Transformer Equivalent Circuit Research Articles

A new approach towards more accurate modeling of mechanical defects in power transformer windings

In many cases, power transformers can continue their normal operation despite mechanical defects in their windings. However, estimating the lifespan and assessing the risk of using a transformer with mechanical defects depend on detailed studies of insulation aging and the distribution of transient voltages along the winding, and consequently, the likelihood of partial discharge. Risk assessment studies can only be effectively conducted through accurate modeling of transformers across a wide frequency range. In this study, an attempt has been made to investigate the impact of winding mechanical defects on the transformer equivalent circuits parameters using finite element method precisely modeling of transformer windings, without applying approximation or common simplifications. To compare the effect of each mechanical defect on the resistance, inductance, and capacitance matrices arrays, an index called fault classification accuracy has been used. The investigations have shown that the capacitance matrix arrays undergo the most significant changes for all types of modeled defects in this research. To examine the impact of defects on the transformer frequency response, a π coupled model that directly uses output matrices of finite element modeling has been employed. The sensitivity of various components of frequency response has also been investigated for the used model.

Accurate transformer equivalent circuit for percentage differential protection simulation under DC bias

Percentage differential protection (PDP) is one of the main protections of the transformer. The traditional transformer T equivalent circuit is insufficient to simulate the uneven saturation characteristics of the core for PDP under DC bias. Therefore, the transformer π equivalent circuit with three-segment component saturation is proposed for transformer PDP circuit simulation. FEM simulation is carried out to analyze the performance of transformer. The simulation and the experiment on PDP operation and restraint currents are conducted. Compared to the experiment, the errors of operation and restraint currents are significantly reduced using the proposed circuit under DC bias. The circuit simulations of transformer internal and external faults are implemented. The electromagnetic field analysis verifies the limitation of T equivalent circuit for PDP. The proposed method can achieve better performance in both transformer internal and external fault circuit simulation than the traditional method.

Comparative Study of Different Topologies of Monolithic On-Chip Planar Transformer for Optical VCSEL Driver

This article presents a comparative study of different topologies of monolithic on-chip planar transformer, operating at high frequencies and suitable for optical VCSEL driver. The vertical cavity surface emitting laser (VCSEL) driver is presented for optical transceiver systems. At the VCSEL driver output stage, the on-chip transformer is used to compensate for large bandwidth and deliver adequate gain. On-chip transformer equivalent circuit model has been proposed and used for simulation and measurement. The eye pattern results show that the VCSEL driver with an on-chip transformer presents good performance. Different topologies of the on-chip transformer are compared and 0,5 µm CMOS technology measurements are considered in the frequency range from 1 GHz to 10 GHz. Square, hexagonal, octagonal, and circular topologies of on-chip transformer have been compared. The circular topology presents a good performance and high-quality factor. The square shape provides a high inductance value and low quality compared to the other topologies.

Estimation of the Equivalent Circuit Parameters in Transformers Using Evolutionary Algorithms

The conventional methods of parameter estimation in transformers, such as the open-circuit and short-circuit tests, are not always available, especially when the transformer is already in operation and its disconnection is impossible. Therefore, alternative (non-interruptive) methods of parameter estimation have become of great importance. In this work, no-interruption, transformer equivalent circuit parameter estimation is presented using the following metaheuristic optimization methods: the genetic algorithm (GA), particle swarm optimization (PSO) and the gravitational search algorithm (GSA). These algorithms provide a maximum average error of 12%, which is twice as better as results found in the literature for estimation of the equivalent circuit parameters in transformers at a frequency of 50 Hz. This demonstrates that the proposed GA, PSO and GSA metaheuristic optimization methods can be applied to estimate the equivalent circuit parameters of single-phase distribution and power transformers with a reasonable degree of accuracy.

Research on Urban High Voltage Power Network Harmonic Transfer and Emission Level

With the rapid growth of urban power transmission cable scale, the harmonic pollution in the high-voltage power grid is more transmitted to other power grids of different voltage levels, which makes the harmonic transmission more complicated, increases the harmonic emission level, and makes it difficult to quantitatively analyze and study the allowable value of users’ electrical pollution emission. Therefore, in this paper, by establishing the harmonic conduction model of the urban high-voltage power grid and considering the equivalent circuit of transformer and transmission cable in the urban power grid, the parameters of transmission cable harmonic transfer coefficient and the allowable emission value of power quality pollution of the urban power grid are deduced and quantitatively analyzed. Then the harmonic transmission and mutual influence of urban power network harmonics in power transmission cable are analyzed through examples, which is helpful to determine the allowable value of harmonic pollution emission scientifically and reasonably.

