This document presents a method to estimate the weights of main materials (copper, iron, oil) for transformers using an artificial neural network (ANN) with the Levenberg-Marquardt backpropagation algorithm. Training data consisting of 24 input/output pairs obtained from a transformer manufacturing company are used to train the ANN, with inputs like short circuit impedance, installation height, and temperature and outputs of material weights. The trained ANN is then able to accurately estimate the material weights of transformers, providing a method to forecast transformer costs for manufacturers.

1. Application Research Based on Artificial Neural Network(ANN) to Estimate the
Weight of Main Material for Transformers
Amit Kr. Yadav,Abdul Azeem,Akhilesh Singh O.P. Rahi
Electrical Engineering Department Assistant Professor, Electrical Engineering Department
National Institute Of Technology National Institute Of Technology
Hamirpur, H.P. India Hamirpur, H.P. India
e-mail: amit1986.529@rediffmail.com e-mail: oprahi2k@gmail.com
Abstract—Transformer is one of the vital components in oil). These are the main components which have been used
electrical network which play important role in the power for designing and cost estimation process.
system. The continuous performance of transformers is In following artificial neural networks with Levenberg-
necessary for retaining the network reliability, forecasting its Marquard back propagation algorithm have been used to
costs for manufacturer and industrial companies. The major
estimate the main material’s weight of transformers. The
amount of transformer costs are related to its raw materials, so
the cost estimation process of transformers are based on extracted data from transformer manufacturing company has
amount of used raw material. been used to train the ANN and the best parameters for this
This paper presents a new method to estimate the network have been presented graphically. Finally result
weight of main materials for transformers. The method is given by trained neural network have been compared with
based on Multilayer Perceptron Neural Network (MPNN) with actual manufactured transformer prove the accuracy of
sigmoid transfer function. The Levenberg-Marquard (LM) presented method to estimate the amount of raw materials,
algorithm is used to adjust the parameters of MPNN. The used in this transformer manufacturing company (in various
required training data are obtained from transformer installation temperature and altitude, various short circuit
company.
impedance and various volt per turn)
II. ARTIFICIAL NEURAL NETWORK
Keywords-Artificial Neural Network (ANN),Levenberg
Marquard(LM)algorithm,estimatingweight,design,powersystem, Neural networks are a relatively new artificial intelligence
transformer. technique. In most cases an ANN is an adaptive system that
changes its structure based on external or internal
I. INTRODUCTION information that flows through the network during the
learning phase. The learning procedure tries is to find a set
The most important components in electrical network are
of connections w that gives a mapping that fits the training
transformers which have an important role in electrification.
set well. Furthermore, neural networks can be viewed as
The continuous performance of transformers is necessary
highly nonlinear functions with the basic the form
for retaining the network reliability, forecasting its costs for
manufacturer and industrial companies. Since the major F ( x, w)  y
amount of transformers costs is related to its raw materials, Where x is the input vector presented to the network, w are
so having amount of used raw material in transformers is an the weights of the network, and y is the corresponding
important task [1]. The aim of the transformer design is to output vector approximated or predicted by the network.
completely obtain the dimensions of all the parts of the The weight vector w is commonly ordered first by layer,
transformer based on the desired characteristics, available then by neurons, and finally by the weights of each neuron
standards, and access to lower cost, lower weight, lower plus its bias. This view of network as an parameterized
size, and better performance [2-3]. Various methods have function will be the basis for applying standard function
been studied and some techniques have been used. optimization methods to solve the problem of neural
Artificial Neural Network is one of methods that mostly network training.
have been used in the recent years, in this field. Transformer
insulation aging diagnoses, the time left from the life of
transformers oil, transformers protection and selection of A. ANN Structure
winding material in order to reduce the cost, are few topics A neural network is determined by its architecture, training
that have been performed [4-8]. method and exciting function. Its architecture determines
In this paper Artificial Neural Network based method have the pattern of connections among neurons. Network training
been used to estimate the weight of main materials for changes the values of weights and biases (network
transformer (weight of copper, weight of iron and weight of

