with a suitable pre-magnetization of its columns and original control switching system with a given/set value of the initial phase in the supply voltage is put to the test. The evolution of the induced inrush phenomenon up to the quasi-steady state under given (forced) conditions is documented (currents, voltages and the dynamics of changes taking place in the core (hysteresis loops)). This article represents a continuation of ongoing work on the study of transient states (dynamics of transformer inrush currents). At present, the Dy three-phase transformer is analyzed because of the requirements of industrial operators.

Enhanced thermal modeling of three-phase dry-type transformers

This work presents an enhanced thermal modeling for dry-type three-phase transformers, addressing the heat exchange mechanisms through conduction, radiation, and convection. Additionally, an equivalent thermal network is proposed to analyze the thermal behavior of these transformers. The thermal model includes several improvements, such as the differentiated representation of the core and windings through different nodes, and the consideration of primary and secondary windings as distinct nodes. Furthermore, the effects of convection and radiation in the inner areas of the core windows are accounted for, providing higher accuracy to the model. This modeling allows for a detailed analysis of the transformer under unbalanced load conditions, considering the complete geometry of the equipment. The results demonstrated that even with just a 5% load imbalance, there was a change in the hot spot temperature (HST). Moreover, the evaluation of temperatures in the coils, both internal and external to the core windows, revealed variations of up to 7 °C in the analyzed load unbalance scenarios. The study also highlighted that the phase of the harmonic component has an impact on the final equipment temperature. Additionally, the overvoltage and overload analyses showed that voltage has a greater impact on increasing the average core temperature, while overload mainly affects the winding temperature. Another relevant finding is that the internal coils near the core windows are most vulnerable to temperature rise when subjected to overload.

Технология построения имитационных моделей силовых трансформаторов с произвольной конструкцией активной части

Existing simulation models of power transformers that operate, for example, in the MATLAM Simulink SimPowerSystem environment, are based on an ideal transformer model. It allows using this model as an autonomous link in a complex electrical circuit. The main disadvantage of such models is the difficulty to consider non-standard versions of the magnetic circuit and special schemes for connecting winding elements when modeling. Particularly significant problems arise when modeling special transformers of the certain classes. At the same time, traditionally, when modeling the transient modes of transformers, a different approach is used. It is based on the use of inductance matrices which allows considering all the design features of the active part of the transformer. The disadvantage of this approach is the need to describe an external electrical circuit in addition to the transformer. Therefore, the problem to develop a modern technology for simulation models of transformers with an arbitrary design of the active part is topical. This model meets the requirement for the autonomy of the transformer model from the external circuit model. The authors have used the methods of modeling electrical and magnetic circuits based on the theory of ordinary differential equations, and simulation method using the MatLab Simulink SimPowerSystems package. A technology has been developed for simulation models of transformers with an arbitrary design of the active part based on the use of typical subsystems. An algorithm for matrix of inductances based on the main magnetic field of the transformer with the existing equivalent circuit of the magnetic circuit is given. The authors have presented a diagram of a three-phase transformer model developed using the proposed technology, as well as the results of comparing the current curves in the primary and secondary windings of the transformer when it is turned on at idle and with a resistive load. The results are obtained using the existing and new models. The results of the study can be used to design general industrial and special transformers in design companies and in manufacturing environment. The developed technology can give a special effect when it is used at the R&D stage to study the operating modes of transformers in case the enterprise has no experience to design and manufacture them.

A new load flow and short‐circuit analysis for unbalanced modern distribution system

This paper proposes a new load flow and short-circuit analysis method for unbalanced distribution system incorporating three-phase transformer models and inverter-based distributed generation (IBDG). Initially, a load flow method of an unbalanced distribution system is developed in this paper, which incorporates the mathematical model of three-phase transformer of any vector group and different modes of operation of IBDG. The advantage of the proposed method is that the required simulation time for the proposed method is smaller than the backward/forward method available in the literature. The fault analysis method developed subsequently in this paper also incorporates three-phase transformer model and IBDG in the short-circuit calculations. The mode of operation of IBDG during short-circuit analysis depends upon the magnitude of its short-circuit capacity. The results obtained from the proposed method have been compared with the time domain simulation studies carried out using PSCAD/EMTDC software to verify the accuracy of the proposed method.

