Paper proposes methodology for calculation of pa-rameters and performance characteristics of single-phase motors based on double-field revolving theory and method of symmetrical components. Permanently split capacitor motor and single-phase shaded pole motor are investigated and their parameters and performance characteristics are calculated and verified by experiment under different operating regimes. Once, the parameters are calculated they are used as input data in numerical models of the mo-tors based on Finite Element Method (FEM). FEM models are used for calculation of magnetic flux density and its distribution in motors’ cross-section as well as in the air gap, since these parameters are difficult to be calculated or exactly predicted by analytical methods. Proposed models enable motor performance under different operating regimes to be analyzed and accurately predicted

Cogelja, Goran

Sarac, Vasilija

Stefanov, Goce

Single phase shaded pole motor and permanently split capacitor motor are analyzed with double-filed revolving theory and method of symmetrical components is used for defining motor mathematical models. As an output from mathematical models steady-state performance characteristics of both motors are calculated for different operating regimes. Results from developed mathematical models are verified with experiments. Calculated currents of stator windings from mathematical models are used as input data in numerical models of the motors analyzed with Finite Element Method (FEM). Magnetic flux density in cross section of the motors is calculated from numerical motor models under different operating regimes. Parts of magnetic cores with high flux density are discovered and construction of the motors is further improved by applying  soft magnetic powders