2. parameters) in each step in order to minimize the mean
square of output error.
Multi-Layer Perceptron (MLP) has been used in load
forecasting, nonlinear control, system identification and
pattern recognition [9], thus in this paper multi-layer
perceptron network (with four inputs, three outputs and a
hidden layer) with Levenberg-Marquardt training algorithm
have been used.
In general, on function approximation problems, for
network that contain up to a few hundred weights, the
Levenberg-Marquardt algorithm have the fastest
convergence. This advantage is especially noticeable if very
accurate training is required. In many cases, trainlm is used
to obtain lower mean square error than any other algorithms
tested. As the number of weights in the network increases,
Figure 2: Schematic of Inputs and Outputs
the advantage of trainlm decreases. In addition trainlm
performance is relatively poor on pattern recognition C. Training of ANN
problems. The storage requirements of trainlm are larger The major justification for the use of ANNs is their
than the other algorithm tested. ability to learn relationships in complex data sets that may
not be easily perceived by engineers. An ANN performs this
function as a result of training that is a process of repetitively
presenting a set of training data (typically a representative
subset of the complete set of data available) to the network
and adjusting the weights so that each input data set produces
the desired output.
Unsupervised and supervised learning process can be used
to adjust the weights in an ANN. Supervised learning
process requires both input/output pairs to train the network
but supervised learning process requires only input pairs to
train the network.Unsupervised learning can be
characterized as a fast, but potentially inaccurate, method of
adjusting the weights. On the other hand, supervised
learning typically requires longer learning times and can be
more accurate. There is no way to tell beforehand which
Figure 1: Artificial Neural Network
learning method will work best for a given application. For
B. Input and Outputs of ANN this reason, we concentrate on the very popular supervised
A neural network is a data modeling tool that is capable to learning approach based on the backpropagation training
represent complex input/output relationships. ANN typically algorithm, which has been shown to produce good results
consists of a set of processing elements called neurons that for a large number of different problems.
interact by sending signals to one another along weighted The back propagation training algorithm is a method of
connections. The required data are the data which have been iteratively adjusting the neural network weights until the
accumulated by Transformer Company. In last recent four desired accuracy level is achieved. It is based on a gradient-
years, are used for estimating the iron, copper and oil search optimization method applied to an error function.
weights of transformers and consequently transformer costs Typical error functions include the mean square error shown
are estimated by proposed method (in various installation in (1), where N is the total number of input/output pairs
height and temperature with different short-circuit (which can be vector quantities) used for training:
impedance and volt per turn). The schematic of the
presented method can be shown by Figure 2. 1 N
mse   [OUTforecast ,i  OUTactual ,i ]2 (1)
N i 1
Where OUT forecast ,i and OUTactual ,i are the output
forecast by the neural network and the actual (desired)
output, respectively, of the ith training example. The set of
training examples (input/output pairs) defines the training
set or learning set. For best results, the training set should

3. adequately represent all expected variations in the complete to change the weights. The learning rate is typically selected
set of data. between 0.01 and 1.0. The coefficient in m (2) is called
A recursive algorithm for adjusting the weights can be momentum and allows the weight updates at one iteration to
developed, such that the error defined by (1) is minimized. utilize information from previous error values. The
The equations (2) and (3) are recursive training equations momentum term helps avoid settling into a local minimum
based on the generalized delta rule and the corresponding and is selected between 0.01 and 1.0.
algorithm is called gradient descent back propagation. The recursive training algorithm (set n= n+1) is executed
until the network satisfactorily predicts the output values.
wpj ,qk (n  1)  lr. qk .OUTpj  m.wpj ,qk (n) (2) Common stopping criteria for the training algorithm involve
monitoring either the mean square error or the maximum
wpj ,qk (n  1)  wpj ,qk (n)  wpj ,qk (n  1) (3) error or both and stopping when the value is less than a
Where : specified tolerance. The selected tolerance is very problem
n : the no. of current iteration of the training algorithm dependent and may or may not be actually achievable.
There is no mathematical proof that the back propagation
wpj ,qk (n) : the value of weight that connects the neuron p training algorithm will ever converge within a given
Of layer j with the neuron q of layer k during tolerance. The only guarantee is that any changes of the
Iteration n. weights will not increase the total error. Note that the
wpj ,qk (n) : the variation in the value of weight wpj ,qk (n) inclusion of the momentum term may allow the error as
defined in (1) to temporarily increase if the optimization
during the iteration n. process is moving away from the local minimum.
 qk : the value of  (delta coefficient) for the neuron
q of layer k.
OUTpj :the output for the neuron p of layer j. III. LEVENBERG MARQUARD FORMULATION
lr : the learning rate. FOR TRANSFORMER
m :the momentum. The LM algorithm has been used in function approximation.
Basically it consists in solving the equation:
The value of d is calculated differently depending on the ( J t J   I )  J t E (6)
specific location of the weight under consideration (4) is the
formula for calculating d for any weight connected from a Where J is the Jacobian matrix for the system, λ is the
hidden layer neuron to an output layer Levenberg's damping factor, δ is the weight update vector
neuron: that we want to find and E is the error vector containing the
2 output errors for each input vector used on training the
 qk  .OUTqk .(1  OUTqk ).(OUTactualqk  OUTqk ) (4) network. The δ tell us by how much we should change our
N network weights to achieve a (possibly) better solution. The
where layer k is the output layer, OUTactualqk is the actual JtJ matrix can also be known as the approximated Hessian.
(desired) output of any neuron q of the output layer k , and The λ damping factor is adjusted at each iteration, and
N is the number of training examples of the training set. guides the optimization process. If reduction of E is rapid, a
The values in (4) are known from the training set. The smaller value can be used, bringing the algorithm closer to
calculated output of the network is compared to the actual the Gauss Newton algorithm, whereas if an iteration gives
value to generate an error signal. The error signal is insufficient reduction in the residual, λ can be increased,
propagated back through the neural network to adjust the giving a step closer to the gradient descent direction.
weights, as shown in (2) and (3). Algorithm:-
For neurons in any other than an output layer, however, an 1. Compute the Jacobian (by using finite differences
error value is not directly obtainable because no desired or the chain rule)
output value is given for these internal neurons as a part of 2. Compute the error gradient
the training set. The error values for any neurons other than ( i) g = JtE
the output neurons are calculated as weighted sums of the 3. Approximate the Hessian using the cross product
output layer errors: Jacobian .
Q ( i )H = JtJ
 pj  OUTpj .(1  OUTpj ).  qk .wpj ,qk (5) 4. Solve (H + λI)δ = g to find δ .
q 1 5. Update the network weights w using δ
where Q is the number of neurons of the output layer. 6. Recalculate the sum of squared errors using the
The coefficient lr in (2) is called learning rate and directly updated weights
controls how much the calculated error values are allowed 7. If the sum of squared errors has not decreased,

