Characteristics Analysis of Single Phase Induction Motor via Equivalent Circuit Method and Considering Saturation Factor

Size: px

Start display at page:

Download "Characteristics Analysis of Single Phase Induction Motor via Equivalent Circuit Method and Considering Saturation Factor"

Joel McLaughlin
5 years ago
Views:

1 J Elec Eng Technol Vol. 8, No.?: 74-?, 03 ISSN(Print) ISSN(Online) Characteristics Analysis of Single Phase Induction Motor via Equivalent Circuit Method and Considering Saturation Factor Su-Yeon Cho, Won-Ho Kim**, Chang-Sung Jin**, Han-Woong Ahn* and Ju Lee* Absact This paper presents a motor characteristics analysis method using an equivalent circuit. Motor characteristics analysis via equivalent circuit is very important for designing a high efficiency single phase induction motor. The accuracy of the motor characteristics depends on the accuracy of the parameters, especially saturation factor, which determines the cyclical relationship in the analysis process. Therefore, using the proposed method, the saturation factor was calculated using the iteration routine and numerical technique. The proposed method was verified by comparing the finite element method results and the dynamo test results of manufactured prototype model. Keywords: Single Phase Induction Motor, Analysis, Equivalent Circuit, Numerical, Iteration, Saturation Factor. Inoduction An elecic motor uses above 50% elecical energy. Among the existing elecic motors, the induction motor is most widely used. Therefore, a high efficiency induction motor has to be developed to overcome the current energy shortage and to meet the requirements of policies like the Minimum Energy Performance Standard []. For designing a high efficiency single phase induction motor, it is important to analyze the characteristics of the motor using an equivalent circuit, to exclude heuristic knowledge like the output coefficient. The accuracy of the characteristics as analyzed using an equivalent circuit depends on the accuracy of the equivalent circuit s parameters. In particular, the magnetization reactance, which is calculated based on the saturation factor, is very important. If the saturation factor is assumed to have a conventional heuristic value, many errors occur in the characteristics analysis results, and the designed motor efficiency will be reduced. In this paper, a motor characteristics analysis method using an equivalent circuit is presented. The key sength of this method is that it can be calculated the saturation factor more accurately.. Equivalent Circuit of Single Phase Induction Motor In the case of the single phase induction motor, the main Corresponding Author: Dept. of Elecical Engineering, Hanyang Univerity, Korea. (julee@hanyang.ac.kr) ** Material&Device Research Center, Samsung Advanced Institute Of Technology, Samsung Eleconics Co., Korea. (wonho79@nate.com) *** Mechaonics Group, Defence Program R&D Center, Samsung Techwin Co., Korea. (c.s.jin@samsung.com) Received: July 8, 03; Accepted: September 5, 03 winding and the auxiliary winding are not the same. Thus, it has the sucture of an unbalanced two phase motor. To determine the characteristics of the motor under unbalanced conditions, a symmeical two phase equivalent circuit was consucted [, 3, 4]. Fig. shows the equivalent circuit as having parameters compensated to the main winding part [5]. The parameters of the equivalent circuit can be calculated based on the motor dimensions, material information and elecical specifications, but magnetization reactance is affected by the saturation factor. The magnetization reactance can be expressed as the following equation [3]. Vs Vs j a Vs Vs + j a 4μ0Wm K Lstk K wm Feτ p Xmm = π f () π pgk cks μ 0 : permeability in free space K s : saturation factor K c : Carter coefficient K Fe : stacking factor of core g : airgap length I m + Rsa R sm a Im R sm R sm jx sm Z a X sa j X sm a jx sm j a ωc jx mm jx mm jx rm Rr s R r s Fig.. Equivalent circuit for the single-phase induction motor with run-capacitor Z + Z jx rm 74

