Considerations on Modelling and Simulation of Stator Winding Distribution of a Permanent Magnet

Synchronous Motor for Driving a Bicycle

Nicolae Digă, Constantin Ghită Doctoral School of Electrical Engineering

University Politehnica of Bucharest Bucharest, Romania

nicolae.diga@yahoo.ro ghita.constantin@gmail.com

Ion Vlad, Silvia-Maria Digă Department of Electrical, Energetic and Aerospace

Engineering University of Craiova, Romania

ivlad@em.ucv.ro sdiga@elth.ucv.ro

Dorinel Constantin CAE Department

SC INAS SA Craiova, Romania dconstantin@inas.ro

Abstract—In this paper, the authors present a comparative analysis by computation and modelling with the dedicated software ANSYS Maxwell 2D of winding distribution on slots and phases for a permanent magnet synchronous motor used for driving a bicycle. In order to facilitate and automate the computation of the stator winding elements (of the armature) was also developed a program of their own conception according to presented algorithm, developed in Visual Basic programming environment.

Keywords—Brushless drive; Design; Device modelling; Permanent magnet motor component; Simulation.

I. INTRODUCTION In operation, the permanent magnet synchronous motor

coils are traversed by currents. For a moment of specified time and a fixed position of the armatures, the operating regime is of the stationary magnetic field. In this case the field source is represented by the instantaneous values of currents in the windings and permanent magnetization. In order to model this operating regime of synchronous motors with permanent magnets is strictly necessary to establish the windings supply.

In this paper, we present the computation algorithm for the elements of the stator winding (of the armature) finalized by winding distributing on slots and phase for the synchronous machines having q the number of slots per pole and phase, fractional. This distribution is more complicated than on machines which have integer number q. The winding scheme so drawn up was checked and corresponds exactly to the one generated by ANSYS ® Maxwell 2D software [1], [2], used for modelling and simulation of the electromagnetic field [3], [4], in the studied motor.

The machine on which the experiments and numerical models were performed is represented by a low power motor

P2N=500 W, with 46 magnetic poles and 51 stator slots, which has a line rated voltage UN1=36 V. An image of the studied motor is given in Fig. 1.

Fig. 1. The winding of permanent magnet synchronous motor for driving an electric bicycle

As it is known [5], the equations that characterize the stationary magnetic field regime are as follows:

- Ampère's law (Law of the magnetic circuit), relation (1):

→→

= JHrot (1) - Gauss's law (Law of magnetic flux) for magnetic field,

relation (2):

0=→Bdiv (2)

- Material constitutive law, relation (3):

→→→→→→

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛= BBHorHHB νμ (3)

978-1-4799-5817-7/14/$31.00 ©2014 IEEE

where: μ

ν 1= - the magnetic reluctivity.

II. COMPUTATION ALGORITHM OF STATOR WINDING ELEMENTS (OF THE ARMATURE)

The stator winding has a special structure with a fractional number of slots per pole and phase q, whose expression is given by (4):

369.04617

233251

2 1==

⋅⋅==

pmZ

q s (4)

The slots distribution per pole and phase necessary to draw up the winding scheme with q = fractional number is thus for q – smaller number than one [5], [6]:

cd

cbaq =−= (5)

(a=1; b=29; c=46; d=17).

- Three horizontal compartments are taken in the order of A, C, B (not A, B, C), each compartment being divided into “d” textboxes.

- “2p” vertical columns are taken in which are signed up the number and polarity of each pole.

- Then fill in order on the horizontal and for all columns, the number of slots in “c” to “c” textboxes, thus it results the grouping of slots (coils) per pole and phase.

- Are set the phase’s beginnings and end for each current path.

In order to make the slots distribution on the pole and phase necessary to draw up the winding scheme, then are checked the conditions of symmetry binding on the three phase windings:

1) At into two layers winding, of the condition that the number of coils per phase and the current path to be the same:

1713

51

11=

⋅=

amZ s (6)

where: a1 – the number of current paths in parallel for single-phase ( 11 =a ).

2) From the condition of balancing current paths in parallel per phase:

4612322

1=⋅=

ap (7)

3) Provided that the number of turns of each phase and the current path in parallel to be the same:

regnumarwam

nZs

css int2 11

== (8)

where: ncs – the number of effective conductors of a slot;

ws – the number of turns of each phase and current path in parallel.

4) From the condition that the induced electromotive forces (emf) per phase to be equal and out of phase with 2π/m1 :

1713

51

1=

⋅=

tmZs (9)

where: t=greatest common factor (p, Zs); t=greatest common factor (23, 51). The winding factor, kws [7] is determined finally (kws=0.944) for the winding pitch y1, determined on the basis of the relation (11), with the following formula applied to q = fractional number:

⎟⎠

⎞⎜⎝

⎛⋅=⋅= yqsssws

dmd

mkkk βππ

π

2sin

2sin

2sin

1

1 (10)

where: ssk - the winding distribution factor in slots; qsk - the shortening factor of the main pitch y1; d - the numerator of the fraction q of the relation (5). The main winding pitch expressed in slots (y1=1):

egerp

Zy s int

21 =−= ε (11)

The diametrical pitch of the winding (yd1=1.109):

p

Zy sd 21 = (12)

The relative value of the main pitch (βy=0.902):

1

1

dy y

y=β (13)