A new method to incorporate three-phase power transformer model into distribution system load flow analysis

This paper proposes a new and simple method to incorporate three-phase power transformer model into distribution system load flow (DSLF) analysis. The objective of the present work is to find a robust and efficient technique for modeling and integrating power transformer in the DSLF analysis. The proposed transformer model is derived based on nodal admittance matrix and formulated by using the symmetrical component theory. Load flow formulation in terms of branch currents and nodal voltages is also proposed in this paper to enable integrating the model into the DSLF analysis. Singularity that makes the calculations in forward/backward sweep (FBS) algorithm is difficult to be carried out. It can be avoided in the method. The proposed model is verified by using the standard IEEE test system.

A new method to incorporate three-phase power transformer model into distribution system load flow analysis

A new method to incorporate three-phase power transformer model into distribution system load flow analysis

Three-Phase Transformer Inrush Current Reduction Strategy Based on Prefluxing and Controlled Switching

Inrush current with high amplitude is generated when the transformer is energized. On the one hand, it will have a negative impact on the safety of the transformer itself, and even cause the relay protection to malfunction. On the other hand, it may reduce operation speed of the protection when there is slight fault because of the protection restraint criteria. Both aspects will affect grid security. Based on the generation mechanism of inrush current, this paper proposes an inrush current reduction strategy that combines prefluxing and controlled switching technology. By constructing an equivalent magnetic circuit model of the large-capacity three-phase transformer with a universal core structure, the analytical formulas of the magnetic flux at each stage of implementing the strategy are obtained, and then the parameters design method of this strategy is proposed. The accuracy of the theoretical analysis of magnetic flux is verified through the accurate simulation. Compared with common inrush current reduction strategies, this strategy can reduce the inrush current to 0.5 times rated current below in any situation where the residual flux is unknown and the “core flux equalization” effect are not obvious, avoiding the problem of residual flux measurement. Finally, in the case of the transformer differential protection, the influence of this strategy on the protection is analyzed from the perspective of theory and simulation, and it shows that it can improve the performance of various protections effectively.

Decomposition of n ‐winding transformers for unbalanced optimal power flow

This study proposes a model for multi-phase, multi-winding, lossy transformers. A methodology is developed to decompose such transformers into a sub-network of multi-conductor Π -sections, shunts and idealised (lossless) two-winding transformers. The approach, therefore, can be used to include three-phase transformer models in any unbalanced power flow or optimal power flow tool that is able to represent these three basic components. The study derives the mathematical formulation and an implementation is provided in Julia/JuMP/PowerModelsDistribution.jl. The obtained voltage profile for several distribution test cases deviates from OpenDSS by at most 4 × 10 − 7 . A case study applies this model to optimise the tap settings in the context of conservative voltage reduction. This illustrates that the optimised tap settings can vary by as much as 30% depending on the vector group of the transformer.

Contribution of inrush current to mechanical failure of power transformers windings

This work presents a study regarding the contribution of inrush current to the occurrence of mechanical fatigue in windings of a power transformer and, consequently, the impact of that phenomenon on the equipment's lifetime. In order to perform the study, electromagnetic transient simulations were used to determine the inrush current in a three-phase transformer model. Then, three-dimensional simulations, based on the finite element method, were performed to determine the electromechanical stresses in the equipment windings, under the effect of the inrush current. Next, the methods of critical plans and Palmgren–Miner were applied to perform the fatigue study. From the results, the impact of inrush current on the integrity of the transformer's windings was determined, as well as, to estimate the reduction of lifespan of the equipment due to inrush occurrence. The number of inrushes needed for the total reduction of lifespan of the equipment due to mechanical fatigue was also determined. The results can be used in the transformers design stage, with the purpose of assisting the evaluation of mechanical withstand of equipment, which can minimise the possibility of failure and increase its lifespan.