University of Niš: Facta Universitatis (E-Journals) / Универзитет у Нишу

STUDY OF PERFORMANCE CHARACTERISTICS OF SINGLE PHASE MOTORS

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12th International Conference on Applied Electromagnetics - ПЕС 2015 August 31 – September 02, 2015, Niš, Serbia FEM AIDED DESIGN OF PERFORMANCE CHARACTERISTICS OF SINGLE PHASE MOTORS Vasilija  SARAC1, Goce STEFANOV2 and Goran COGELJA3                                                           1 University “Goce Delcev”, Faculty of Electrical Engineering, P.O. Box 201, 2000 Štip,Macedonia, e-mail: vasilija.sarac@ugd.edu.mk  2 Univeristy “Goce Delcev”, Faculty of Electrical Engineering , P.O.Box 201, 2000 Štip,Macedonia, e-mail: goce.stefanov@ugd.edu.mk  3 Univeristy “Goce Delcev”, Faculty of Electrical Engineering , P.O.Box 201, 2000 Štip,Macedonia, e-mail: goran.cogelja@ugd.edu.mk  Abstract: Paper proposes methodology for calculation of pa-rameters and performance characteristics of single-phase motors based on double-field revolving theory and method of symmetrical components. Permanently split capacitor motor and single-phase shaded pole motor are investigated and their parameters and per-formance characteristics are calculated and verified by experiment under different operating regimes. Once, the parameters are calcu-lated they are used as input data in numerical models of the mo-tors based on Finite Element Method (FEM). FEM models are used for calculation of magnetic flux density and its distribution in motors’ cross-section as well as in the air gap, since these parame-ters are difficult to be calculated or exactly predicted by analytical methods. Proposed models enable motor performance under dif-ferent operating regimes to be analyzed and accurately predicted. Keywords: Finite element method, method of symmetrical components, performance characteristics, single-phase motors. INTRODUCTION Single phase motors have wide application in many household devices since most small power (generally bel-low 2 kW) induction machines have to operate with single phase a.c. power supplies that are readily available at homes and remote rural areas. As the name suggests, this type of motor has only one stator winding (main winding) while the rotor is a squirrel cage type. The single-phase induction motor is not a self-starting. When the motor is connected to single-phase supply the main winding carries, the altering current, which produces a pulsating magnetic filed. As the main magnetic filed is pulsating, torque necessary for the motor rotation is not generated. Consequently, it is neces-sary to have start/auxiliary winding. At single-phase shaded-pole motor (SPSPM) it is a short-circuit coil placed in stator poles while in permanently split capacitor motor (PSCM) it is a permanently connected capacitor in motor auxiliary winding. In this paper, two single-phase motors are investi-gated: permanently split capacitor motor (PSCM), type FMR 35/6 and single-phase shaded pole motor (SPSPM) type AKO-16, both product of company MikronTech (Fig.1). Based on motor exact geometry, obtained from the producer, parameters of the motors are calculated. Method of symmetrical components based on double-field revolving theory is implemented as mathematical tool for calculation of motor performance characteristics. Obtained values of characteristics from mathematical models are compared with data from experiment performed at producer premises. FEM models of motors are constructed, based on motor geometry, calculated parameters and characteristics of im-plemented materials. Magnetic flux density distribution in cross-sections of the motors is obtained using time-harmonic approach, meaning all quantities are oscillating at frequency f=50 Hz and currents in rotor windings are freely induced.   (a) SPSPM            (b) PSCM 1–main stator winding, 2–squirrel cage winding, 3–auxiliary winding Fig.1 – Cross section of single phase motors. PERFORMANCE CHARACTERISTICS  During recent years, an extensive number of models of single-phase machines are constructed in order steady-state and transient performance characteristics to be determined. Some authors propose motor model based on d-q transfor-mation mainly for calculation of single-phase motors’ tran-sient characteristics [1-3]. Others propose method of revolv-ing filed polygon technique mainly applied for calculation of performance characteristics of single phase split-phase motors where split phase (auxiliary) winding is replace by three phase winding enabling motor to be analyzed as   symmetrical three phase motor under different operating regimes [4]. In this paper, calculation of performance char-acteristics of single-phase motors is based on double-field revolving theory and methods of symmetrical components as a result of the existence of two stator windings mutually coupled one to another which produces elliptical electro-magnetic field in machine air-gap. The unsymmetrical mag-neto motive forces (mmf), currents and voltages corre-sponding to the two windings of single phase induction mo-tor denoted as general vector A may be decomposed into two symmetrical systems (Fig. 2) consisted of forward and backward components (f&b) of the symmetrical systems [5]. On that way, all the electromagnetic processes inside the machine are analyzed as in the symmetrical three phase induction machine and all motor characteristics are obtained as sum of forward (direct “+”)  and backward (inverse “-“) components. 1 3 2  Fig.2 – Symmetrical components of a two-phase system. From Figure 2:    ma AjA ;   ma AjA .  (1) The superposition principle yields:    mmm AAA ;   aaa AAA .  (2) From (1) through (2):   amm AjAA 21, (3)    *21  mamm AAjAA .  (4) The first step in performance characteristics calculation is to determine all motor parameters: Rsm-main stator wind-ing resistance, Xsm-main winding leakage reactance, Rsa-auxiliary stator winding resistance, Xsa-auxiliary stator winding leakage reactance, Xmm-the magnetizing reactance , Rrm-rotor winding resistance, Xrm-rotor winding leakage reactance, based on the motor dimensions and cross-section obtained from the producer (Fig.1). Afterwards direct and inverse impedances of main stator winding mZ  and mZ  are determined as well as mutual impedance between main and auxiliary winding maZ  and consequently they are used for calculation of direct and inverse components of current in main stator winding mI  and mI . Direct and inverse components of rotor winding impedance rZ  and rZ are calculated as well [6]. They are used for calculation of di-rect and inverse components of rotor currents rI  and rI . Supply current is calculated from:  aIIjIIImmmms . (5) Currents in main stator winding-Im, auxiliary winding-Ia and rotor winding-Ir are calculated respectively:    mmm III ,      rrr III ,  (6)  aIIjImma  ,  (7) where a is the reduction ration of auxiliary winding to main winding i.e. ratio between the number of turns of auxiliary stator winding- Na and main winding-Nm. Developed electromagnetic power is calculated from pa-rameters of rotor winding and motor slip-s:  sIRsIRPrrmrrmem22222.  (8) Mechanical power is calculated from:   sPP emmech  1 .  (9) The motor output power is expressed as:  015.12mechPP  .  (10) The motor output power is obtained from the mechanical power decreased by the value of stray losses, often difficult for measurement and IEEE-125 specifies them as 0.9-1.8% of the motor output power. Direct and inverse components of motor torque are found from:    smm RZIpM   Re2 21,  (11)    smm RZIpM   Re2 21,  (12) where p is the number of pair of poles and 1 is the angular frequency [rad/s]. Z+ and Z- are direct and inverse imped-ance obtained from main and rotor winding parameters as well as from magnetizing reactance [5].  Torque is obtained form:    MMM   (13) Input power is calculated from:  cos1 ss IVP   . (14) sV  is the motor supply voltage, sI is the supply current and cos  is the power factor.  Power factor is calculated from:   ssIIrealcos .  (15) Efficiency factor is calculated from:  12PP  . (16)  Obtained values of motor characteristics at rated load operating regime are compared with data from experiment for the purpose of verification of proposed methodology and they are presented in Table I for PSCM at rated load operating point or motor slip-s of 0.04, and in Table II for SPSPM. Table I Comparison - calculated and measured data of PSCM. Parameter Analytical approach Measur. Rated torque Mn [Nm] 0.412 0.402 Rated supply current Is[A] 1.6 1.32 Maximum output  power P2[W] 215 210 Maximal torque Mmax[Nm] 0.766 0.80 In Fig.3 are presented performance characteristics of SPSPM for currents in all windings, efficiency factor  and power factor-cos for different motor slips.   Table II Comparison-calculated and measured data of SPSPM Parameter  Analyt. Measur. Rated current I1 [A] 0.125 0.1259 Input power P1[W] 18 18.114 Power factor cos [/] 0.6545 0.6538 Main st. wind. resistance Rsm [] 498 493  No-load current I0 [A] 0.111 0.1134 No load input power P0 [W] 13.8 10.21  Short-circuit current Ik[A] 0.14 0.181  Short circuit power Pk[W] 19.87 29  Short-circuit p. f. cosk [/] 0.6683 0.7389 00,10,20,30,40,50,60,70,80,04 0,24 0,44 0,64 0,84slip [/] cosfi [/] -0,1-0,0500,050,10,150,20,25 Ia [A]eta [/]Im [A]Ir[A]ImIrIa Fig.3  – Performance characteristics of currents, power factor and efficiency of SPSPM. Characteristic of output torque of SPSPM is presented in Fig.4.  00,0050,010,0150,020,0250,04 0,24 0,44 0,64 0,84slip [/] M2 [Nm] Fig.4  – Performance characteristics of  torque of SPSPM. In Fig.5 are presented characteristics of output torque-M2, efficiency factor- and power factor-cos for PSCM.   Fig.5  – Performance characteristics of output torque, power factor and efficiency of PSCM. Currents in all motor windings of PSCM: main, auxiliary and rotor winding are presented in Fig.6. 0,000,501,001,502,002,503,003,504,004,500,00 0,20 0,40 0,60 0,80 1,00Is [A]Im [A]Ia [A]slip [/]ImIaIs Fig.6  – Performance characteristics of currents of PSCM. FEM MODELS   Throughout the recent years, FEM has proved itself as valuable tool in electrical machine analysis when calculat-ing parameters and characteristics of the variety of electro-magnetic devices [7-8]. The analysis of the electromagnetic phenomena inside single-phase machines is always a chal-lenging task due to the existence of the two stator windings mutually electromagnetically coupled, which together with the rotor winding produce an elliptic electromagnetic field in the motor air gap. Therefore, a special attention is paid on the proper motor modeling regarding current distribution in motor FEM model, by taking into account the currents in the main and the auxiliary stator winding and their phase displacement. Another important issue is the proper model-ing of different operating regimes such us: no-load, rated load or locked rotor. Therefore, the rotor bars conductivity is adjusted to the motor slips correspondingly, i.e. the motor operating regimes.  