2010 International Conference on Future Power and Energy Engineering
Non-conventional Transformers Cost Estimation Using Neural Network Hamid-Reza Reza-Alikhani Dept. of Elec. Eng. University of Tafresh Tafresh, Iran
Peyman Salah Dept. of Elec. Eng. University of Tafresh Tafresh, Iran
[email protected]
Seyed Siavash Karimi Madahi Dept. of Elec. Eng. University of Tafresh Tafresh, Iran
[email protected]
Abstract Since the cost of transformer can be divided into 5060% for material, and the rest being labor costs and modest profit, therefore as the major amount of transformers costs is related to its raw materials, so it has a high importance in costs estimating process. This paper presents a new method to estimate transformers pricing. The method is based on multilayer perceptron neural network (MPNN) with sigmoid transfer function. The back-propagation (BP) algorithm is used to adjust the parameters of MPNN. The required training data for MPNN are the obtained information from the transformers made by IranTransfo Company during last 4 years. A Multi-Layer Perceptron (MLP) neural network has been designed for 132/33KV transformers (which is classed as nonconventional in Iran). By finding suitable coefficients for weight of the copper, iron and transformer oil (that are MLP neural network outputs) and a constant coefficient that is related to manpower cost and other transformer components costs, the cost of transformer is estimated.
1. Introduction Power transformer is one of the most important components in electrical network which play effective role in the electrification. Thus its suitable performance is most desirable. In the same way that continuous performance of transformers is necessary to retaining the network reliability, forecasting its costs is important for manufacturer and industrial companies. The initial steps of project evaluating, having a good estimated costs in short time is useful. In Iran as a whole, 63/20KV and 132/20KV super distribution transformers are used, but in some Southern part of Iran 132/33KV non-conventional 978-0-7695-4073-3/10 $26.00 © 2010 IEEE DOI 10.1109/ICFPEE.2010.24
Shahrokh Akhlaghi Dept. of Elec. Eng. University of Tafresh Tafresh, Iran
[email protected]
[email protected]
transformers are used. That makes the price evaluation a hard and cumbersome task. The goal to design a transformer is to access all dimensions, based on the desired characteristics, available standards, and access to lower cost, lower weight, lower size and better performance. Various methods have been studied and some techniques such as genetic algorithm , finite element method [1], neural network [2] and some other new techniques [3-4] were performed. Since the cost of transformer can be divided into50%-60% for material, and the rest being labor costs and modest profit [5], so the major amount of transformers costs is related with its raw materials, so it has a high importance in costs estimating process. In the recent years, in the field of transformers design, neural network have quite often been used transformer insulation aging diagnosis [6]. The time left from the life of transformers oil [7], transformers protection [8], and Selection of Winding Material in order to reduce the cost [9] are few topics that have been performed. In this paper, a method by means of artificial neural network (ANN) based on data that were extracted from a transformer manufacturer is introduced for estimating transformers costs. A Multi-Layer Perceptron (MLP) neural network has been designed for 132/33KV transformers (which is classed as non-conventional in Iran). By finding suitable coefficients for weight of the copper, iron and transformer oil (that are MLP neural network outputs) and a constant coefficient that is related to manpower cost and other transformer components costs, the cost of transformer is estimated. In following artificial neural networks are revised, then the ANN configuration is used and for estimating transformer costs ANN has been trained using the last four years IRAN-TRANSFO.CO data and the parameters of this network have been obtained. Finally, resulted outputs of trained neural network are 71
presented which will prove the accuracy of price estimation and consumed material.
circuit impedance and volt per turn). The schematic of the presented method can be shown by figure 2.
2. Artificial Neural Network Neural network is a system of nonlinear, self adaptation, and self-organization, which is made up of large numbers of processing units.
2.1. Neural Network Structure A neural network is determined by its architecture, training method, and exciting function. Its architecture determines the pattern of connections among neurons. Network training changes the values of weights and biases (network parameters) in each step in order to minimize the mean square of output error. Multi-Layer Perceptron network is the most popular neural network type that used in engineering applications such as load forecasting, nonlinear control, system identification, and pattern recognition [10-11], thus in this paper multi-layer perceptron network (with four inputs, three outputs, and a hidden layer) with back-propagation training algorithm have been used. Since in this method which is based on error gradient method, function differential is used then differentiable functions like sigmoid, hyperbolic tangent should be used which in this case the activation function used in the hidden layer is non-linear sigmoid function and the activation function in the output layer is a linear function. Figure 1 shows the MLP network that is used in this study.
