Artificial Intelligence combined with Hybrid FEM-BE Techniques
for Global Transformer Optimization
E. I. Amoiralis
1
, P. S. Georgilakis
1
, M. A. Tsili
2
, A. G. Kladas
2
1
Department of Production Engineering & Management, Technical University of Crete
2
School of Electrical & Computer Engineering, National Technical University of Athens,
kladasel@central.ntua.gr
Abstract— The aim of the transformer design optimization is
to define in detail the dimensions of all the parts of the
transformer, based on the given specification, using available
materials economically in order to achieve lower cost, lower
weight, reduced size and better operating performance. In this
paper, a hybrid artificial intelligence – numerical technique is
proposed for the selection of winding material in power
transformers. The technique uses decision trees for attribute
selection and neural networks for winding material classification,
along with finite element – boundary element modeling of the
transformer for the calculation of the performance
characteristics of each considered design. The accuracy of the
proposed method is 95.5% (classification success rate for the
winding material on an unknown test set), which makes it very
efficient for industrial use.
I. INTRODUCTION
The variation in the cost of the materials used in the
transformer manufacturing has direct impact in the design of
the technical and economical optimum transformer. The
material of the transformer windings can be copper (CU) or
aluminum (AL). In order to check which material results to a
more economical solution, there is a need to optimize twice
the transformer (once with CU and once with AL windings)
and afterwards to select the most economical design. The
solution of winding selection problem can be implemented
using Artificial Intelligence (AI).
II. PROPOSED METHODOLOGY
In this paper, decision tree (DT) is proposed for attribute
selection and artificial neural networks (ANN) for winding
material classification. The method is composed of the
following steps:
1. Selection of candidate attributes, i.e. parameters affecting
the selection of transformer winding material;
2. Creation of the learning and test sets;
3. DT training;
4. Attribute selection based on DT;
5. ANN training using the attributes selected by the DT;
6. Incorporation of the ANN model in the transformer
optimization process as an efficient tool for winding
material selection.
For the creation of the learning and test sets, 6 power
ratings (250, 400, 630, 800, 1000 and 1600 kVA) and, 9
categories of losses are taken into account (according to
CENELEC harmonization document 428.1 S1, 1992). Seven
different unit costs (in €/kg) are considered for the CU and the
AL winding. Based on the above, 6
.
9
.
7=378 transformer
design optimizations with CU winding (CU designs) and 378
transformer design optimizations with AL winding (AL
designs) are realized. For each design, either the CU design or
the AL design is the final optimum design (with the least
cost). In total, 6
.
9
.
7
2
=2646 final optimum designs are collected
and stored into databases. The performance and parameters of
each considered design (short-circuit impedance, no load loss
etc.) are calculated with the use of a particular hybrid finite
element – boundary element model, [1]. This model is
particularly suitable for use with optimization algorithms, as it
reduces the total time needed for the magnetic field
calculation during each iteration and provides high accuracy,
which is crucial during the design stage. The databases are
composed of sets of final optimum designs (FOD) and each
FOD is composed of a collection of input/output pairs. The
input pairs or attributes are the 13 parameters shown in Table
I. The output pairs comprise the type of winding (CU or AL)
that corresponds to each FOD. The learning set is composed
of 1350 sets of FODs and the test set has 1296 sets of FODs.
TABLE I
CANDIDATE ATTRIBUTES
Symbol Attribute Name Symbol Attribute Name
I
1
CU unit cost (€/kg)
I
7
Guaranteed FE losses (W)
I
2
AL unit cost (€/kg)
I
8
Guar. winding losses (W)
I
3
I
1
/ I
2
I
9
I
7
/ I
8
I
4
FE unit cost (€/kg)
I
10
Rated power (kVA)
I
5
I
4
/ I
1
I
11
Guar. short-circuit voltage (%)
I
6
I
4
/ I
2
I
12
I
7
/ I
10
I
13
I
8
/ I
10
III. RESULTS AND DISCUSSION
The trained DT has classification success rate 94.06% and
96.37%, on the learning set and test set, respectively. In the
various correlation nodes of the DT, the following 6 attributes
are appearing: I
3
, I
5
, I
7
, I
8
, I
9
, and I
13
. In this way, the DT has
automatically selected only 6 attributes among the 13
candidate ones. The selected ANN architecture is the three-
layer feed-forward system with back-propagation. The
number of input neurons is 6, corresponding to the 6 attributes
automatically selected by the DT. The output layer comprises
a single neuron, corresponding to the optimum winding
material. It was found that for 8 hidden neurons, the best
classification results are obtained, namely 97.77% for the
learning set and 95.52% for the test set.
The ANN model for winding selection has been
incorporated in the transformer design optimization. This
development divides by two the effort of the designer to
optimize the transformer.
IV. REFERENCE
[1] M. A. Tsili, A. G. Kladas, P. S. Georgilakis, A. T. Souflaris, D. G.
Paparigas, “Geometry Optimization of Magnetic Shunts in Power
Transformers Based on a Particular Hybrid Finite Element - Boundary
Element Model and Sensitivity Analysis,” IEEE Trans.on Magn., Vol.
41, No 5, pp. 1776–9, May 2005.
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