4. (i)Discard the new weights, increase λ T17 27500 11110 7387
using different values and go to step 4. T18 25600 10630 2780
T19 9500 7250 6300
8. Else decrease λ using different values and stop. T20 16700 8900 8479
T21 27000 12250 5199
T22 15550 8550 7550
IV. SIMULATION T23 25400 12250 17450
For network learning, some input vectors (P) and some T24 53100 2550 8479
output vectors (T) are needed. By considering extracted data
the belong type of 63/20kV transformer from transformer A two layer feed-forward network with sigmoid hidden
manufacturing during last 4 years, simulating has been neurons and linear output neurons has been used. The
performed in the following case. In Table II and III, 24 network has been trained with Levenberg-Marquard back
inputs vector and 24 outputs vector that are used for propagation algorithm. The number of neurons in hidden
network learning. layer is twenty.
TABLE II
INPUTS FOR TRASFORMER 63/20 KV
Inputs Short circuit Installation Volt per Environment
Impedance height turn temperature V. RESULT AND DISCUSSION
percent
P1 8 1000 87.719 50
P2 10 1000 76.336 55
P3 10 1000 84.034 50
P4 10 1000 60.79 45
P5 10 1000 68.027 40
P6 12 1500 68.027 40
P7 12 2200 54.795 50
P8 12.5 1364 99.502 40
P9 12.5 1500 54.201 40
P10 12.5 1500 67.34 40
P11 12.5 1500 76.923 50
P12 12.5 1500 106.952 45
P13 12.5 1700 97.087 45
P14 12.5 1900 49.948 39
P15 13 2000 66.67 50
P16 13.5 1000 79.94 47
P17 13.5 1500 75.76 45
P18 13.5 1500 75.785 40
P19 13.5 1700 37.88 40
P20 13.5 1700 47.17 55
P21 13.5 1700 66.007 42
P22 13.5 2000 46.62 50
P23 13.7 1500 75.753 55
P24 14 1000 121.212 45
Figure3: Mean Square Error
TABLE III
OUTPUTS FOR TRANSFORMER 63/20 KV
The performance curve is shown in Figure 1. In this figure
Outputs Weight of iron Weight of Oil Weight of mean squared error have become small by increasing the
Copper number of epoch. The test set error and the validation set
T1 31200 13500 7700 error has similar characteristics and no significant over
T2 25600 11500 7770 fitting has occurred by iteration 6(where best validation
T3 27000 11400 7094
performance has occurred).
T4 22100 8500 7000
T5 22700 9900 6894
T6 24000 10600 8000
T7 15100 7500 4124
T8 38000 18000 11720
T9 15250 7700 8667
T10 22400 10300 6891
T11 30160 13700 10000
T12 45470 19000 9765
T13 33200 14100 6600
T14 17450 8800 9700
T15 25562 11820 8950
T16 28750 11850 9500

5. Figure6: Regression plot of weight of main material of transformer
Figure4: Prediction of weight of main material of transformer during The output tracks the targets very well for training, testing,
training analysis. and validation, and the R-value is over 0.95 for the total
The output has tracked the targets very well for training, in response.
estimation of weight of main material in transformer. The
value of regression is one which indicates a close correlation CONCLUSIONS
between outputs and targets. The major amount of transformers costs is related to its
raw materials, so having the amount of used raw material in
various conditions in transformers has been used in costs
analysis process. This paper presented a new method to
estimate the weight of main material (weight of copper,
weight of iron and weight of oil) for 63/20kV transformers.
The method is based on two layer feed-forward network
with sigmoid transfer function in hidden layer and linear
transfer function in output neuron. The Levenberg-
Marquard (LM) algorithm is used to adjust the parameters
of MPNN. The required training data for MPNN are the
obtained information from the transformers manufacturing
company during last 4 years. The advantage of using
ANN in the design and optimization is that ANN is required
to be trained only once. After the completion of training, the
ANN gives the transformers weight without any iterative
process. Thus, this model can be used confidently for the
design, cost estimating and development of transformers.
Developed model has very fast, reliable and robust
structure.
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