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DesignandcontrolofasinglestatordualPMrotorsaxialsynchronousmachineforhybridelectricvehicles

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SorinIoanDeaconu

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FabrizioMarignetti

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GabrielNicolaePopa

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Design and Control of a Single Stator Dual PM Rotors Axial Synchronous Machine for Hybrid Electric Vehicles

Lucian Nicolae Tutelea1, Sorin Ioan Deaconu1, Ion Boldea1, Fabrizio Marignetti2, Gabriel Nicolae Popa1

1“POLITEHNICA” UNIVERSITY OF TIMISOARA Revolutiei str., no. 5, Hunedoara, Romania

Tel.: +0040 / (254) – 207.529. Fax: +0040 / (254) – 207.501.

E-Mail: sorin.deaconu@fih.upt.ro URL: http://www.fih.upt.ro

2UNIVERSITY OF CASSINO

Keywords «Hybrid electric vehicle», «Control of drive», «Design», «Permanent magnet motor».

Abstract In this paper is presenting the preliminary designing and control of a synchronous machine with axial airgap single stator dual-rotor with permanent surface magnets and different pole pairs number, destined for hybrid electric vehicles (HEV) applications. For machine’s designing was used the equivalent magnetic circuits method that takes into account the saturation and dispersion of the magnetic field. The control model is developed for a single inverter that produces three phase output voltage with two frequencies components; the torque current for each rotor is controlled through the stator current that passes the two serial windings. The machine, coupled with the thermal engine (ICE), can operate as starter for short time at start-up and as generator, when the rotational speed is established by the thermal engine’s regulator. The other machine can operate as motor in wide speed range (both inferior and superior to the generator’s), but also in generator regime with power recovery at braking.

Introduction The concept of the electric vehicle (EV) was conceived in the middle of the 19 Century. After the introduction of the internal combustion engine (ICE), EVs remained in existence side by side with the ICE for several years. The energy density of gasoline is for more than what the electrical battery could offer [1]. The early air quality concerns in the 1960’s and the energy crisis in the 1970’s have brought EV’s back to the street again. Hence, the problem associated with ICE automobiles is threefold: environmental, economical and political. These concerns have forced governments all over the world to consider alternative vehicle concepts. EV’s and hybrid-electric vehicles (HEV’s) offer the most promising solutions to reduce vehicular emissions [1]-[3]. Axial Flux Permanent Magnet (AFPM) Machines first appeared in the technical literature in mid 70’s. Soon their field of application spread widely. Today, among the most prominent appliances are fans, elevators, ships, vehicles and airplane propulsion [4]-[8]. Beside the enumerated applications, the synchronous machine with permanent magnets and axial air-gap can also be used in the field of hybrid vehicles. Basically, a hybrid propulsion system includes two electric machines: one is used to while drive; while the other is mainly used for battery charge. Although these machines play different roles, their operating cycles are more or less linked. Moreover, their locations within the power train represent a

drawback from the point of view of volume optimization. Therefore, the integration of both machines into an electromechanical set, in an attempt to improve the compactness and the cost-effectiveness, is currently considered a challenging technology. Of particular interest is the so called “single-stator dual-rotor permanent-magnet machine” [9], [10]. Radial permanent magnet motor types with one or two rotors are presented in [9], [10]. Axial air-gap with one stator and two disc permanent magnets rotors is proposed due to the reduced volume available in automotive applications. Chapter II approaches the constructive problems and the designing and chapter III, the problems related to the control of this machine, being approached the control version with a single inverter of the two serial windings.

Design and Construction An important advantage of using the synchronous axial air-gap single stator dual-rotor permanent magnet machine is representing the smaller length, this being able to be introduced in the clutch’s place between the motor and the gearbox. A 3D drawing of the machine is shown in fig. 1.

Fig. 1: Three-dimensional exploded view of the proposed machine It consists of two rotors with different pole pairs (p1 = 7, p2 = 5) and both shafts are totally independent, so that different operation of the two electric machines could be accessed. The stator is sandwiched between the two rotors, being provided with slots on one side and another in which are introduced the phases’ coils, the winding being of fractional concentrated type. The concentrated windings make it possible to significantly increase the machine inductance in order to reduce the characteristic current to the point of establishing equality with the rated current. This offers the possibility of optimal flux weakening [11], [12]. Beyond this capability, concentrated winding PM machines have been gaining an increasing interest over the last few years due to several advantages. Of particular interest are [9], [13]-[16]:

• high efficiency thanks to their end windings; • improved cost-effectiveness associated to their simple manufacturability especially with

segmented stator structures; • low cogging torque; • high fault-tolerance; • suitable integration in flux-switching machines.

