Transformers copper losses

Note that when we come to designing off-line transformers, for various reasons like reducing high-frequency copper loss, reducing size of transformer, and so on, it is more common to set r at around 0.5. So the primary-side inductance must then be (from the L x I rule)... 

As a corollary, the core loss in the transformer is independent of the input voltage. The copper loss, on the other hand, is always worse at low inputs (except for the dc-dc buck) — simply because the average input current has to increase so as to continue to satisfy the basic power requirement Pin = Vin x Iin = Po-... 

Though we can pick any specific input voltage point for assuring ourselves that the core does not saturate anywhere within its input range, since the copper loss is at its worst at Vinmin, we conclude that the worst-case for a forward converter transformer is at Vinmin For the choke, it is still Vinmax-... 

Figure 4d shows the equivalent x-0.158 material, prepared by copreclpltatlon. In this sample, the large, smooth, dark areas are replaced by 5-10 pm chunks. These contain Y, Ba, Cu, and traces of Ca, and Sr, as In the composite sample, but they also contain a trace of bismuth. The presence of B1 may Induce the Y-123 phase to adopt the tetragonal structure seen In the x-ray pattern of this siaterlal. This behavior has been observed In Y-123 that has been doped with iron (3-6) as little as a 2% substitution of iron for copper in Y-123 can lead to an orthorhomblc-to-tetragonal transformation, without loss of superconductivity. The Region B particles are also present In the coprecipitated sample and have a similar Y-Bl-Ba composition (with traces of Ca and Cu) to those seen In the composite material. 

While an increased kV A requirement is a direct burden on the supplier, it does not increase the kW consumption by the user. Generation and transmission losses, however, are proportional to the kV A transferred, and we saw in Section 8.3.1.1 that copper losses in transformers are proportional to the square of the kV A load. The same is true of the resistive losses in the generators, overhead lines, and cables. These losses do show up in the true power (i.e., kW) consumption of a utility supplier s system. 

Voltage control is accomplished with an AC transformer by means of a stator and a rotor. As a result, a given input voltage can be infinitely varied to poduce an output voltage under power. Somewhat higher losses result from the combination of a fixed and a rotary transformer. This condition results in conversion losses in the form of magnetization and copper losses due to the combination of the transformer systems. 

As they have no moving parts causing frictional losses, most transformers have a very high efficiency, usually better than 90%. However, the losses which do occur in a transformer can be grouped under two general headings copper losses and iron losses. 

The term channel induction furnace is appHed to those in which the energy for the process is produced in a channel of molten metal that forms the secondary circuit of an iron core transformer. The primary circuit consists of a copper cod which also encircles the core. This arrangement is quite similar to that used in a utdity transformer. Metal is heated within the loop by the passage of electric current and circulates to the hearth above to overcome the thermal losses of the furnace and provide power to melt additional metal as it is added. Figure 9 illustrates the simplest configuration of a single-channel induction melting furnace. Multiple inductors are also used for appHcations where additional power is required or increased rehabdity is necessary for continuous operation (11). 

Six iron anodes are required for corrosion protection of each condenser, each weighing 13 kg. Every outflow chamber contains 14 titanium rod anodes, with a platinum coating 5 /tm thick and weighing 0.73 g. The mass loss rate for the anodes is 10 kg A a for Fe (see Table 7-1) and 10 mg A a for Pt (see Table 7-3). A protection current density of 0.1 A m is assumed for the coated condenser surfaces and 1 A m for the copper alloy tubes. This corresponds to a protection current of 27 A. An automatic potential-control transformer-rectifier with a capacity of 125 A/10 V is installed for each main condenser. Potential control and monitoring are provided by fixed zinc reference electrodes. Figure 21-2 shows the anode arrangement in the inlet chamber [9]. 

Martensitic phase transformations are discussed for the last hundred years without loss of actuality. A concise definition of these structural phase transformations has been given by G.B. Olson stating that martensite is a diffusionless, lattice distortive, shear dominant transformation by nucleation and growth . In this work we present ab initio zero temperature calculations for two model systems, FeaNi and CuZn close in concentration to the martensitic region. Iron-nickel is a typical representative of the ferrous alloys with fee bet transition whereas the copper-zink alloy undergoes a transformation from the open to close packed structure. ... 

