Download Tensor Analysis Application to Characterize the Motor of

Tensor Analysis Application to Characterize the
Motor of Asynchronous 3-Entwine Rotor Phase
at the Operation Voltage of 350 Volts
Mukhtar Saleh1)
1
Electrical Engineering Department, Hasanuddin University
Abstract: This research applied for a three-phase asynchronous motor with rotor winding
at a voltage of 350 Volt. This work is the continuation of the previous research which is
aimed to investigate whether changes occurs at the motor characteristics. In order to
address the problem, several methods have been used, for example, the tensor analysis.
Observation and laboratory measurement cannot longer to be performed, due to low
voltage supply. All characteristics, therefore, are derived from computer calculation and
comparison with the characteristics obtained through the tensor analysis method as a
reference. The comparison results indicate that tensor analysis method is typically
accurate as the previous work suggested.
Keywords: asynchronous motor, characteristic, and tensor analysis.
1. INTRODUCTION
Implementation of electric engines as electronic equipments has been greatly
increased, especially in supporting the development of industry and technology. Within advance
development in electric motor technology, human civilization experiences a major development.
Asynchronous motors which are the integral part of asynchronous machines are the most
widely used electric equipment. Electric motors introduce several advantages such as simple
in terms of the physical form, sturdy, relatively very cheap, easy maintenances and a relative
low technical failure. Besides, it has a wide range characteristic of operation, between 0,2 K
Watt until 250 K Watt, with a wide range voltage coverage.
In order to obtain optimum performances and results, details of machinery characteristic
should be involved in the design, implementation and operations. This information is collected
through mathematical calculation or electronic measurements, including electric current,
electric power and electric couple. This process utilizes mathematical formula derived from
circuit analysis. Specific method must be used in obtaining accurate characteristic information.
Saleh (1993) suggests the same hypotheses. Several methods are utilized in calculating those
electric values. For instance, through equivalent circuit formulas and circle diagram (Zuhal
1988) followed by Thevenin equivalent circuit calculation. This equivalent circuit represents a
linear circuit with a fixed voltage source which is a single voltage source arranged in series.
Similarly, Kron, G. (1938) introduces a method called Tensor analysis which was used earlier in
pure mathematic purposes. As a pure mathematic concept, Tensor analysis is assumed as an
abstract object with specific features on coordinate transformation. In terms of dynamic objects
such as a moving electric machine, the concept transforms rotor axes to a new frame reference.
This reference has one pair rotor axis which is not necessarily to be coinciding and intersected
perpendicularly with the diagonal and length axis of the stator. Then, the tensor equation is
mapped into a matrix form.
PROCEEDINGS OF THE FIRST INTERNATIONAL WORKSHOP ON MODERN RESEARCH METHODS IN
ELECTRICAL ENGINEERING 2009 (IWoRMEE’09)
3 – 6 Agustus 2009, Hotel Horison – Hasanuddin University, Makassar City, Indonesia
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2. RESEARCH METHODOLOGY
This project involves the circle diagram, tensor analysis, equivalent circuit and the equivalent
thevenin circuit at the operational voltage of machine is 350 Volts.
Initially, computer program is used in the calculation process. Due to unavailability of
measurement at the operational voltage of 350 Volts, the results are then compared with the
results from the tensor analysis method as a reference.
Datasheet of the machine:
Asynchronous Machine: LK-503
Factory: Siemens, Former Western Germany
Machine Type: Universal Machine - DUM 2550-214, Asynchronous 3-phase, Spool Rotor
Power Consumption: 3.5 K Watt
Operating Voltage: 380 Volts, Y
Stator Current: 8.1 Ampere
Power Factor: 0.8
Frequency: 50 Hz
Total Pole: Four unit
Rotor: 140 Volt. Y. 1 7 Ampere
Machine Constanta: Rs: 1.0340 Ohm, Xs: 4.0484 Ohm, Rr =2.0143 Ohm, Xr = 3.7906 Ohm,
Xm= 59.5315 Ohm.
3. RESULTS AND DISCUSSION
3.1 Experiments with variety of calculation approaches
3.1.1 Tensor Analysis
Mathematical formulas used in this analysis are obtained from static current, electric
couple and electric power of the machine.
a. Stator Current or I stator
b. 3-Phase Couple, T3phase
c. 3-Phase Power Factor
With the assumption of:
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Calculation results:
The results can be shown in Table 1, below.
Characteristics curve:
Figure 1: Characteristic curve of Current-Power factor-Couple versus Slip
PROCEEDINGS OF THE FIRST INTERNATIONAL WORKSHOP ON MODERN RESEARCH METHODS IN
ELECTRICAL ENGINEERING 2009 (IWoRMEE’09)
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© Elecetrical Engineering Department, Hasanuddin University
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3.1.2 Equivalent Circuit
To simplify complex analysis of equivalent circuit of the asynchronous motor, the
analysis is mapped onto a single phase analyses. Asynchronous motor can be represented
as a transformator with a rotating secondary circuit. Similarly, the process is iterated in
order to obtain the Current, Couple and Power factor of the machine.
