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Accurate and nonuniform CFD-based thermal behavior analysis of distribution transformers: voltage imbalance effect

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Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript


Thermal condition monitoring of distribution transformers (DTs) as the most important and expensive equipment of the power grid is undeniable, and by accurate investigation of its thermal status, its failure can be prevented because the insulation condition of the transformer is directly related to the hotspot temperature (HST). In this paper, accurate and nonuniform magnetic-thermal analysis of DT is proposed for precise HST prediction. In the magnetic analysis, the DT is modeled as a 2D axial symmetry, and the losses calculation of the windings has been fulfilled as a nonuniform. In the thermal analysis, the DT is modeled as 3D and nonuniform, and the conservator and core stacking, which has a considerable effect on the HST, is precisely modeled. By taking advantage of optical fiber sensors (OFSs) in the understudied 500 kVA DT, the accuracy of the proposed nonuniform 3D CFD-based modeling during the temperature rise test (TRT) is validated. The empirical evaluation results depict that the presented nonuniform CFD-based thermal analysis for HST prediction is very precise, and there is an appropriate vicinity to the experimental values. The error percentage of the proposed 3D CFD-based thermal analysis is 0.11% (0.1 °C) compared to the OFSs measurements, which demonstrates the precision and effectiveness of the presented modeling. Also, the verification of the results of nonuniform 3D CFD-based thermal analysis in top-oil temperature (TOT) and bottom-oil temperature (BOT) during the experimental TRT is fulfilled via thermography. According to the attained evaluated results, temperatures of 3D CFD-based thermal analysis and thermography in the noted two points are in good accordance with each other. In short, the error percentage is less than 0.65%, which indicates the correctness and proper performance of the proposed nonuniform 3D CFD-based modeling. Finally, the proposed nonuniform 3D model was subjected to voltage imbalance of 0.95, 1.05, 1.1, 1.15, and 1.2 of rated voltage. The results demonstrate the HST increases by − 0.4, 0.4, 0.9, 1.3, and 1.8 °C, respectively, over the original model without voltage imbalance, which represents that this issue should be considered in the design and operation of the DT.

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A :

Area [\({\mathrm{m}}^{2}\)]

\({c}_{p}\) :

Specific heat capacity \([\mathrm{J}/(\mathrm{ kg}\,\mathrm{ K})]\)

D :

Diameter [\(\mathrm{m}\)]

H :

Height [\(\mathrm{m}\)]

h :

Heat transfer coefficient [\(\mathrm{W}/ {(\mathrm{m}}^{2} \,\mathrm{K})\)]


Hotspot temperature [°C]

k :

Thermal conductivity \([\mathrm{W}/ (\mathrm{m}\,\mathrm{ K})]\)

L :

Length [\(\mathrm{m}\)]


Loading capacity increment (rated load + increment load) [kW]

m :

Mass [\(\mathrm{kg}\)]


Nusselt number

P :

Losses [\(\mathrm{W}\)]

Pr :

Prandtl Number


Rayleigh number

T :

Temperature [K], [°C]


Thickness [\(\mathrm{m}\)]

w :


W :

Width \(\mathrm{m}\)

\(\varnothing\) :

Volumetric concentrations percentage (%)

\(\alpha\) :

Thermal diffusivity \({[{{\mathrm{m}}^{2}\,\mathrm{s}}^{ }]}\)

\(\beta\) :

Thermal expansion coefficient \([1/ \mathrm{K}]\)

ε :


\(\upsilon\) :

Kinematic viscosity \({[{{\mathrm{m}}^{2}\,\mathrm{s}}^{ }]}\)

\(\rho\) :

Density \([\mathrm{kg }/{\mathrm{m}}^{3}]\)

\(\mu\) :

Dynamic viscosity \({[{\mathrm{Pa}\,\mathrm{s}}^{ }]}\)

σ :

Stefan–Boltzmann constant \([\mathrm{W}/ ({\mathrm{m}}^{2} \,{\mathrm{K}}^{4})]\)








Corrugated wall


Windings + additional










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Authors and Affiliations



AA involved in conceptualization, methodology, software, validation, formal analysis, resources, writing—original draft preparation, visualization, and project administration. HM involved in software, investigation, and visualization. KM involved in validation, data curation, writing—review and editing, and supervision. AR involved in investigation, data curation, writing—review and editing, and supervision.

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Correspondence to Ali Abdali or Kazem Mazlumi.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Technical Editor: Guilherme Ribeiro.

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In Table 13, the complete details and characteristics of the understudied 500 kVA DT are shown, including tank dimensions, conservator, core, corrugated walls, core, LV and HV windings, and LV and HV oil canals (OCs).

Table 13 Specifications of geometrical dimensions of studied DT

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Abdali, A., Maosumkhani, H., Mazlumi, K. et al. Accurate and nonuniform CFD-based thermal behavior analysis of distribution transformers: voltage imbalance effect. J Braz. Soc. Mech. Sci. Eng. 45, 613 (2023).

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