Advanced
Characteristics Analysis of Single Phase Induction Motor via Equivalent Circuit Method and Considering Saturation Factor
Characteristics Analysis of Single Phase Induction Motor via Equivalent Circuit Method and Considering Saturation Factor
Journal of Electrical Engineering and Technology. 2014. Jan, 9(1): 178-183
Copyright © 2014, The Korean Institute of Electrical Engineers
  • Received : July 08, 2013
  • Accepted : September 25, 2013
  • Published : January 01, 2014
Download
PDF
e-PUB
PubReader
PPT
Export by style
Article
Author
Metrics
Cited by
TagCloud
About the Authors
Su-Yeon Cho
Dept. of Electrical Engineering, Hanyang Univerity, Korea. (julee@hanyang.ac.kr)
Won-Ho Kim
Material&Device Research Center, Samsung Advanced Institute Of Technology, Samsung Electronics Co., Korea. (wonho79@nate.com)
Chang-Sung Jin
Mechatronics Group, Defence Program R&D Center, Samsung Techwin Co., Korea. (c.s.jin@samsung.com)
Dong-Woo Kang
Corresponding Author : R&D Team, Digital Appliances, Samsung Electronics Co., Korea. (dwkang1222@gmail.com)
Ju Lee
Dept. of Electrical Engineering, Hanyang Univerity, Korea. (julee@hanyang.ac.kr)

Abstract
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
1. Introduction
An electric motor uses above 50% electrical energy. Among the existing electric 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 [1] . 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 strength of this method is that it can be calculated the saturation factor more accurately.
2. Equivalent Circuit of Single Phase Induction Motor
In the case of the single phase induction motor, the main winding and the auxiliary winding are not the same. Thus, it has the structure of an unbalanced two phase motor. To determine the characteristics of the motor under unbalanced conditions, a symmetrical two phase equivalent circuit was constructed [2 , 3 , 4] . Fig. 1 shows the equivalent circuit as having parameters compensated to the main winding part [5] .
PPT Slide
Lager Image
Equivalent circuit for the single-phase induction motor with run-capacitor
The parameters of the equivalent circuit can be calculated based on the motor dimensions, material information and electrical specifications, but magnetization reactance is affected by the saturation factor. The magnetization reactance can be expressed as the following Eq. [3] .
PPT Slide
Lager Image
  • μ0: permeability in free space
  • Ks: saturation factor
  • Kc: Carter coefficient
  • KFe: stacking factor of core
  • g: airgap length
  • Lstk: stack length
  • τp: pole pitch
  • Wm: number of turns for main winding
  • Kwm: winding factor of main winding
  • f1: stator frequency
  • p1: 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:
PPT Slide
Lager Image
  • Fg: magnetomotive force in airgap
  • Fts,tr: magnetomotive force in teeth of stator, rotor
  • Fcs,cr: 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 Eq. [3].
PPT Slide
Lager Image
  • I0: 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:
PPT Slide
Lager Image
  • Fm1: magnetomotive force of main winding
  • Fa1: magnetomotive force of auxiliary winding
  • γ: phase difference between main winding current and auxiliary winding current
  • θes: electrical angle of stator position
  • ω1: stator angular speed
When using the equivalent circuit, the phase difference should be considered. Thus, the saturation factor required 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. 2 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+1 step value of the saturation factor is computed. The convergence condition of the iteration routine is that the error between the N+1 step value and the N step value is lower than the criterion.
PPT Slide
Lager Image
Flow chart of the iteration routine for considering the saturation factor
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.
PPT Slide
Lager Image
Magnetic circuit and magnetic flux path
Using the magnetic circuit method, the total magnetomotive force can be calculated as the following:
PPT Slide
Lager Image
The magnetomotive force equation in the airgap can also be calculated as the following:
PPT Slide
Lager Image
  • Bg1,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 strength 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 trust region reflective Newton algorithm [6] , the Gaussian 4th fitting function was fitted as the following:
PPT Slide
Lager Image
  • 𝑎1= 1.189ℯ + 17, 𝑎2= 1.725ℯ + 4, 𝑎3= 467.4, 𝑎4= 2.987ℯ + 4
  • 𝑏1= 2.9, 𝑏2= 2.135, 𝑏3= 1.838, 𝑏4= 2.251
  • 𝑐1= 0.1613, 𝑐2= 0.1535, 𝑐3= 0.0263, 𝑐4= 0.4038
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.
PPT Slide
Lager Image
Original H-B curve points and the fitted points using Gaussian 4th fitting function
The magnetic flux densities in yoke and teeth of the core can be expressed as the following:
PPT Slide
Lager Image
  • hcs,cr: yoke width of stator, rotor
PPT Slide
Lager Image
  • bts,tr: teeth width of stator, rotor
Using Eq. (7), the magnetic field strength 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:
PPT Slide
Lager Image
  • lcs,cr: average flux path length in yoke of stator, rotor
  • Hcs,cr: magnetic field strength in yoke of stator, rotor
PPT Slide
Lager Image
  • lts,tr: teeth height of stator, rotor
  • Hts,tr: magnetic field strength in teeth of stator, rotor
5. Comparison Between Proposed Method and Finite Element Method
Table 1 shows the design specifications, constraints, 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 - 11] . Due to the designed motor type was capacitor start and run, the FEM model was connected with 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 10%. Table 2 compares the results. Except for the rotor loss, the results were very close.
