编号：时间：2021年x月x日书山有路勤为径，学海无涯苦作舟页码：第1页 共1页Selection and Rating of TransformersA). IntroductionThe number of non-linear loads which draw non-sinusoidal currents even if fed with sinusoidal voltage -connected to the power supply system is large and is continuing to grow rapidly. These currents can bedefined in terms of a fundamental component and harmonic components of higher order.In power transformers the main consequence of harmonic currents is an increase in losses, mainly inwindings, because of the deformation of the leakage fields. Higher losses mean that more heat is generatedin the transformer so that the operating temperature increases, leading to deterioration of the insulationand a potential reduction in lifetime.As a result, it is necessary to reduce the maximum power load on the transformer, a practice referred to asde-rating, or to take extra care in the design of the transformer to reduce these losses.To estimate the de-rating of the transformer, the loads K-factor may be used. This factor is calculatedaccording to the harmonic spectrum of the load current and is an indication of the additional eddy currentload losses. It reflects the excess losses experienced in a traditional wire wound transformer.Modern transformers use alternative winding designs such as foil windings or mixed wire/foil windings.B). Transformer lossesTransformer losses consists of no-load (or core loss) and load losses. This can be expressed by the equationbelow.where:PC = core or no-load loss,PLL = load lossPT = total loss.Core or no-load loss is due to the voltage excitation of the core. Although the magnetizing current doesinclude harmonics, these are extremely small compared with the load current and their effect on the lossesis minimal. Load losses are made up of I R loss, eddy current loss and stray loss, or in equation form:Where:IR = loss due to load current and DC resistance of the windingsPEC = winding eddy current lossPSL = stray losses in clamps, tanks, etc. The IR loss is due to the current flowing in the resistance of the windings. It is also called ohmic loss ordc ohmic loss. The ohmic loss is proportional to the square of the magnitude of the load current,including the harmonic components, but is independent of the frequency. It is determined by measuringthe dc resistance and calculating the resulting loss using the winding currents at full load.There are no test methods available to determine individual winding eddy current loss or to separatetransformer stray loss from eddy current loss. Instead, the total stray and eddy current loss is determinedby determining the total load loss and subtracting the calculated ohmic losses, i.e.,The eddy current loss is assumed to vary with the square of the rms current and the square of the frequency(harmonic order h), i.e.,Where:h = harmonic order, 1,2,3, etc.hmax = the greatest harmonic order to be consideredIh = current at harmonic order h, amperes h，IR = rated current, amperes，PEC,R = eddy current loss at rated current and frequency.The eddy current loss depends on the square of the conductor dimension perpendicular to the leakage fluxfield. At the ends of the winding the flux field bends and the larger dimension of the rectangular conductoris perpendicular to a vector component of the leakage flux field. Equalizing the height of die primary andsecondary windings, which can be achieved with any winding design, reduces the concentrated eddy lossat the winding ends. Using Foil windings or multiple strands per winding reduces both eddy current loss.Stray loss occurs due to the stray flux which introduces losses in the core, clamps, tank and other iron parts.Stray loss may raise the temperatures of the structural parts of the transformer. For dry-type transformersincreased temperatures in these regions do not contribute to an increase in the winding hot spot temperature. Stray losses are difficult to calculate and it is common to assume that the losses will vary as the square of the current times the frequency (harmonic order), as shown by:C). Transformers and K-factorThere are different approaches to accounting for additional losses in selecting a transformer. Here we would suggest the way applied by transformer manufacturers in conjunction with Underwriters Laboratories in the United States, it is to calculate the factor increase in eddy current loss and specify a transformer designed to cope; this is known as the K-factor.Where:h = harmonic numberIh = the fraction of total rms load current at harmonic number hMany power quality meters read the K-factor of the load current directly. Once the K-factor of the load isknown, it is a simple matter to specify a transformer with a higher K-rating from the standard range of 4, 9,13, 20, 30, 40, 50.Note that a pure linear load one that draws a sin