Electrical Engineering

, Volume 100, Issue 2, pp 823–838 | Cite as

Power transformer optimal design (PTOD) using an innovative heuristic method combined with FEM technique

  • Milad Yadollahi
  • Hamid Lesani
Original Paper


Power transformer optimal design (PTOD) is a complex multi-objective optimization problem including numerous design variables that aim to design a transformer with minimal material costs. Due to large variables search space (SS), most optimization methods proposed in the literature for PTOD are prone to find local minimum instead of the global one. So, some design variables and constraints are neglected to reduce the SS size and alleviate the problem. They also suffer from a random nature which makes it impossible for them to explore all the SS. To prevail over the aforementioned problems, this work aims to propose a new heuristic algorithm, and also, some modifications to conventional PTOD procedure. Some promising features of the proposed method in comparison with the previously proposed methods are (1) it considers all design variables as a gene for transformer constructing chromosome (TCC), (2) before building the main TCC, it divides the PTOD algorithm into some sub-algorithms and starts to construct some sub-chromosomes with lower number of genes as parts of the main TCC, which allows us to detect improper genes based on a sensitivity analysis and design constraints, and ignore them, automatically narrowing the SS by simply ignoring its bad parts (the solutions which do not meet design constraints), and (3) not only it considers all technical and consumer constrains, but it also takes manufacturing constraints into account. To verify the effectiveness of the proposed method in achieving the global minimum, it is used to design a 200 MVA and 15.75/400 KV power transformer. The validity of obtained optimal solution is further assessed by presenting comprehensive finite element method using JMAG software.


Power transformer optimal design (PTOD) Heuristic method (HM) Finite element method (FEM) Constructing cost (CC) Short circuit impedance (SCI) 

List of symbols




Volt per turn


Number of turns in low-voltage winding


Number of turns in high-voltage winding


Number of turns in regulating voltage winding

\({D}_{{S}}\) (mm)

Core diameter

\({Q}_{{S}}\) (\(\hbox {cm}^{2}\))

Cross section of core

B (Tesla)

Flux density


Number of layers

H (mm)

Height of wire

W (mm)

Width of wire


Number of radial parallel wires


Number of axial parallel wires


Number of parallel wires in subdivided wires

HW (mm)

Height of winding

T (mm)

Width of winding

LL (kw)

Load loss

NLL (kw)

No-load loss

SCI (%)

Short circuit impedance

Supplementary material

202_2017_537_MOESM1_ESM.docx (1.6 mb)
Supplementary material 1 (docx 1591 KB)
202_2017_537_MOESM2_ESM.pdf (260 kb)
Supplementary material 2 (pdf 259 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of TehranTehranIran

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