Dezincification is readily apparent, since the yellow colour of the brass is replaced by the characteristic red of copper, which may take the form of small plugs or of layers that in some cases can extend over the whole of the surface (Fig. 1.60). In plug-type dezincification a mechanically weak, porous residue of copper is produced, which may remain in situ or become removed by the pressure of water, leading to a perforation. In the layer type the transformation of the alloy into a mechanically weak layer of copper results in loss of strength, and failure may occur by splitting when the metal is subjected to water pressure or to external stress. 

In addition to their formation by transformation of smaller ring heterocycles, oxazepines are capable of contraction as demonstrated by the carbene transformation of the oxazepane dione (97) in the presence of catalytic amounts of copper or rhodium to the dihydropyrrolone (98) by loss of C02 <95AG(K)78)>. 

Apart from copper(I)-mediated reactions, few studies of the treatment of vinyliodonium salts with carbanions have appeared. The vinylations of the 2-phenyl- and 2- -hexyl-l,3-indandionate ions shown in equations 222 and 223 are the only reported examples of vinyliodonium-enolate reactions known to this author26,126. ( ,)-l-Dichloroiodo-2-chloroethene has been employed with aryl- and heteroarvllithium reagents for the synthesis of symmetrical diaryliodonium salts (equation 224)149,150. These transformations are thought to occur via the sequential displacement of both chloride ions with ArLi to give diaryl (/ -chlorovinyl)iodanes which then decompose with loss of acetylene (equation 225). That aryl(/ -chlorovinyl)iodonium chlorides are viable intermediates in such reactions has been shown by the conversion of ( )-(/ chlorovinyl)phenyliodonium chloride to diaryliodonium salts with 2-naphthyl- and 2-thienyllithium (equation 226)149,150. 

To check the hypothesis that steam causes volatilization of copper, nickel and cobalt, two experiments were performed with a clean X-AI2O3 slice above a NiO/a-Al2C>3 sample [29]. The sample and the slice were separated from each other by two pieces of platinum wire (0 0.25 mm). The experimental set-up is shown in the inset of fig, 6, After treatment at 1000 °C for 70 hours in N2/O2/30% HjO or a dry N2/O2 gas flow, the bottom side of the upper a-AI2O3 slice was analyzed with RBS (figure 6). Clearly, in the presence of steam some nickel had been deposited onto the slice, but when steam had been absent no nickel was detected. We thus conclude that some nickel species, formed under the influence of steam, disappeared from the Ni0/a-Al203 sample into the vapour phase. We attribute this loss to the formation of volatile metal hydroxides 29,30. This is supported by Fourier Transform Infra Red (FTIR) Spectroscopy experiments [31]. 

For example, the works cited in the review [11] showed that the mentioned processes are very sensitive to the deviations of the component ratio Me(II) Me(III) in solution from the stoichiometry corresponding to the composition of the final product M"M" 204. When the composition deviates from stoichiometry, the co-precipitated hydroxides appear to be mechanical mixtures only. On contrary, when the composition exactly corresponds to the stoichiometry of the final product, chemical interaction occurs resulting in the formation of nano-sized X-ray amorphous product. This is evident by the data on the loss of chemical individuality of co-precipitated hydroxides. For example, in co-precipitated mixtures, like Cu(OH)2 - Me(OH)j, copper hydroxide becomes insoluble in ammonia and is not transformed into CuO under heating. For some oxides bound in this manner, the braking of dehydration is observed. X-ray amorphous product obtained by coprecipitation can be crystallized in the form of double hydroxide or even as a complex oxide. 

Amino acid synthons can be prepared from iodoalanine with no loss of optical integrity (Scheme 48). The amino acid was transformed into a novel zinc reagent through reductive metallation with a zinc-copper couple in benzene/dimethyl acetamide. This organometallic was acylated under palladium catalysis in good overall yield. ... 

For styrene-based random copolymers, functional groups can be introduced into the polymer chains via copolymerization with functional styrene derivatives, because the electronic effects of the substituents are small in the metal-catalyzed polymerizations in comparison to the ionic counterparts. Random copolymer R-6 is of this category, synthesized from styrene and />acetoxystyrene.372 It can be transformed into styrene// -vinylphenol copolymers by hydrolysis.380 The benzyl acetate and the benzyl ether groups randomly distributed in R-7 and R-8 were transformed into benzyl bromide, which can initiate the controlled radical polymerizations of styrene in the presence of copper catalysts to give graft copolymers.209 Epoxy groups can be introduced, as in R-9, by the copper-catalyzed copolymerizations without loss of epoxy functions, while the nitroxide-mediated systems suffer from side reactions due to the high-temperature reaction.317... 

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