Optimized high-frequency white-box transformer model for implementation in ATP-EMTP.

• High-frequency white-box transformer models can be implemented in EMTP. • ATP can be used to calculate fast transients in power systems. • Transformer models can be formulated as equivalent circuit or in state-space form. • The electromagnetic model can be obtained using FEMM. • Vector fitting and particle swarm optimization are combined to obtain de model parameters. Although several high frequency white-box transformer models have been proposed in the literature, the methodology for their implementation in some programs based on EMTP has not been addressed in detail. This is true in particular for ATP, for which the representation of large transformer models is particularly problematic. This work aims to enable the use of ATP to model detailed transformer equivalent circuits, which would otherwise be seriously questioned. To establish these circuit models, the following must be taken into account: model reduction, magnetic circuit decoupling, avoid numerical instability, limit and optimize the use of resistors, generate ATP versions capable of processing large models. To this end, three generally valid methodologies are presented to reduce the model without compromising the accuracy of the calculation results and, finally, additional specific methodologies are implemented to reduce and adapt the models in the ATP environment. The application of these methodologies results in six possible variants of reduced models, which were successfully validated through a case study used by CIGRE JWG A2/C4.52 to verify the accuracy of transformer models.

Practical Aspects of Instantaneous Magnetization Power Functions of Silicon Iron Laminations

Magnetic energy loss P of SiFe steel represents a key factor for the efficiency of soft magnetic machine cores. Traditionally, they are operated with 50 Hz (or 60 Hz), a frequency value that yields rather balanced portions of hysteresis loss and eddy current loss. In equivalent circuits of transformers, P tends to be represented by a magnetic power resistance RM, as a constant. For the most important case of sinusoidal induction B of 50 Hz, this would correspond to an instantaneous magnetization power function p(t) that is sinusoidal as well, however, with 100 Hz (or 120 Hz). On the other hand, from complex, non-linear mechanisms of hysteresis, it is obvious that p(t) should be strongly non-sinusoidal, even for exactly sinusoidal B(t). So far, almost all corresponding instantaneous investigations were restricted to calculated modelling of loss portions and transient modelling. On the other hand, for the first time, the present study was focussed on functions p(t) as measured at IEC-standardized samples of industrially relevant steel. Practical evaluations are discussed with respect to the revealed “history” of magnetization processes, as well as for product characterization. For these tasks, a novel digitized “Low-mass Single Sheet Tester” was developed that was applied for both non-oriented steel (NO) and grain-oriented steel (GO), for 50 Hz. Interpretations proved to be favoured by relating p(t) to total P, according to an instantaneous power ratio. As a result, both steel types revealed strongly non-sinusoidal power functions, with short durations of negative p. Negative p proved to be most pronounced for NO steel, as a measure for the onset of reversible turns of atomic moments. As a consequence, p(t) comprises strong upper harmonics of 200 Hz and even 300 Hz. Based on theoretical considerations, we split p(t) in a dissipative loss power function pL(t) and in a potential energy power function pP(t). Finally, we used p(t) to determine the corresponding power resistance RM(t) that proves to be a distinctly nonlinear function as well. It resembles a rectified co-sinus, also exhibiting short negative spikes that reflect the crystallographic dis-orientation of the polycrystalline material.