2 Su-Yeon Cho, Won-Ho Kim, Chang-Sung Jin, Han-Woong Ahn and Ju Lee L stk : stack length τ p : pole pitch W m : number of turns for main winding K wm : winding factor of main winding f : stator frequency p : pole pair As the accuracy of the motor characteristics depends on the accuracy of the saturation factor, it is very important to determine the saturation factor accurately. 3. Saturation factor The saturation factor is defined as the following: ( Fts + F ) + ( Fcs + F ) Ks = + () Fg F g : magnetomotive force in airgap F ts, : magnetomotive force in teeth of stator, rotor F cs, : magnetomotive force in yoke of stator, rotor To calculate the saturation factor, the magnetomotive force in each part of the motor must be determined. For this step, the magnetic circuit method was used. The total magnetomotive force of the induction motor can be expressed as the following equation [3]. again. Thus, the saturation factor determined the cyclical relationship in the process. Based on this cyclical relationship, the iteration routine and the numerical technique were applied. 4. Iteration Routine and Numerical Technique Fig. shows the iteration routine for the more accurate calculation of the saturation factor. For the basic designed model, the iteration routine starts the calculation process with an initial saturation factor value. After the analysis of the motor characteristics through the equivalent circuit, the airgap magnetic flux density is recalculated with the main and auxiliary winding currents and the phase difference between them. Using the recalculated airgap magnetic flux density, N+ step value of the saturation factor is computed. The convergence condition of the iteration routine is that the error between the N+ step value and the N step value is lower than the iterion. In the process, the magnetomotive force in each part can be obtained through the magnetic circuit method. Fig. 3 shows the magnetic circuit and magnetic flux path of the induction motor. Using the magnetic circuit method, the total magnetomotive force can be calculated as the following: 0 F WI 0 K w π p = (3) I : maximum current value at no load To calculate the magnetomotive force in each part of the motor, the airgap magnetic flux density should be considered. Unlike the three phase induction motor, in the case of the single phase induction motor, the phase difference between the main winding current and the auxiliary winding current should be considered for the airgap magnetic flux density. The airgap magnetic flux density equation can be expressed as following: μ 0 Bg = Fmcosωtcosθes gkcks μ0 + Facos( ωt+ γ)cos( θes + π / ) gkcks (4) F m : magnetomotive force of main winding F a : magnetomotive force of auxiliary winding γ : phase difference between main winding current and auxiliary winding current θ es : elecical angle of stator position ω : stator angular speed When using the equivalent circuit, the phase difference should be considered. Thus, the saturation factor required Fig.. Flow chart of the iteration routine for considering the saturation factor 743

3 Characteristics Analysis of Single Phase Induction Motor via Equivalent Circuit Method and Considering Saturation Factor F cs F ts F g F F Fig. 3. Magnetic circuit and magnetic flux path F = Fg + Fts + F + Fcs + F (5) The magnetomotive force equation in the airgap can also be calculated as the following: Fg Bg, mag Kcg μ0 = (6) B g, mag : fundamental element of airgap flux density The magnetomotive force in the airgap can be calculated based on the magnitude of the airgap magnetic flux density, which the iteration routine converged with the initial saturation factor value. As the magnetic field sength depends on the magnetic characteristics of the iron material and the magnetic flux density, the magnetomotive force calculation in the yoke and teeth of the core requires the H-B curve characteristics of the iron material. In this paper, H-B curve of iron was fitted using a numerical technique, such as the Gaussian 4th fitting function. Using ust region reflective Newton algorithm [6], the Gaussian 4th fitting function was fitted as the following: B b B b H = aexp + aexp c c (7) B b 3 B b 4 + a3exp + a4exp c 3 c 4 a =.89e+ 7, a =.75e+ 4, a3 = 467.4, a4 =.987e+ 4 b =.9, b =.35, b3 =.838, b4 =.5 c = 0.63, c = 0.535, c = 0.063, c = This fitting function fit the H-B curve better compared to the conventional fitting function model [7, 8]. Fig. 4 compares the original H-B curve points and the Gaussian 4th fitting function. The magnetic flux densities in yoke and teeth of the core can be expressed as the following: Fig. 4. Original H-B curve points and the fitted points using Gaussian 4 th fitting function Bcs, τ = (8) Bg, mag p π hcs, h cs, : yoke width of stator, rotor Bts, τ = (9) pbg, mag p Nb s ts, b ts, : teeth width of stator, rotor Using Eq. (7), the magnetic field sength in each part can be calculated from the precalculated magnetic flux densities in the airgap, yoke, and teeth. The magnetomotive forces in the yoke and teeth of the core can be calculated as the following: = (0) Fcs, Hcs, lcs, l cs, : average flux path length in yoke of stator, rotor H : magnetic field sength in yoke of stator, rotor cs, F H l ts, = ts, ts, () l ts, : teeth height of stator, rotor H : magnetic field sength in teeth of stator, rotor ts, 5. Comparison Between Proposed Method and Finite Element Method Table shows the design specifications, consaints, and heuristic knowledge of the single phase induction motor. The analysis results using the proposed method were compared with FEM results of the designed model. Fig. 5 shows the FEM model and the external circuit with run capacitor [9-]. Due to the designed motor type was capacitor start and run, the FEM model was connected with 744

Su-Yeon Cho, Won-Ho Kim, Chang-Sung Jin, Han-Woong Ahn and Ju Lee Table. Design specifications, consaints, and heuristic knowledge Spec.