The DC Bias Model and Simulation Analysis of Three-phase Five-limps Transformer Based on EIC Principle

In this paper, the model of transformer DC bias simulation is established based on EIC principle. This model considers the hysteresis loss and eddy current loss of the transformer core through the J-A model and the Bertotti theory. This model simulates the electromagnetic characteristics of the transformer under DC bias more accurately, providing a basis for reliable evaluation of transformer resistance to DC bias and determination of effective and reasonable control measures. Based on this model, the effects of DC bias on the operating characteristics of single-phase transformers are analyzed. Moreover, this paper summarizes the variation of field current and leakage flux as well.

APPROACH TO DETERMINATION OF NO LOAD CURRENT OF THREE-PHASE POWER TRANSFORMERS WITH PLANE RODS MAGNETIC SYSTEMS

Purpose. Development a new effective approach for determining the open-circuited transformer parameters by implementing a combination of a schematic and spatial mathematical model of nonstationary electromagnetic fields in three-phase transformers, taking into account the constructive structure of the active part, the nonlinearity of the magnetic properties of electrical steels providing high accuracy and computational efficiency.Methods. The researches were carried out using the methods of the electromagnetic field theory, the theory of electrical circuits, the theory of power transformers, mathematical physics, the finite element method, regression analysis methods.Results. Theoretical researches of electromagnetic processes based on numerical realization of a three-dimensional mathematical model of a power three-phase transformer in open-circuited operation are carried out. An approach is proposed for improving the field simulation efficiency of the open-circuited operation, which consists in reducing the dimension of the computational domain and the transition to 2D models. It allow reducing the computing resources cost more than 2.8 times, time resources more than 250 times at a weighted average discrepancy of not more than 3.6%. The regularities of the distribution of flux density and the energy of the magnetic field for the active part of the transformer in open-circuited operation are determined. Their quantitative ratio value for the rods of different phases, which determining the ratio of the currents and resistances of the forward and reverse sequences of the transformer are calculated. A new approach to determine the open-circuited parameters of three-phase transformers with flat rod magnetic systems, based on the methods of circuit and 3D modeling, harmonic analysis and symmetrical components is realized. It characterized by high efficiency of numerical realization and accuracy for transient processes in switching moment of the three-phase transformer without loads. System of phase idle currents, characterized by non-sinusoidality and asymmetry, is proved. The harmonic composition of these currents is dominated by the 1st, 5th and 7th harmonics, but the first harmonic component predominates. The parameters of the forward and reverse sequence of the phases of the first harmonic for open-circuited operation, based on symmetrical components method were determinated. A corrective technique, which clarifies the traditional engineering approach, is proposed. The use of parameter correction for the researched ratios of the currents of the forward and reverse sequences will been increase the accuracy of calculation of the idle current by 12-14% and the idle losses by 9-11% in comparison with the generally known engineering design techniques.Originality. An approach is proposed for improving the efficiency of field simulation of the open-circuited operation, which consists in reducing the dimension of the computational domain and the transition to 2D models. A new approach of determination of the open-circuited parameters of three-phase transformers with flat rod magnetic systems based on the methods of circuit and 3D modeling, harmonic analysis and symmetrical components is realized. It characterized by high efficiency of numerical realization and accuracy for transient processes in switching moment of the three-phase transformer without loads.Practical value. The approaches and techniques allows to reduce the cost of computing resources by more than 2.8 times, time resources more than 250 times, with a weighted average discrepancy of not more than 3.6%, and increasing the accuracy of calculation of idle currents by 12-14% and losses of idling by 9-11% in comparison with the well-known engineering methods of designing.

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.

Parameter Estimation of Three-Phase Transformer Models for Low-Frequency Transient Studies From Terminal Measurements

This paper introduces a three-phase reversible transformer model for the study of low-frequency transients. The model topology is obtained from the direct application of the principle of duality by drawing basic circuit elements on top of the transformer frame. The model parameters are obtained from terminal and physical size measurements as well as the characteristics of the iron core. The implementation of the model is based on standard drag-and-drop circuit elements available in electric circuit simulation programs. The model is validated with inrush current and normal open circuit laboratory measurements. The main advantage of this model is that the parameters remain the same for the simulation of different operating conditions from all terminals. This is true for transients involving deep saturation, normal loading operation, or open circuit.