Research on Variable Weight Synthesizing Model for Transformer Condition Assessment

Transformer is one of the important equipment in the power grid, which helps to integrate renewable energy into the transmission and distribution network efficiently. The safe and stable operation of transformer is of great importance for the reliable transmission of electricity generated from renewable energy and for the reliable use of electricity by the end users. Therefore, it is important to assess the condition to avoid the faults of the transformer. In this paper, a variable weight synthesizing assessment model is presented that combines the G1 method, the entropy weight method, and a variable-weight method proposed in this paper to assess the condition of transformer based on the offset of the transformer equivalent circuit parameters. First, we propose deterioration indexes oriented to the maintenance management needs, which can well reflect the degree of deterioration of each transformer component. Second, the various defects of the transformer are used as the assessment indexes, and the initial weight is given to the assessment indexes according to the damage degree of the defect. The initial weight is calculated comprehensively by the G1 method and the entropy weight method. Then, each index is scored according to the offset of the equivalent circuit parameters, and the weights are adjusted appropriately according to the scores of the indicators using a variable weighting method to emphasize the severity of the defect or the “sub-health” condition of the transformer. Finally, the respective scores and combined weights of the assessment indexes are weighted to obtain a comprehensive score. The simulation shows that the model is more sensitive to abnormal and “subhealth” conditions of the transformer, which verifies the feasibility of the variable weight synthesizing model to assess the condtion of the transformer.

Influence of saturation levels on transformer equivalent circuit model

Abstract This paper presents a modelling approach for a transformer with different saturation levels. First, the magnetic field distributions at different saturation levels in the transformer are analyzed by using numerical simulations. Then, the characteristics of the leakage magnetic flux are analyzed, and the magnetic circuits with varying leakage reluctance topologies are modeled. Finally, based on the mature duality relationship between electric and magnetic circuits, the equivalent electric circuit models are obtained. These kinds of models embody the effect of different saturation levels on the connection points of the leakage flux branches, and it can fully reflect the various working states of the transformer. The accuracy of the models is verified by comparing the circuit simulation results with those of FEM transient simulations.

STUDY OF THE NATURE OF OVERVOLTAGES IN THE ELECTRICAL NETWORK ARISING FROM VOLTAGE TRANSFORMERS

A non-linear dynamic mathematical model of voltage transformer has been considered and overvoltages arising on the elements of voltage transformer equivalent circuit during transient processes have been investigated. The influence of voltage transformer secondary circuit capacitance on overvoltage multiplicity in the primary circuits and the duration of transients has been determined. The advantages of approximation of nonlinearity of voltage transformers by hyperbolic sine are used. Mathematical expressions determining the nature of changes in the forced and free components of the transient process in an electrical network with a voltage transformer have been obtained. It is shown that with the increase of the electric network capacitance the duration of the transition process damping increases and the frequency of the forced oscillations and the level of overvoltage decrease. It is proved that even small, in comparison with the primary nominal sinusoidal voltage, aperiodic components of the voltage transient process can lead to significant overvoltages during voltage transformer outages. It has been substantiated that both the secondary resistance and the switching torque influence the overvoltage multiplicity arising in the primary winding of voltage transformers. It is shown that the closed secondary winding worsens the disconnection process of non-linear inductance of voltage transformers. The values to which overvoltages increase in this case are determined. According to the results of calculations it is determined that with open secondary winding of voltage transformers the duration of transient process significantly increases. It has been found that the decrease of frequency of forced oscillations, which occurs in this case, is accompanied by an increase of currents in the primary winding of the voltage transformer, which is dangerous in terms of thermal stability of the winding insulation. It is shown, that closing the secondary winding of voltage transformers leads to significant reduction of transient damping time. It is suggested that this algorithm can be used to provide a rapid breakdown (suppression) of ferroresonant processes. The effectiveness of such a measure of stopping of ferroresonance processes as short-term shunting of secondary winding of voltage transformers has been investigated. The correlation of parameters of electric networks (capacity of busbar sections, nonlinearity of characteristics of voltage transformers, disconnection torque, etc.) at which ferroresonance process may occur and consideration of which may allow, in terms of prevention of ferroresonance processes, to identify substations (electric networks) that require more detailed research has been determined. The results of analytical studies were tested in the electric networks of JSC "Kharkivoblenergo" and used in the electricity distribution system for the selection of specific voltage transformers for certain configurations of electrical networks.

Transformation of Transient Overvoltages by Inductive Voltage Transformers.