Analysis results using the proposed method and finite element method Value[Unit]. kw 4 0 Vrms 60 Hz Capacitor start & run.3t 36/48 45% 4.

W 69.53 W 47.3 W 9.73 W 88.5 % 0.965 6. Manufactured Model and Test Results The prototype model was manufactured to compare the results of the proposed method.

As no standards have been established for the loss separation test method for the single phase induction motor, the input power, output power, and efficiency were measured using a dynamo test set and

4 Su-Yeon Cho, Won-Ho Kim, Chang-Sung Jin, Han-Woong Ahn and Ju Lee Table. Design specifications, consaints, and heuristic knowledge Spec. & Parameters Rated power Number of pole Rated voltage Frequency Type Magnetic flux density in teeth Stator / rotor slots Slot fill factor Minimum current density Table. Analysis results using the proposed method and finite element method Value[Unit]. kw 4 0 Vrms 60 Hz Capacitor start & run.3t 36/48 45% 4.5 A/mm Proposed method Torque Speed Power Stator copper loss Rotor Al loss Iron loss Efficiency Power factor 6.06 Nm 766 RPM 0.6 W 64.3 W 3 W 30 W 89.9 % Finite element method 6.8 Nm 760 RPM 8. W W 47.3 W 9.73 W 88.5 % Manufactured Model and Test Results The prototype model was manufactured to compare the results of the proposed method. The rotor of the prototype model had aluminum die-casting rotor bars. Fig. 7 shows the prototype model. As no standards have been established for the loss separation test method for the single phase induction motor, the input power, output power, and efficiency were measured using a dynamo test set and a power analyzer, under the state of saturated temperature. Table 3 shows the comparison. There seems to be a little difference between the measurements and the analysis results using the proposed method. It is for this reason that the motor test condition was set to meet the equal output power for efficiency comparison. The efficiency of the prototype motor was determined to be 6% lower than the value obtained through the proposed method. It is thought that self-cooling fan loss, cenifugal force switch that is a device adjoined to the motor s rotor, automatically changes from start capacitor to run capacitor and the manufacturing Fig. 5. The finite element model and the external circuit with run-capacitor (a) Stator core and frame (b) Al die-casting rotor Fig. 7. Manufactured prototype model Fig. 6. Airgap magnetic flux densities from the finite element method and the proposed method Table 3. Comparison of results using the proposed method and dynamo test results of the manufactured motor the external circuit, including run capacitor. Using the proposed method and FEM analysis, the airgap magnetic flux density was calculated. Fig. 6 shows the airgap magnetic flux density. The error between the magnetic flux density results was less than 0%. Table compares the results. Except for the rotor loss, the results were very close. Torque Speed Input power Output power Efficiency 745 Proposed method 6.06 Nm 766 RPM 46.5 W 0.7 W 89.9 % Test results 6.05 Nm 735 RPM 30 W 0 W 84.4 %

Characteristics Analysis of Single Phase Induction Motor via Equivalent Circuit Method and Considering Saturation Factor error were reasons of the efficiency error.

As a result, it seems that the proposed method result and the tested result of the manufactured model had a slight error.

Conclusion In this paper, characteristics analysis method by equivalent circuit considering the saturation factor was proposed.

