Transformer No-load Losses Research Articles

Расчет характеристик маломощных трансформаторов по каталожным данным

The article proposes an algorithm for calculating the characteristics of low-capacity (up to 5 kVA) transformers for the given values of power supply voltage, its frequency, current, and load type (power factor) through the use of solely catalogue data and without resorting to iteration procedures (as is known, the datasheets provided for such transformers contain a fewer number of parameters than that for transformers of a larger capacity). The calculations make it possible to avoid the need of determining the transformer characteristics by experiment. The transformer characteristics computation algorithm includes means for determining the equivalent circuit parameters and the transformer no-load and short-circuit power losses, as well as means for taking into account the nonlinear dependence of the no-load current on the power supply voltage. The nonlinear characteristics are taken into account in calculating the relative magnetic flux value in the transformer core and in calculating the relative magnetization current value from the relative magnetization and no-load current characteristic. By using the proposed algorithm it is possible to calculate the characteristics of transformers of any capacity. An example of calculating the transformer characteristics from catalogue data is given.

Optimization of High Voltage Distribution System

This study presents a technique applied during the conversion of an existing Low Voltage Distribution System into a proposed High Voltage Distribution System in a radial distribution network. High Voltage Distribution System optimization is demonstrated using linear programming techniques in MATLAB optimization toolbox. An application has been developed to illustrate the methodology. The optimization technique estimates the optimal number of unit transformers in the proposed network which is equivalent to a bulk transformer in the existing network. Results showed that the optimization process produced nine 16 kVA and four 25 kVA unit transformers which is equivalent to a 315 kVA bulk transformer. This procedure is effective for converting the bulk transformer in the existing network into an equivalent population of unit transformers in the proposed network. To achieve the benefit of the conversion process, High Voltage Distribution System optimization has been recommended to minimize transformer no-load losses. As a result, the economy of distribution transformers is improved by savings in operational cost.

Influence of voltage harmonics on transformer no-load loss measurements and calculation of magnetization curves

This paper investigates the voltage distortion phenomenon during no-load testing of transformers, its influence on no-load loss calculations, and a novel measurement technique that is unaffected by harmonics for obtaining transformer magnetization curves. Owing to economic reasons, no-load loss correction for distorted test waveforms has been addressed to some extent in existing standards, while not much has been done on the aspect of calculation of magnetization characteristics. This is important for parameter estimation and transformer modeling in power system transient simulations. Results from two test cases are presented, one is based on factory testing with 290-MVA, three-phase, three-legged power transformer and second is a more comprehensive analysis using a laboratory test setup with a 22-kVA single-phase transformer. Application of loss correction equations and limits based on existing testing standards was evaluated and found to result in overcompensation, while calculation of magnetization curves based on existing methods resulted in error up to 20%. Whereas, application of proposed measurement technique based on voltage “Zero-Crossing” detection is shown to result in negligible error. The proposed measurement technique uses the same input signals as in a standard no-load test procedure. Hence, it can be easily implemented in parallel with existing instrumentation.

Reduction of Power Grid Losses by Using Energy Efficient Distribution Transformers

The importance of distribution transformer no-load loss on the operation of modern electrical grids is often underestimated. Internationally, distribution transformer no-load loss constitutes nearly 25% of the transmission and distribution losses of electrical grids. The losses in European Union distribution transformers are estimated at about 33 TWh/year whereas, reactive power and harmonic losses add a further 5 TWh/year. In the Greek electrical grid the no-load losses of 140,000 distribution transformers are estimated at about 490 GWh/year. This paper has two goals the first one is to illustrate the significance of distribution transformer no-load loss in periods of high electric energy cost and the second goal is the presentation of a novel numerical methodology for wound core transformers no-load loss analysis, enabling to determine the economically and technically optimum transformer for every use.

Experimental and Numerical Investigation of Flux Density Distribution in the Individual Packets of a 100 kVA Transformer Core

The accurate measurement and calculation of transformer no-load losses is of high importance to transformer users and manufacturers alike. There are various ways of calculating no-load losses of transformers based on empirical formulas and experimentally obtained coefficients but these tend to mostly apply to known and tested core designs. The most important factors that contribute to the no-load loss of transformer cores are the grade of steel used, the core and corner geometry and stacking configuration. This paper presents re- sults and analysis for a 100 kVA, 3-phase model transformer core, consisting of 11 packets of different width laminations, over a range of flux densities up to 1.8 T. The results show the average magnetic flux desnity across the core cross section as well as the magnetic flux density of the individual packets. Using this information in combination with the magnetising current the no-load loss can be derived for the whole core as well as for the individual packets. The paper also shows numerical calculations of the excitation current required to magnetise the core. The FEA software used was developed in ALSTOM and allows the calculation of flux density distribution as well as the determination of the magnetising current necessary to magnetise the core at different flux density levels. It is believed that the combination of measurements and FE modelling will enable the calculation of local power loss thus allowing for optimisation of the various core parameters.

