Electr Eng (2011) 93:237–246 DOI 10.1007/s00202-011-0211-9 ORIGINAL PAPER Optimal design of single-phase shell-type distribution transformers based on a multiple design method validated by measurements Juan C. Olivares-Galvan · Pavlos S. Georgilakis · Rafael Escarela-Perez · Eduardo Campero-Littlewood Received: 17 February 2010 / Accepted: 22 May 2011 / Published online: 7 June 2011 © Springer-Verlag 2011 Abstract This paper presents a method for the design of shell-type, single-phase distribution transformers to obtain the manufacturing specifications. The method is simple, effi- cient and accurate. By an exhaustive analysis, it is concluded that the obtained solution is the global optimum. The fol- lowing constraints are imposed: excitation current, no-load losses, total losses, impedance and efficiency. The method- ology of this paper requires only six input data: transformer rating, low voltage, high voltage, connection of low-voltage coil, connection of high-voltage coil, and frequency. These data are included in the transformer nameplate. In this paper, the minimization of the following four objective functions is considered: total owing cost, mass, total losses and mate- rial cost. The consideration of these four objective functions is implemented automatically by running the optimization algorithm four times without intervention of a designer. Con- sequently, transformer manufacturers save design man-hours and increase capacity. A design example on a 25 kVA trans- former is presented for illustration. The optimized solutions of transformer design are validated with laboratory and pro- cess measurements. Keywords Conductor selection · Design · Design optimization · Distribution · Excitation current · Transformer J. C. Olivares-Galvan (B ) · R. Escarela-Perez · E. Campero-Littlewood Departamento de Energia, Universidad Autonoma Metropolitana-Azcapotzalco, 02200 Mexico, Mexico e-mail: jolivare_1999@yahoo.com P. S. Georgilakis School of Electrical and Computer Engineering, National Technical University of Athens (NTUA), 15780 Athens, Greece e-mail: pgeorg@power.ece.ntua.gr List of symbols Constants ρ Al Aluminum conductor density (kg/m 3 ) ρ Cu Copper conductor density (kg/m 3 ) ρ core Core density (kg/m 3 ) LF Lamination factor (%) B Load loss cost rate (US$/W) W k Loss factor of stray losses (dimensionless) A No-load loss cost rate (US$/W) AV accsa Number of alternative values of aluminum conductor cross-sectional area AV cccsa Number of alternative values of copper conductor cross-sectional areas AV lw Number of alternative values of lamination width AV mfd Number of alternative values of magnetic flux density AV lvt Number of alternative values of turns of low voltage W d(Al) Volumetric resistivity and material density factor for aluminum ( mm 4 /kg) W d(Cu) Volumetric resistivity and material density factor for copper ( mm 4 /kg) Dependent variables J Al Aluminum conductor current density (A/mm 2 ) LL Al Aluminum conductor losses (W) M Al Aluminum conductor mass (kg) J Cu Copper conductor current density (A/mm 2 ) LL Cu Copper conductor losses (W) M Cu Copper conductor mass (kg) M c Core mass (kg) E Core thickness (mm) 123