Design specifications, constraints, and heuristic knowledge
PPT Slide
Lager Image
Design specifications, constraints, and heuristic knowledge
Analysis results using the proposed method and finite element method
PPT Slide
Lager Image
Analysis results using the proposed method and finite element method
PPT Slide
Lager Image
The finite element model and the external circuit with run-capacitor
PPT Slide
Lager Image
Airgap magnetic flux densities from the finite element method and the proposed method
6. 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.
PPT Slide
Lager Image
Manufactured 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, centrifugal force switch that is a device adjoined to the motor’s rotor, automatically changes from start capacitor to run capacitor and the manufacturing 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.
Comparison of results using the proposed method and dynamo test results of the manufactured motor
PPT Slide
Lager Image
Comparison of results using the proposed method and dynamo test results of the manufactured motor
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.2013R1A2A1A01015171)
BIO
Su-Yeon Cho He received his B.S. and M.S. degrees in Electrical Engineering from Hanyang University, Seoul, Korea in 2008 and 2010, respectively. Since 2010, he has been pursuing the Ph.D. degree at the Department of Electrical Engineering, Hanyang University. His research interests include design, analysis, testing and control of motor/generator; power conversion systems; and applications of motor drive, such as electric vehicles, high-speed maglev train and renewable energy systems.
Won-Ho Kim He received his B.S., M.S. and Ph.D. degrees in Electrical Engineering from Hanyang University, Seoul, Korea in 2005, 2007 and 2011 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 electric vehicles, home appliances
Chang-Sung Jin He received his B.S., M.S. and Ph.D. degrees in Electrical Engineering from Hanyang University, Seoul, Korea in 2001, 2003 and 2011 respectively. He worked in Daewoo electronics from 2003-2007 in between. He is now working in Samsung Techwin. His research interests include motor design, analysis of motor/generator; power conversion systems; and applications of motor/generator, such as vehicles, automated drive system
Dong-Woo Kang He received his B.S., M.S. and Ph.D. degrees in Electrical Engineering from Hanyang University, Seoul, Korea in 2006, 2008 and 2011 respectively. He is now working in Samsung Electronics Co. His research interests include design, analysis, of motor/generator; power conversion systems; and applications of spherical motor for robots; home appliances.
Ju Lee He received his M.S. degree from Hanyang University, Seoul, South Korea, in 1988, and his Ph.D. from Kyusyu University, Japan in 1997, both in Electrical Engineering, He joined Hanyang University in September, 1997 and is currently a Professor of the Division of Electrical and Biomedical Engineering. His main research interests include electric machinery and its drives, electromagnetic field analysis, new transformation systems such as hybrid electric vehicles (HEV), and high-speed electric trains and standardization. He is a member of the IEEE Industry Applications Society, Magnetics Society, and Power Electronics Society.
References
Almeida A. 2009 Electric motor MEPS guide Zurich
Kim Byung-Taek , Lee Sung-Ho , Kwon Byung-Il 2006 “Analysis of Torque Characteristics for the Single-phase Induction Motor Considering Space Harmonics” Journal of Electrical Engineering & Technology 1 (3) 327 - 331    DOI : 10.5370/JEET.2006.1.3.327
Boldea Ion , Nasar Syed A. 2002 The Induction Machine Handbook CRC PRESS
Fortescue C. 2009 “Method of symmetrical coordinates applied to the solution of polyphase networks,” Transactions of the American Institute of Electrical Engineers American Institute of Electrical Engineers 37 1027 - 1140
Fitzgeral A. 2002 Electric machinery Tata McGraw-Hill
Coleman T.F. , Li Y. 1996 “An Interior, Trust Region Approach for Nonlinear Minimization Subject to Bounds” SIAM Journal on Optimization 6 418 - 445    DOI : 10.1137/0806023
EL-Sherbiny M. K. 1973 “Representation of the Magnetization Characteristic by a Sum of Exponentials” IEEE Trans. on Magn. 9 60 - 61    DOI : 10.1109/TMAG.1973.1067562
Brauer John R. 1975 “Simple Equations for the Magnetization and Reluctivity Curves of Steel” IEEE Trans. on Magn. 11 81 -
Murthy S. S. , Nagaraj H. S. , Kuriyan Annie 1988 “Design-based computational procedure for performance prediction and analysis of self-excited induction generators using motor design packages”, Pt. B IEE PROCEEDINGS 135 (1) 8 - 16
Umans Stephen D. 1996 “Steady-State, Lumped-Parameter Model for Capacitor-Run, Single-Phase Induction Motors,” IEEE Trans. on Magn. 32 (1) 169 - 179
Sadowski N. , Carlson R. , Arruda S.R. , da Silva C. A. , Lajoic-Mazcnc M. 1995 “Simulation of Single-phase Induction Motor by a General Method Coupling Field and Circuit Equations.” IEEE Trans. on Magn. 31 (3) 1908 - 1911    DOI : 10.1109/20.376412