Calculation results:
Table 2 presents the results of the calculation.
Characteristics curve:
Figure 2 illustrates the curve of characteristics.
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3.1.3 Equivalent Thevenin Circuit
Through the replacement of any network from the circuit with a linear circuit
and a fixed voltage source, the complexity of the calculation can be reduced. The
implementation is by arranging a single voltage source, Vs and single Z impedance
in series. Similarly, the calculation process is repeated till the values of Current,
Couple and Power factor of the machine is acquired.
Calculation results:
Table 3 presents the results of the calculation.
Characteristics curve:
Figure 3 illustrates the curve of characteristics of the Current-Power factor- Couple versus Slip.
PROCEEDINGS OF THE FIRST INTERNATIONAL WORKSHOP ON MODERN RESEARCH METHODS IN
ELECTRICAL ENGINEERING 2009 (IWoRMEE’09)
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© Elecetrical Engineering Department, Hasanuddin University
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3.1.3 Circle Diagram
Similar procedure used in obtaining the values of Current, Couple and Power factor of
the machine.
Calculation results:
Table 4 presents the results of the calculation.
Characteristics curve:
Figure 4 illustrates the curve of characteristics of the Current-Power factor- Couple versus Slip.
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From the experiments’ results, Figure 1 until Figure 4, the aforementioned methods, Tensor
analysis method, Equivalent Circuit, Equivalent Thevenin Circuit and Circle Diagram, produce
similar characteristic curves. By merging the whole curves, we can obtain a characteristic curve
of the whole methods and it can be seen in the Figure 5 below,
Figure 5: characteristic curve of the whole methods
3.2 Comparison of the Four-Mentioned Approaches
Another experiment was conducted in order to obtain a comparison data. In this
experiment, the nominal rotation speed of the machine is set to n = 1410 rpm, except the
Circle Diagram method, the speed is set to n = 1392,4538 rpm, for each of the Current,
Power factor and Couple of the machine. Table 5 depicts the overall results of the
experiment.
Table 5: The overall results of the experiment.
From Table 5 above, it can be seen that the difference between Tensor Analysis Method
and the other three methods is relatively small, except Circle Diagram Method which uses
different scale. Hence, the accuracy of the Circle Diagram Method is not accurate.
PROCEEDINGS OF THE FIRST INTERNATIONAL WORKSHOP ON MODERN RESEARCH METHODS IN
ELECTRICAL ENGINEERING 2009 (IWoRMEE’09)
3 – 6 Agustus 2009, Hotel Horison – Hasanuddin University, Makassar City, Indonesia
© Elecetrical Engineering Department, Hasanuddin University
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4. CONCLUSION AND SUGGESTION
Based on the results of our previous research and current work, both suggest that the Tensor
Analysis Method is the most accurate method among the other three methods.
To obtain a comprehensive conclusion, we suggest that for the future research, experiments
should involve different operating voltage of the machine, for example, 300 and different rotor
resistance.
Referrences
[1] Gibbs, W.J. 1950, "Tensor in Electrical Machinery Theory", Chapman & Hall Ltd. 37,
ESSEX, W.C.2
[2] Hancook, N.N. 1974, "Matrix Analysis of Electrical Machinery", Second Edition, Bergamon
Press, Oxford.
[3] IEEE.112. 1978, "Standard Test Procedure for Poliphase Induction Motors and
Generators",
[4] Krause, Paul. C 1978, Analysis of Electrical Machinery", MacGraw-Hill, Book Company.
1st Edition.
7
[5] Kron Gabriel, 1949, "Tensor Analysis of Network", Willey & Son, InC. New York.
(1942), "Tensor for Circuit
Network. Dover Publication, Inc. New York.
1942, "Tensor for Circuit",
Publication, Inc. New York.
", Part I, General Asymmetrical
Part II, Rotating Machinery. Dover
[8] Lynn, J.W., 1963, "Tensor in Electrical Engineering". Edward, Arnold Publishing Ltd.,
London.
[9] Saleh, Mukhtar 2000, "Penggunaan Analisis Tensor untuk Menggambarkan Karakteristik
Motor Asinkron 3 fasa Rotor Belitan", Buletin Penelitian Teknologi, Lembaga Penelitian
Universitas Hasanuddin Makassar
[10] ------------------------ 2008, "Beberapa Metoda untuk Menghitung Besaran Generator
Asinkron". Jurnal Perpustakaan, Informasi dan Komputer, Vol. VI No. 1 Maret 2008, UPT
Perpustakaan Universitas Hasanuddin Makassar.
[11] Say, M.G., 1974. "Alternative Current Machine", the English Language Book Society
and Pitman, Fourth Edition.
PROCEEDINGS OF THE FIRST INTERNATIONAL WORKSHOP ON MODERN RESEARCH METHODS IN
ELECTRICAL ENGINEERING 2009 (IWoRMEE’09)
3 – 6 Agustus 2009, Hotel Horison – Hasanuddin University, Makassar City, Indonesia
© Elecetrical Engineering Department, Hasanuddin University
30