Improved low‐frequency transformer model based on Jiles–Atherton hysteresis theory

Transformers are the most widely used apparatus in power systems to transfer electrical energy from one side to another. Despite remarkable achievements in transformer modelling over the past few years, three-phase transformer modelling techniques have not progressed to that of their single-phase counterparts, mainly because of topological correctness of core and coil structure, complicated interaction between fluxes of the three iron core legs, and non-linear saturation of ferromagnetic material. An improved three-phase transformer model with extended inverse Jiles-Atherton (JA) hysteresis theory is proposed in this study. The extended inverse JA model with anisotropic anhysteretic magnetisation function is addressed, and the classical eddy-current-loss term and anomalous-loss term are directly incorporated into the original energy balance equation to represent the non-linearity and iron core losses rather than representing them with a parallel combination of resistances and saturable inductances (R//L model) as most previous studies have done. The results of inrush current case indicate that the proposed transformer model can predict the residual flux, include eddy-current-loss and anomalous-loss, and predict the inrush current peak values with relative error less than 6%.

三相変圧器モデル鉄心の局所二次元磁気ひずみ測定

三相変圧器モデル鉄心の局所二次元磁気ひずみ測定

Transformer Leakage Flux Models for Electromagnetic Transients: Critical Review and Validation of a New Model

This paper presents experimental validation of the coupled leakage inductance transformer model. It is shown that the coupled approach yields the same results as the indefinite admittance matrix method of BCTRAN. A topologically correct three-phase shell-type transformer model is proposed. The connection points between the leakage and magnetizing inductances are properly identified, which makes the new model superior to BCTRAN and the hybrid models by providing physical consistency. In addition, experimental verification of a method to calculate the short-circuit inductances is presented. New explanations on the division of leakage flux and on the mathematical equivalence between the T- and Π-equivalent models are also given.

Local Vector Magnetic Characteristic Analysis of a Three-Phase Three-Leg Transformer Model Core

This paper presents results of magnetic characteristic analysis of a three-phase three-leg transformer model core. In the analysis, the finite element method considering vector magnetic properties expressed by the integration-type E&S modelling is used. In this research, in order to reduce total iron loss, local vector magnetic properties for some different T-jointed models are compared in detail. Distributions of maximum flux density, maximum field strength, axis ratio and iron loss depending on the T-jointed position are clarified.

Control of Rotating Magnetic Flux Distribution in a Transformer Model Core by Laser Irradiation

To reduce power loss of transformers further from now on and to raise efficiency, we have measured magnetic property distributions in a three-phase tripod V-connection transformer model core. For the measurement, we have developed a localized vector magnetic property measurement system consisting of a three-axis positioning system, a vector magnetic sensor (V-H sensor), and PC. The measured results showed that rotational magnetic fluxes with a large axis ratio were generated in the V-junction parts of the transformer model core, and large iron loss was observed. To reduce the iron loss near the V-junction parts, we have tried to change local magnetic characteristics of the electrical steel sheet near the V-junction parts by using laser irradiation. The effect of the laser irradiation on the local magnetic properties is evaluated by measuring distributions of the local magnetic properties.

Model of three-limb three-phase transformer based on nonlinear open circuit characteristic with experimental verification

This paper describes the realization of a three phase transformer model based on a non-linear open-circuit characteristic. The proposed model is based on the fact that in case of a star connection with a neutral wire on the primary windings for all three phases, the applied voltage presents phase voltage and line (phase) currents are magnetization currents. These variables are available for measuring and it is easy to obtain three non-linear open circuit characteristics. The results of simulations and a comparison with references and experimental results verified this approach.

Vector magnetic property of electrical steel sheet and its influence on distributions of magnetic field and iron loss for electrical machines

Purpose – The purpose of this paper is to present the vector magnetic properties of the electrical steel sheet and investigate its influences on the magnetic field and iron loss distributions for the electrical machines. Design/methodology/approach – The vector magnetic property of the electrical steel sheet is measured by using a two-dimensional single sheet tester and modelled through an E&S vector hysteresis model to be applied to finite element analysis. Findings – The magnetic field and iron loss distributions are calculated by finite element analysis combined with the E&S vector hysteresis model for the three-phase transformer and induction motor models. Originality/value – The influences of the vector magnetic property on the electrical machines are verified by comparing with the numerical results from a scalar magnetic property.