Power Transformer No-Load Loss Prediction with FEM Modeling and Building Factor Optimization

Estimation of power transformer no-load loss is a critical issue in the design of distribution transformers. Any deviation in estimation of the core losses during the design stage can lead to a financial penalty for the transformer manufacturer. In this paper an effective and novel method is proposed to determine all components of the iron core losses applying a combination of the empirical and numerical techniques. In this method at the first stage all computable components of the core losses are calculated, using Finite Element Method (FEM) modeling and analysis of the transformer iron core. This method takes into account magnetic sheets anisotropy, joint losses and stacking holes. Next, a Quadratic Programming (QP) optimization technique is employed to estimate the incomputable components of the core losses. This method provides a chance for improvement of the core loss estimation over the time when more measured data become available. The optimization process handles the singular deviations caused by different manufacturing machineries and labor during the transformer manufacturing and overhaul process. Therefore, application of this method enables different companies to obtain different results for the same designs and materials employed, using their historical data. Effectiveness of this method is verified by inspection of 54 full size distribution transformer measurement data.

Harmonic Impact on Distribution Transformer No-Load Loss

The losses in European Union distribution transformers are estimated at about 33 TW ·h/year, whereas reactive power and harmonic losses add a further 5 TW ·h/year. The reduction of distribution transformer no-load loss is particularly important as the ratio of no-load to load losses is nearly three. In this paper, the no-load operation of wound-core transformers under sinusoidal and distorted supply-voltage conditions is investigated. For that purpose, a 2-D nonlinear transient finite-element analysis taking into account hysteresis has been developed. The hysteresis model is based on a modified Jiles-Atherton representation, and the proposed analysis is compared to experimental data.

Differential evolution solution to transformer no-load loss reduction problem

After the completion of core manufacturing and before the assembly of transformer active part, 2N small individual cores and 2N large individual cores are available and have to be optimally combined into N transformers so as to minimise the total no-load loss (NLL) of N transformers. This complex combinatorial optimisation problem is called transformer no-load loss reduction (TNLLR) problem. A new approach combining differential evolution (DE) and multilayer perceptrons (MLPs) to solve TNLLR problem is proposed. MLPs are used to predict NLL of wound core distribution transformers. An improved differential evolution (IDE) method is proposed for the solution of TNLLR problem. The modifications of IDE in comparison to the simple DE method are (i) the scaling factor F is varied randomly within some range, (ii) an auxiliary set is employed to enhance the population diversity, (iii) the newly generated trial vector is compared with the nearest parent and (iv) the simple feasibility rule is used to treat the constraints. Application results show that the performance of the proposed method is better than that of two other methods, that is, conventional grouping process and genetic algorithm. Moreover, the proposed method provides 7.3% reduction in the cost of transformer main materials.

Normal Flux Distribution in a Three-Phase Transformer Core Under Sinusoidal and PWM Excitation

Transformer no-load loss and noise have been reduced considerably because of improved core material and improved core design. The variation of normal or interlaminar flux distribution (z direction) in a three-phase transformer core has been measured under pulse width modulation (PWM) excitation (no-load) with switching frequencies in the range of 1-3 kHz. The planar eddy current loss and attractive interlaminar force were analyzed for selected values of modulation index and magnetization condition (frequency 50 Hz; induction 1.5 T). Results showed significant reduction of the planar eddy current component and attractive interlaminar force for low modulation index with increasing switching frequency

Correction of power transformer no-load losses, measured under nonsinusoidal voltage waveforms

A method to calculate the iron losses in power transformers with highly distorted supply voltages is introduced. The appearance of small loops inside the main hysteresis loop is analysed and a method is proposed that takes into account the relative height of the small loops, as well as the position of the small loops inside the main loop. The percentage of hysteresis and eddy current losses in the total no-load loss is evaluated. Results obtained by means of different methods of calculation are compared to the 50/50 criterion. This method is proposed for correcting the no-load losses measured in transformer tests when the applied voltage is highly distorted. An experiment corroborates the corrective method proposed.

Approximating the system losses equation (power systems)

A methodology that develops a quadratic equation to express power system losses based on hourly system loads, transformer no-load loss data, and corona loss data is presented. The data are readily available, often from a utility's Federal Energy Regulatory Commission (FERC) Form 1. Correct application of the equivalent hours loss factor is required by the methodology. A specific utility was selected, data were derived, and an equation developed and verified. This entire procedure is documented here. >

Approximating the System Losses Equation

It is possible to quickly approximate the system losses equation in parabolic form from data readily available to the engineer. This approximation is adequate in a variety of applications, particularly rate analyses and cost-of-service studies, for which losses are used by the utility engineer. The methodology presented in the paper develops a quadratic equation to express system losses based on hourly system loads, transformer no-load losses data, and corona losses data. The data are readily available, often from a utility's Federal Energy Regulatory Commission (FERC) Form 1. Correct application of the equivalent hours loss factor is required by the methodology. A specific utility was selected, data derived, and an equation developed and verified. This entire procedure is documented in the paper.

An Application of Uncertainty Calculations to Distribution Transformer Loss Testing

The classical method of uncertainty calculation is presented as a means to evaluate the requirements for accurate measurement in performance testing of electrical equipment. Specific formulas are derived for transformer load loss and no-load loss measurements. The resulting expressions are then used to illustrate how the uncertainty calculation can provide insight into testing problems. A similar technique could be applied to any equipment performance test.