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Figure 2. Developed 2D FEM model: 40 MVA 88/11 kV. The assessment of the winding Eddy losses using 3D FEM would yield unerring results; however, the computational complexity would widen. Fortunately, in many instances, an alleviation of 2D is feasible without appreciable imprecision. The 2D FEM technique is the most prevalent in the computation of the Eddy losses. By taking into consideration transformer symmetry, one-half of the transformer can be modelled in contrast to the entire unit. The ability of higher-order elements to capture complex data representation is employed to enhance the accuracy of the field solution. The case studies presented herein have been simulated using plane axisymmetric solutions. The main components of the developed FEM model are demonstrated in Figure 2. — Figure 2 Developed 2D FEM model: 40 MVA 88/11 kV. The assessment of the winding Eddy losses using 3D FEM would yield unerring results; however, the computational complexity would widen. Fortunately, in many instances, an alleviation of 2D is feasible without appreciable imprecision. The 2D FEM technique is the most prevalent in the computation of the Eddy losses. By taking into consideration transformer symmetry, one-half of the transformer can be modelled in contrast to the entire unit. The ability of higher-order elements to capture complex data representation is employed to enhance the accuracy of the field solution. The case studies presented herein have been simulated using plane axisymmetric solutions. The main components of the developed FEM model are demonstrated in Figure 2.

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Figure 1. Comparison of the winding Eddy loss correction functions.

Figure 3. 40 MVA, 88/11 kV transformer field solution. In Figure 3, a field solution of a 40 MVA, 88/11 kV transformer is presented. It is observed that the magnetic flux leakage between the LV and HV projects upwards and curves radially across the windings. The magnetic flux leakage is further more concentrated at the interface between the windings and then declines observed to be o diverge away from the winding interspace. As a result of the high magnetic core permeance, the inner LV winding has a significant inclination to draw the magnetic flux leakage. On the HV winding, the magnetic flux leakage is segregated among the tank walls, flitch plate, core clamping structure, and other metallic structures.

Figure 4. No-load loss test arrangement drawing. The no-load and loss measurements at the manufacturer’s premises were performe in accordance with the IEC 60076-7 standard [20-23] to attain the copper losses and th no-load losses at a fundamental frequency (50 Hz) and current. The arrangement drawin, of the no-load and load loss test is illustrated in Figures 4 and 5, respectively.

Figure 5. Load loss test arrangement drawing.

Table 2. Estimated losses per disc (W/m) on the LV winding—Case 1

Table 3. Losses in metallic structures—Case 1.

Table 4. Measured rated losses (kW)—Case 1. The developed 2D FEM model can further be employed to compute the hotspot factor of the windings. This factor can be estimated as the density of the maximum winding loss that triggers the hotspot temperature to the average winding loss. The estimation of the HSF for the LV winding can then be estimated as shown below in Equation (22).

Table 5. Estimated losses per disc (W/m) on the LV winding—Case 2 Table 6. Losses in metallic structures—Case 2.

Table 7. Measured rated losses (kW)—Case 2.

It can be observed that the supplied harmonic profile has a significant third and fifth 1armonic content. If a new transformer is designed to facilitate a solar PV application with | significant harmonic content, it must be specified with a harmonic current profile, as neasured at the point of common coupling. The electrical designer cannot estimate nor an the IPP require the designer to apply standard harmonic current distribution tables. n case the harmonic profile of the load to be supplied by a transformer is unknown, hen the IPP and the electrical designer are likely to suffer from short unit service life ind premature failure. Subsequently, adequate measures must be undertaken in order to ruarantee a conservative design for solar PV plant application. Guiding principles on how his information can be applied to establish adequate unit sizing are also detailed in the ubsequent section.

Figure 6. Harmonic current profile.

Table 8. Computation of the harmonic loss factor (IEEE Std. C57.110-2018). In Table 8, the computation of the harmonic loss factors based on the IEEE Std. C57.110- 2018 are presented by contemplating the supplied harmonic spectrum in Figure 6. For an existing unit, this method presumes that the winding currents are measured at the rated currents of the unit in-service.

Table 9. Computation of the harmonic loss factor. In order to calculate the total increased losses on account of the supplied harmonic profile, a 40 MVA, 88/11 kV transformer, presented as Case study 1 in the previous section, are examined and tabulated. This transformer has a full load current of 2099A on the LV winding and the winding Eddy loss at the region of peak loss ratio is 11% of the local copper loss. To calculate the load losses in Table 9 under the supplied harmonic current profile, the rated loss components are carried out as follows in Equation (24).

Table 10. Computation of the harmonic loss factor (Emanuel et al.). It follows that the effective winding Eddy loss is the ratio of column 6 and column 3 above, yielding 8.426. The total particular standardized losses are 2.378. The value of the maximum harmonic load current producing this loss as a sinusoidal current is 0.759 and the maximum permissible per-unit harmonic load current provided the supplied harmonic current is 1593 A. Consequently, with the supplied harmonic current profile, the studied transformer capability is estimated at 75.8% of the rated full-load current capability, or 1593 :.A.

Table 11. Computation of the harmonic loss factor (Thango et al. method). It follows that the effective winding Eddy loss is the ratio of column 6 and column 3 above, yielding 6.948. The total particular standardised load loss is 2.178 and the value of the maximum harmonic load current producing this loss as sinusoidal current is 0.793, calculated using Equations (22) and (23). The maximum permissible per-unit harmonic load current provided the supplied harmonic current i is 1665 A. pan ai a ae tif . po” rf

Figure 7. Harmonic loss factor comparison (conductor dimension of 6.4 mm). Figure 7 presents a graphical comparison of the different correction factor methods. The figure demonstrates the significance of the proposed winding Eddy loss factor where the factors are presented with respect to the harmonic order for the compared methods.

Table 12. Harmonic loss factor comparison.

Table 13. Computation of the K-Factor. Provided with the harmonic current profile, the initial step is to calculate the r.m.s load current on a per-unit basis, which is 1.234 in this instance. Subsequently, the squares of the proportional values for individual harmonic currents are evaluated, carrying out the K-Factor. Based on the K-Factor value of 8.144 and the range of rating, the studied unit can be specified as a K-9 rating transformer. The maximum permissible p.u harmonic load current with the given harmonic profile is 1890 A. The amount of derating necessary for the studied unit to handle the supply of the considered harmonic current profile is calculated in Table 14.

Table 14. Computation of the Factor-K. The initial step to determine the Factor-K is to ascertain the value of e, which is the ratio of the winding Eddy loss to the load losses at a fundamental frequency of 50 Hz. The electrical designer should be able to supply this value; alternatively, the value ranges from 0.05 to 0.1. In this case study, a value of 0.01 is applied. The empirical exponent q. is heavily reliant on the transformer design and is generally obtainable from the manufacturer. This value ranges from 1.5 to 1.7, and a value of 1.7 is considered in this case study. Finally, the transformer would need to be de-rated to 85. 52% (1/1.17) of the nominal power rating, which is 34. 21 MVA when supplying this spectrum.

Table 15. Derating factor comparison. The amount of derating by the methods above yields an error of estimate of 11% and 17.6%, respectively, on the adequate power rating supply for the supplied harmonic current profile. The maximum permissible harmonic load current increases by 30.45% and 11%, respectively.

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