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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 © Elecetrical Engineering Department, Hasanuddin University 24 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: 25 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) 3 – 6 Agustus 2009, Hotel Horison – Hasanuddin University, Makassar City, Indonesia © Elecetrical Engineering Department, Hasanuddin University 26 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. 27 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) 3 – 6 Agustus 2009, Hotel Horison – Hasanuddin University, Makassar City, Indonesia © Elecetrical Engineering Department, Hasanuddin University 28 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. 29 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 30 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