Overvoltage transients occur after any type of switching activity in a power network, such as breaker operation, fault occurrence/clearance and rapid load change. This distortion of voltage is transformed to the secondary circuit of a voltage transformer. The maximum values of such impulses may many times exceed the rated value of its secondary voltage. This can lead to malfunction of measuring or protection devices connected to the secondary circuit of a voltage transformer and even their damage. The paper presents the application of determined values of ratio error at harmonics of the inductive voltage of the transformer to predict the value of transformed slow-front transient overvoltage to their secondary circuits. This will help to prevent malfunction of measuring or protection devices connected to the secondary side of the voltage transformer and increase their safety of operation. The inductive voltage transformer equivalent circuit for transformation of higher frequency components of distorted voltage must be extended with internal capacitances of windings. This is caused by the fact that the resonance phenomenon of the slow-front transient overvoltage results from leakage inductance and capacitance of primary winding, not from the magnetic core. Therefore, this behaviour is independent from the value of the applied voltage.

Once again about the indivisibility of the scattered inductance of the transformer

Purpose. The purpose of the article is to show the inadequacy of the traditional T-shaped equivalent circuit for modeling transformer operations with saturated core. The aim is to point out the unreasonableness of the separation of the transformer leakage inductance into components. The aim is also to explain the need to apply the П-shaped transformer equivalent circuits to transformers with two and three windings with finite radial thickness.
 Methodology. Analysis of magnetic fields in the transformer window and simulation of transient processes in equivalent circuits of the transformer using a preprocessor ATPDraw to the program ATP.
 Findings. The unfoundedness of the well-known T-shaped transformer equivalent circuit is shown. Differences in the processes in the core legs and yokes when transformer is connected to the network and during short circuits of the windings are noted. Equivalent circuits of a transformer with two and three windings of finite thickness are proposed, reproducing these differences.
 Originality. The absence of physical meaning in dividing the transformer leakage inductance into components is stated. The advantages of the П-shaped equivalent circuit are shown when calculating inrush currents accompanying the transformer switching to the network on its inner and outer windings.
 Practical value. We show theoretical insolvency and practical unsuitability of the Т-shaped equivalent circuit for studying transformer operations accompanied by saturation of the magnetic circuit. Advantages of the П-shaped equivalent circuit are clarified.

Slime Mold Optimizer for Transformer Parameters Identification with Experimental Validation

The problem of parameters identification for transformer equivalent circuit can be solved by optimizing a nonlinear formula. The objective function attempts to minimize the sum of squared relative errors amongst the accompany... | Find, read and cite all the research you need on Tech Science Press

The Simulation Analysis on the Transient Process of Transformer

Power transformer is one of the important equipment in the power grid, we must ensure its reliable operation. To achieve that goal, the insulation property of power transformer must be fine, for its breakdown mainly caused by the insulation damage. When the power transformer suffered from the lightning surges, the windings insulation is damaged easily, so we should optimize and design on the power transformers windings insulation structure. Firstly, the computational methods of the inductance, capacitance and the resistance parameter were introduced in this paper, then the inductance, capacitance and the resistance parameters of a SFP-180000/220 three-phase transformer were calculated. Based on the equivalent circuit of transformer, the circuit model in the Matlab was established and simulated when the neutral is grounded or insulated respectively. The relevant initial potential distribution, the oscillating potential distribution, and the final potential distribution were gotten by the simulation. Finally, the characteristics of each potential distribution were analysed, which could provide some references to the insulation structure design for transformers.

Multi-regional modeling and operational analysis of LC/S-compensated inductive wireless power transfer link with load-independent current output

When feeding a constant-resistance or constant-voltage type load, inductive wireless power transfer link (IWPTL) operating as current source is typically desired. Moreover, in case coupling coefficient between transmitter and receiver is constant, load-independent current output (LICO) characteristics are beneficial, allowing the system to operate without feedback. Moreover, near zero phase angle (ZPA) operation is also valuable, allowing to minimize volt-ampere rating of the transmitting-side inverter. A new LC/S compensated IWPTL topology, capable of simultaneously achieving LICO and ZPA, was recently revealed in the literature. The proposed compensation network consists of one inductor and two capacitors. This paper generalizes the LC/S compensated IWPTL topology by first deriving the compensating elements set based on a novel loosely-coupled transformer (LCT) equivalent circuit and then enlightening that for certain values of primary compensation inductor, secondary compensation capacitor should either be omitted or replaced by an inductor in order to preserve LICO and ZPA. Thus, an LC/S compensated IWPTL may actually operate in three different regions, each calling for specific sub-type of LC/S compensation. Design guidelines for compensation parameters selection are provided in this paper, allowing to achieve virtually any value of load-independent current output for a given LCT coils pair. Moreover, expressions for calculating normalized component stresses are obtained for all three regions of operation, taking into account nonlinear nature of transmitting-side inverter and receiving-side rectifier, as opposed to typical phasor-domain based approach, which ignores higher-order harmonics. Analytical results based on obtained expressions are well-supported by their real-time-domain counterparts.