Figure 2. Schematic of Inputs and Outputs
2.3. Training of ANN In order to train a neural network we need data for training. The last four years transformer data obtained from Iran-Transfo Co. are used. These data for the transformers 132/33KV are shown in the tables II, III. An Artificial Neural Network MLP-Multi Layer Perceptron with back-propagation (BP) method can be used to reach this goal. To determine weights and biases of neural network a number of data are needed to learn the network. In table I structure of neural network and it training parameter are shown. Table I Architecture of ANN and Training Parameters Architecture of ANN The number of layers The number of neuron on the layers Input Hidden Output The initial weights and biases Activation functions
3 4 2 3 Random Sigmoid
Training parameters Learning rule Learning rate Momentum constant Mean squared error
back-propagation 5e-3 1 1e-2
Figure 1. Artificial Neural Network
2.2. Inputs and Outputs of ANN The required data are the data which have been accumulated by Iran-Transfo Co. in last recent four years, are used for estimating the iron, copper, and oil weights of transformers and consequently transformer costs are estimated by proposed method (in various installation height and temperature with different short-
3. Simulation For network learning, some input vectors (P) and some output vectors (t) are needed. By considering extracted data the belong type of 132/33KV transformer from Iran-Transfo Co. during last 4 years, simulating has been performed in the following case. In table II and III, 27 inputs vector and 27 outputs vector that are used for network learning.
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Table II
After learning of each network and converging of all weights and biases, each of weights and biases of proposed network layer will be as following:
Inputs for Transformer 132/33 KV
Inputs P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22 P23 P24 P25 P26 P27
Short circuit impedance percent 6 8 10 10 10 10 10 10 10.7 11 11 11 11.5 12 12 12 12 12.5 12.5 12.5 12.5 14 15.5 15.7 16 17 17
Installation height 1000 1900 1000 1000 1000 1000 1000 1000 2500 1000 1000 2200 1000 1500 1000 1000 1000 1000 1000 1000 2200 1000 1000 1000 1000 1000 1000
Volt per turn 81.784 73.171 115.789 120.879 141.13 146.558 156.169 164.286 120.438 99.593 130.187 121.771 109.987 59.524 79.473 93.476 104.414 48.728 117.021 160.634 135.125 113.82 93.75 61.983 107.813 168.224 186.441
Environment temperature 50 40 45 40 50 53 55 40 40 50 50 50 55 50 55 55 52 55 60 48 50 50 45 35 40 55 50
Table III
W1
ª 17.8823 2.1790 101.6126 29.4056º « 14.8470 1.6649 83.3914 59.0671 »» « « 1.4708 0.4929 4.8988 2.0615 » « » 91.2111 69.4587 ¼ ¬ 21.1834 0.8792
W2
ª 26.1214 16.1820 0.9762 19.7013º « 12.3860 16.5792 2.4966 11.4944 » ¬ ¼
W3
ª41.5469 17.6252º « 12.9137 8.1596 » » « ¬« 10.7532 3.8002 ¼»
b1
ª 10.7759 º « 19.6529 » « » b2 « 5.6881 » « » ¬ 21.3734¼
ª 0.2873º «8.9625 » b3 ¬ ¼
ª20.6282º «12.3130 » » « «¬ 5.3913 »¼
The learning curve is shown in figure 3. In this figure mean squared error decreasing by increasing the number of repeats is illustrated.