Motors are analyzed for time-harmonic case, i.e. the currents are input only in the stator windings while in the rotor winding, the current is freely induced at frequency f=50 Hz due to the specific motor modeling. On that way, the analysis of electromagnetic phenomena inside the motor is closer to the real electromagnetic processes inside the machine when it is supplied with voltage 220 V, 50 Hz. In order to determine the magnetic vector potential A, it is necessary for the whole domain i.e. motor’s cross-section to be divided into numerous elements. When analyz-ing induction machines, considering their AC excitation, the air gap magnetic field is always a time-varying quantity. In the materials with non-zero conductivity, the eddy currents are induced, consequently the field problem turns into mag-neto-dynamic i.e. non-linear time-harmonic problem. When the rotor is moving, the rotor quantities oscillate at slip fre-quency. In this case, the rotor bars conductivity  is adjust-ed correspondingly to the slip. Consequently, the following partial equation is going to be solved numerically:   Vxx src JAAB1,  (17) where srcJ represents the applied current sources. The addi-tional voltage gradient V in 2-D field problems is constant over the conduction body.   In Fig. 7 and 8 is presented magnetic flux density distri-bution at cross-section of both motors for no-load and rated operating regime, respectively.  (a) SPSPM  (b) PSCM Fig.7 – Magnetic flux density distribution in motor cross-section-no load.  (a) SPSPM  (b) PSCM Fig.8 – Magnetic flux density distribution in motor cross-section-rated load. In Fig. 9 is presented magnetic flux density distribution in air gap for both motor models at rated load. From presented results in Figs. 7 and 8 it is evident the presence of high values of magnetic flux density especially for SPSPM in the area of stators’ bridge which can be lowered by implementing high quality magnetic materials or soft magnetic powders at critical points of motor con-struction.   (a) SPSPM  (b) PSCM Fig.9  – Flux density distribution in air gap--rated load. CONCLUSION  Two types of single-phase motors (shaded pole and permanently split capacitor) are analyzed under different operating regimes. Method of symmetrical components is applied as mathematical tool for obtaining parameters and characteristic of the motors. Proposed mathematical modes of the motors and obtained results from them are verified by experiments. Complete set of performance characteristics for different motor operating regimes i.e. different motor slips are plotted enabling motors operating regimes to be easily predicted and analyzed.  Obtained parameters and characteristics are used as input data in FEM based motor models.  FEM models are analyzed for time-harmonic case, when 220 V, 50 Hz is applied at motor power supply. As a result, of FEM models magnetic flux density in motor cross- section and air gap is obtained. Usually, values of magnetic flux density in the air gap during motor design are pre-dicted, based on designer experience and reference values. Obtained models enable their accurate calculation, which improves overall motor design. REFERENCES [1] K.Makowski, M.J. Wilk: “Determination of Dynamic Charac-teristics of the Single Phase Capacitor Induction Motor”, Prezglad Electrotechniczny, R87, 2011, No. 5, pp. 231-237. [2] S. Sunter, M. Odzemir, B. Gumus: “Modeling and simulation of single phase induction motor with adjustable switched ca-pacitor”, 9th International Conference on Power Electronics and Motion Control, Kosice, 2000, pp. 5-1-5-5. [3] A. Leicht, K. Makowski: “Analysis of a single-phase capacitor induction motor operating at two power line frequencies”, Archives of electrical engineering”, Vol. 61(2), 2012, pp. 251-266. [4] C.B.Rasmussen, T.J.E.Miller: “Revolvig-Field Polygon Tech-nique for Performance Prediction of Single-Phase Induction Motor”, IEEE Transactions on Industry Applications, vol. 39, No. 5, 2003, pp. 1300-1306. [5] I. Boldea, S.A.Nasar: “The Induction Machines Design Handbook”, CRC Press, 2010, New York,  pp. 791-811. [6] I.E.Davidson> “Performance Calculation of a Shaded-Pole Single Sided Linear Induction Motor Using Symmetrical Components and Finite Element Method,” Journal Electromotion, Vol 4,  No.4, 1997, pp.139-145. [7] V. Hrabovcova, P. Rafajdus, “Radial Magnetic Forces of Sin-gle Phase Permanent Split-Capacitor Motor”, Journal of Elec-trical Engineering, Vol.57, No.4, 2006, pp. 185-192. [8] T.Vaimann, A.Belahcen, A.Kallaste: “Changing of Magnetic-flux Density Distribution in a Squirrel-Cage Induction Motor with Broken rotor Bars”, Elektronika ir Elektrotechnika, Vol.20, No.7, 2014, pp. 11-14.  

FEM aided design of performance characteristics of single phase motors

Single phase shaded pole motor and permanently split capacitor motor are analyzed with double-filed revolving theory and method of symmetrical components is used for defining motor mathematical models. As an output from mathematical models steady-state performance characteristics of both motors are calculated for different operating regimes. Results from developed mathematical models are verified with experiments. Calculated currents of stator windings from mathematical models are used as input data in numerical models of the motors analyzed with Finite Element Method (FEM). Magnetic flux density in cross section of the motors is calculated from numerical motor models under different operating regimes. Parts of magnetic cores with high flux density are discovered and construction of the motors is further improved by applying soft magnetic powders

Study of performance characteristics of single phase motors

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FEM aided design of performance characteristics of single phase motors

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