TABLE I. THE DISTRIBUTION ON THE POLE AND PHASE OF WINDINGS SLOTS FOR THE PERMANENT MAGNET SYNCHRONOUS MOTOR FOR DRIVING A BICYCLE, WITH q=17/46=0.37 FRACTIONAL NUMBER (IT

CORRESPONDS TO ZS=51 SLOTS)

No. crt. coil

Phase A C B

Polarity Slot number

Polarity Slot number

Polarity Slot number

1 N 1 S 5 N 2 2 N 8 N 6 S 3 3 S 9 S 7 N 4 4 N 10 N 15 S 12 5 S 11 S 16 N 13 6 N 19 N 17 S 14 7 S 20 S 18 N 22 8 N 21 S 25 S 23 9 S 29 N 26 N 24

10 N 30 S 27 S 32 11 S 31 N 28 N 33 12 N 39 S 36 S 34 13 S 40 N 37 N 35 14 N 41 S 38 N 42 15 S 49 N 46 S 43 16 N 50 S 47 N 44 17 S 51 N 48 S 45

The coil windings are made of round wire and are called

soft coils (used in low voltage). The sides of the coils are disposed in slots, two sides of two different coils in a slot, resulting in two-layer winding [8], [9].

Fig. 4. a. Maxwell 2D interface - distribution of the winding per slots, phase A

Fig. 4. b. Maxwell 2D interface - distribution of the winding per slots, phase C

Fig. 4. c. Maxwell 2D interface - distribution of the winding per slots, phase B

Each coil has one duction side that is the top layer of the slot and a return side which is the lower layer of the slot.

Each coil has a beginning and an end. If the slot into which the coil enters is below the North Pole, it enters through beginning coil and if the slot into which the coil enters is below the South Pole, it enters through end coil (Table I).

So is determined the displacement in slots between the beginnings of phases. The entry of phases is the beginning slots 1 (A), 2 (B) and 5 (C) for the current path, so as to comply with the polarity poles.

The direction of the coil browsing by currents appears conventionally (+) (up/input) and (-) (down/out).

Thus, to facilitate and automate the computation of stator winding elements (armature) was made a programme own conception according to the presented computation algorithm. This was developed in the programming environment (language) Visual Basic which generates the graphical user interface of the type shown in Fig. 2.

Fig. 2. Graphical user interface - computation stator winding elements (armature)

III. DETERMINATION OF WINDINGS SUPPLY BY MODELLING AND SIMULATION WITH ANSYS ® MAXWELL 2D

OF THE ELECTROMAGNETIC FIELD IN THE STUDIED MOTOR The following ANSYS Electromagnetics LF products

were used in this study, [1], [2]: ANSYS® RMxprt and ANSYS® Maxwell.

ANSYS Maxwell is the most advanced simulation software of electromagnetic field for engineers involved in the design and 2D and 3D analysis of electromechanical and electromagnetic devices and motors, actuators, transformers, coils and sensors.

ANSYS RMxprt is an additional software tool to ANSYS Maxwell solution, dedicated to electric machines designers offering a standardized system of design tools in this domain.

The project may then be transferred to ANSYS Maxwell (2D/3D). Here will be defined materials, boundary conditions, including the cases of symmetry, excitations and can be coupled with circuits topology for a time-varying electromagnetic analysis required of a complex process multi-criteria optimization.

Is configured (set) general winding - phase (A, C, B) external type: stranded wire and also the excitation coil: number of conductors - 17 (Fig. 3).

Fig. 3. Maxwell 2D interface - general, the excitation coil

IV. CONCLUSION As a result of this comparative study, it was found that

the winding scheme obtained by following the proposed algorithm, corresponds exactly to the one generated by the dedicated software ANSYS Maxwell 2D, Fig. 4. a, Fig. 4. b and Fig. 4. c.

REFERENCES [1] Ansys-Ansoft 13, User’ guide, 2008, ansoft-

corporation.software.informer.com. [2] INAS S.A., http://www.inas.ro/ [3] C. Ghită, A. I. Chirilă, I. D. Deaconu, I. D. Ilina, “Wind turbine

permanent magnet synchronous generator magnetic field study”, International Conference of Renewable Energy and Power Quality (ICREPQ'08), Santander, Spain, March 12-14, 2008, paper 247.

[4] C. Ghită, S. Nedelcu, I. Trifu, T. Tudorache, „Finite Element Analysis of the Useful Magnetic Flux of a Low Speed PMSG”, University Politehnica of Bucharest, Scientific Bulletin, 2009, ISSN 1454-2331.

[5] I. Cioc, C. Nică, The design of electrical machines, Didactic and Pedagogic, R. A. Publishing House, Bucharest, 1994 (Romanian).

[6] Ø. Krøvel, Design of Large Permanent Magnetized Synchronous Electric Machines, NTNU Trondheim - Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Electric Power Engineering, Thesis for the degree of Philosophiae Doctor, February 2011.

[7] S. E. Skaar, Ø. Krøvel, R. Nilssen, “Distribution, coil-span and winding factors for PM machines with concentrated windings”, ICEM 2006.

[8] Ø. Krøvel, R. Nilssen, A. Nysveen, “A Study of the Research Activity in the Nordic Countries on Large Permanent Magnet Synchronous Machines”, NORPIE 2004.

[9] Ø. Krøvel, R. Nilssen, “Design and Measurements on a Small Radial Flux Permanent Magnet Generator with Concentrated Coils”, COMSOL Conference 2006.