Computation of Power Transformer Reactance using Finite Element Method

The reactance of the transformer windings is an important component for the design which has a direct effect on its operation. Reactance is used for computation of not only the transformer equivalent circuit parameters and also for designing its protection. The Roth’s method, Rabin method, method of images, and classical methods are the traditional methods used for its calculation. The finite element method can be used for the calculation of transformer reactance. In the industrial revolution 4.0 all manufactured transformers would be evaluated through their 3D design and performance analyzed by computational methods. In this work the reactance calculated by the finite element method has been compared to that calculated by the classical method. The calculated values of energy stored in the windings and other parts and the reactance can be found.

Identification of transformer equivalent circuit parameters for transients simulation

The paper deals with experimental identification of transformer equivalent circuit parameters for simulation purpose. Dependences of transformer voltage and power from primary winding current in open circuit configuration were measured. Current to voltage characteristic of magnetic losses nonlinear resistor, flux to current characteristic of magnetic core, resistance and leakage inductance of primary and secondary windings of one-phase transformer were calculated from the measured parameters. Equivalent circuit of the transformer allowing calculation of transformer transients, such as inrush and overload, was obtained as a result.

Estimating Power Transformer High Frequency Model Parameters Using Frequency Response Analysis

Frequency response analysis (FRA) has become a widely accepted technique by worldwide utilities to detect winding and core deformations within power transformers. The main drawback of this technique is its reliance on the personnel level of expertise more than standard or automated codes. To establish reliable FRA interpretation codes, accurate high frequency transformer model that can emulate the frequency characteristics of real transformers in a wide frequency range is essential. The model can be used to investigate the impact of various winding and core deformations on the transformer FRA signature. The transformer equivalent high frequency electric circuit parameters can be calculated based on design data, which are rarely available, especially for old transformers. As such, this paper presents an artificial intelligence technique to estimate these parameters from the transformer FRA signature. The robustness of the proposed technique is assessed through its application on three, 3-phase power transformers of different ratings, sizes, and winding structures to estimate their high frequency electric circuit parameters during normal and fault conditions. Results show that the proposed technique can estimate equivalent circuit parameters with high accuracy and helps interpret the FRA signature based on the numerical changes of these parameters. The main advantage of this approach is the physical meaning of the model parameters facilitates reliable identification of various faults and hence aids in establishing reliable interpretation codes for transformer FRA signatures.

Theoretical and Simulation Study on On-line Monitoring Technology of Transformer Short-Circuit Impedance

Based on the equivalent circuit of transformer, this paper deduces the calculation method of short-circuit impedance of three-phase transformer based on multiple measurement data. Taking a single-phase transformer as the research object, the ‘magnetic field-circuit’ simulation model is established. The normal operation and winding deformation caused by different axial displacements are simulated and analyzed. The results show that short-circuit impedance changes when transformer winding is axially deformed, and the degree of change is related to the degree of deformation. Compared with the normal situation, the short-circuit impedance increases by 52.1% when the four transformer coils are moved 15 mm each. Therefore, on-line monitoring of the transformer short-circuit impedance can reflect the abnormal deformation of the transformer winding to a certain extent.

GIC calculation of Gansu power grid based on Power World

The geomagnetic induced current (GIC) caused by the geomagnetic storm flows into the transformer, which will saturate the transformer.It will cause the system’s reactive power loss and harmonic increase, which will adversely affect the operation of the transformer. Therefore, it is of great significance to study the impact of GIC on the power grid. In this paper, the calculation method of grid GIC and the transformer equivalent circuit model are given. The Gansu power grid GIC is calculated by using Power World Simulator. Finally, based on the contour plot, the distribution law of GIC in Gansu Power Grid is analyzed.