Outputs for Transformer 132/33 KV Outputs t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 t21 t22 t23 t24 t25 t26 t27
Weight of iron 33492 25150 45320 47200 60550 57100 67750 67200 44750 38000 52500 46200 42300 17600 28700 40000 31000 18500 46000 65300 53200 37050 33500 25170 41250 83500 80250
Weight of oil 14829 12100 17800 20000 25700 25000 33860 27500 21700 22000 29000 21400 23500 11250 15200 19850 15000 15500 25800 24350 29100 19700 23000 13620 20250 37300 33100
Weight of copper 4054 6367 10399 11198 19850 12470 15183 13800 8900 8500 11464 11158 10550 4580 6700 10270 5580 5311 11380 17200 17530 8138 8522 8400 11000 24700 16978
Figure 3. Mean Square Output Error
4. Transformers Cost Function A new method which is based on cost estimating is presented as following:
f
c1 wi c2 wo c3 wc c4
where c1, c2, c3 are the cost of iron, oil and copper of transformer per ton. And wi, wo, wc that by applying of properties of related transformer in neural network
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their values are obtaining. The coefficient, c4 is constant which is related to manpower cost and other components of transformer. As an example if we need to estimate transformer cost with the following characteristics with help of employing neural network, the equations for manufacturing cost point of view are as follow: Short circuit impedance percent 12
f
Installation height 1000
Volt per turn 80
Environment temperature 55
[6]
[7]
[8]
28.912c1 15.357c2 6.736c3 c4
5. Conclusion Since the cost of transformer can be divided into5060% for the material, and the rest being the labor costs and a modest profit, therefore as the major amount of transformers cost is related with its raw materials, giving a high importance in costs estimating process. In this article, a method by means of artificial neural network (ANN) based on data that were extracted from one transformer manufacturer is introduced (a cost function) for estimating transformers costs. In the cost function weight of iron, oil, and copper are effective which are suggested by the neural network according to the last four years of data from the transformers made by Iran-Transfo Co.
[9]
[10]
[11]
6. References [1]
[2]
[3]
[4]
[5]
P. S. Georgilakis, ” Recursive genetic algorithm-finite element method technique for the solution of transformer manufacturing cost minimization problem”, IET Electr. Power Appl., 2009, Vol. 3, Iss. 6, pp. 514– 519. Geromel, Luiz H., Souza, Carlos R., ”THE APPLICATION OF INTELLIGENT SYSTEMS IN POWER TRANSFORMER DESIGN”, IEEE Conference, 2002, pp. 1504-1509. Manish Kumar Srivastava, ”An innovative method for design of distribution transformer”, e-Journal of Science & Technology(e-JST), April 2009, pp. 49-54. Pavlos S. Georgilakis, Marina A. Tsili and Athanassios T. Souflaris, ” A Heuristic Solution to the Transformer Manufacturing Cost Optimization Problem”, JAPMED’4-4th Japanese-Mediterranean Workshop on Applied Electromagnetic Engineering for Magnetic, Superconducting and Nano Materials, Poster Session, Paper 103_PS_1 nology (e-JST), September 2005, pp. 83-84. A report on “Transformer and Switchgear: Where is it all Going?” (27th Aug 2008). www.powertechnology.com
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Wang He-Xing, Yang Qi-Ping, Zheng Qun-Ming, ”Artificial Neural Network for Transformer Insulation Aging Diagnosis”, Nanjing China, April 2008, pp. 2233-2238. Tetsuro Matsui, Yasuo Nakahara, Kazuo Nishiyama, Noboru Urabe and Masayoshi Itoh, ”Development of Remaining Life Assessment for Oil-immersed Transformer Using Structured Neural Networks”, ICROS-SICE International Joint Conference, August 2009, pp. 1855-1858. Manoj Tripathy, Rudra Prakash Maheshwari and H. K. Verma, ”Power Transformer Differential Protection Based On Optimal Probabilistic Neural Network”, IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 1, JANUARY 2010, pp. 102-112. Eleftherios I. Amoiralis, Pavlos S. Georgilakis and Alkiviadis T. Gioulekas, ”An Artificial Neural Network for the Selection of Winding Material in Power Transformers”, Springer-Verlag Berlin Heidelberg, 2006, pp. 465-468. Khaled Shaban, Ayman EL-Hag and Andrei Matveev, ”Predicting Transformers Oil Parameters”, IEEE Electrical Insulation Conference, Montreal, QC, Canada, 31 May - 3 June 2009, pp. 196-199. L. Mokhnache, A. Boubakeur, B. Ould Noureddine, M.A.R. Bedja and A. Feliachi , ”Application of Neural Networks in the Thermal Ageing Prediction of Transformer Oil”, IEEE Conference, 2001, pp. 18651868.