5 Characteristics Analysis of Single Phase Induction Motor via Equivalent Circuit Method and Considering Saturation Factor error were reasons of the efficiency error. It caused a slip difference at operating condition had the same motor output. The slip difference reduced the measured efficiency of the manufactured model. As a result, it seems that the proposed method result and the tested result of the manufactured model had a slight error. Despite those errors, the proposed method can be said to be precise and effective for designing a high efficiency motor. 7. Conclusion In this paper, characteristics analysis method by equivalent circuit considering the saturation factor was proposed. In order to calculate a more accurate saturation factor, iteration routine and numerical techniques were applied. By comparing with FEM results of designed model and dynamo test results of prototype model, it can be stated that the proposed method can guarantee more accurate analysis results and design output. And the proposed characteristics analysis method can be applied to basic design process in motors like permanent magnet motor. Acknowledgements This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No.03RAAA0057) References [] A. Almeida, et al., Elecic motor MEPS guide, Zurich, 009. [] Byung-Taek Kim, Sung-Ho Lee, and Byung-Il Kwon, Analysis of Torque Characteristics for the Singlephase Induction Motor Considering Space Harmonics, Journal of Elecical Engineering & Technology, vol., No.3, pp.37-33, 006 [3] Ion Boldea, and Syed A. Nasar, The Induction Machine Handbook, CRC PRESS, 00 [4] C. Fortescue, Method of symmeical coordinates applied to the solution of polyphase networks, American Institute of Elecical Engineers, Transactions of the American Institute of Elecical Engineers, vol.37, pp , 009. [5] A. Fitzgeral, et al., Elecic machinery, Tata McGraw- Hill, 00. [6] Coleman, T.F. and Y. Li, An Interior, Trust Region Approach for Nonlinear Minimization Subject to Bounds, SIAM Journal on Optimization, Vol. 6, pp , 996. [7] M. K. EL-Sherbiny, Representation of the Magnetization Characteristic by a Sum of Exponentials, IEEE Trans. on Magn., vol. 9, pp. 60-6, 973. [8] John R. Brauer, Simple Equations for the Magnetization and Reluctivity Curves of Steel, IEEE Trans. on Magn., vol., pp. 8, 975. [9] S. S. Murthy, H. S. Nagaraj, Annie Kuriyan, Designbased computational procedure for performance prediction and analysis of self-excited induction generators using motor design packages, IEE PROCEEDINGS, vol.35,pt. B, no., pp. 8-6, 988. [0] Stephen D. Umans, Steady-State, Lumped-Parameter Model for Capacitor-Run, Single-Phase Induction Motors, IEEE Trans. on Magn., vol.3, no., pp , 996. [] N. Sadowski, R. Carlson, S.R. Arruda, C. A. da Silva, M. Lajoic-Mazcnc, Simulation of Single-phase Induction Motor by a General Method Coupling Field and Circuit Equations., IEEE Trans. on Magn., vol.3, no.3, pp , 995. Su-Yeon Cho He received his B.S. and M.S. degrees in Elecical Engineering from Hanyang University, Seoul, Korea in 008 and 00, respectively. Since 00, he has been pursuing the Ph.D. degree at the Department of Elecical Engineering, Hanyang University. His research interests include design, analysis, testing and conol of motor/generator; power conversion systems; and applications of motor drive, such as elecic vehicles, high-speed maglev ain and renewable energy systems. Won-Ho Kim He received his B.S., M.S. and Ph.D. degrees in Elecical Engineering from Hanyang University, Seoul, Korea in 005, 007 and 0 respectively. He is now working in Samsung Advanced Institute Of Technology. His research interests include motor design, analysis of motor/ generator; and applications of motor drive, such as elecic vehicles, home appliances Chang-Sung Jin He received his B.S., M.S. and Ph.D. degrees in Elecical Engineering from Hanyang University, Seoul, Korea in 00, 003 and 0 respectively. He worked in Daewoo eleconics from in between. He is now working in Samsung Techwin. His research interests include 746

Su-Yeon Cho, Won-Ho Kim, Chang-Sung Jin, Han-Woong Ahn and Ju Lee motor design, analysis of motor/generator; power conversion systems; and applications of motor/generator, such as vehicles, automated

degree at the Department of Elecical Engineering, Hanyang University. His research interests include testing and conol of motor/generator; DSP conol systems; and power applications of motor drive.

6 Su-Yeon Cho, Won-Ho Kim, Chang-Sung Jin, Han-Woong Ahn and Ju Lee motor design, analysis of motor/generator; power conversion systems; and applications of motor/generator, such as vehicles, automated drive system Han-Woong Ahn He received his B.S. and M.S. degrees in Elecical Engineering from Hanyang University, Seoul, Korea in 00 and 0, respectively. Since 0, he has been pursuing the Ph.D. degree at the Department of Elecical Engineering, Hanyang University. His research interests include testing and conol of motor/generator; DSP conol systems; and power applications of motor drive. Ju Lee He received his M.S. degree from Hanyang University, Seoul, South Korea, in 988, and his Ph.D. from Kyusyu University, Japan in 997, both in Elecical Engineering, He joined Hanyang University in September, 997 and is currently a Professor of the Division of Elecical and Biomedical Engineering. His main research interests include elecic machinery and its drives, elecomagnetic field analysis, new ansformation systems such as hybrid elecic vehicles (HEV), and high-speed elecic ains and standardization. He is a member of the IEEE Indusy Applications Society, Magnetics Society, and Power Eleconics Society. 747

Analysis on Harmonic Loss of IPMSM for the Variable DC-link Voltage through the FEM-Control Coupled Analysis

J Electr Eng Technol.2017; 12(1): 225-229 http://dx.doi.org/10.5370/jeet.2017.12.1.225 ISSN(Print) 1975-0102 ISSN(Online) 2093-7423 Analysis on Harmonic Loss of IPMSM for the Variable DC-link Voltage through