Fig. 2 presents spread-out the magnetic circuit for a pair of the machine’s poles, a rotor, the axial air-gap and half of the magnetic stator’s yoke. For the other rotor the representation is identical, being different only the number of the pole pairs. Shall be noted by index 1 the measures that correspond to the rotor with 2p1 poles and with index 2 the measures that correspond to the rotor with 2p2 poles.

Γ (field line)

Rotor disc

Permanent magnet

Stator tooth

Stator yoke

Concentrated-type winding

C’ A A’ C

Fig. 2: The magnetic circuit for rotor 1 (one pole pair) and two stator teeth The equivalent magnetic circuit for a pole is presented in fig. 3. By Rmry was noted the magnetic reluctance of the portion from the rotor disc that corresponds to one pole, by RmPM1,2 the magnetic reluctance of a permanent magnet, by ePM the magneto-motor voltage of a permanent magnet, by Rmag1,2 – the magnetic reluctance of the air-gap, by Rmsz1,2 the magnetic reluctance of one stator teeth and by Rmsy the magnetic reluctance of the portion from the stator yoke that corresponds to one pole. It was not taken into account the armature reaction (fig. 3a).

Rmss1,2

Rmry1,2

RmPM1,2

ePM1,2

Rmag1,2

Rmsz1,2

Rmsy

Rmry1,2

RmPM1,2

ePM1,2

Rmag1,2

Rmsz1,2

Rmsy

es1,2

RmPMσ1,2

a) b) Fig. 3: The equivalent magnetic circuit for a pole: a) by neglecting the armature reaction b) taking into account the armature reaction and the dispersion The definition relationships for the measures from the equivalent diagram (fig. 3) are:

inoutcsinout

medmed

medprycsry

pRRhRRR

pRπτ

hhμ

τR med +=

+==

⋅⋅= ,

2,

2,

4

22

2,12,1mry

2,12,1

2,11,2

, (1)

where τp1,2 med is the medium polar pitch that corresponds to a medium radius Rmed, ranged between Rout (exterior radius) and Rin (interior radius) in such way that the fluxes through the surfaces which they limit to be equal, μry1,2 the relative magnetic permeability in the rotor discs, hry1,2 the thickness of the rotor discs on which are bonded the permanent magnets,

( )21

22mPM

221

211,2

,

inoutPMPM

PM

pRRπ

αμ

hR

,

,

−⋅⋅⋅

= ,

211,2PM ,PMc hHe ⋅= , (2)

where hPM1,2 represents the height of the permanent magnets, μPM1,2 the permeability of he permanent magnets, αPM polar coverage factor for permanent magnets, Hc the cohercitive intensity of the permanent magnets,

( )2,1

22

0

mag

2

2,11,2

pRRπ

μ

khR

inout

cag

−⋅⋅

⋅=

, 2121

214

1,241

msz,,

,

zz

systs

Sμ

hhhR

⋅

++= , ( )

211,2

22

z ,stcsst

inout whN

RRπS ⋅−

−⋅= , (3)

by hag the air-gap, kc1,2 the Carter’s coefficient, hs4 the part from the slot’s height where we don’t have winding, hst1,2 the slot’s height, hsy thickness of the stator yoke, μz1,2 the magnetic permeability between the stator teeth, Sz1,2 the teeth’s surface passed by the polar flux, Nst number of stator slots and wst1,2 slots’ width,

sycsmsy

medc

hhμτ

R⋅⋅

=4msy

, (4)

where τc med is the average slot pitch and μmsy is the stator yoke’s magnetic permeability. Taken into account the one pole armature mmf es1,2, the magnetic leakage reluctance of the slot Rmss1,2 and the leakage reluctance of the permanent magnet RmPMσ1,2 we have (fig. 3b),

1

0s

2,1

4

2,1

2,12,11,2 3

11,

−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ⋅+

⋅⋅=⋅=

st

css

st

csstmsssmc w

hhw

hh

μRise , (5)

by sc number of coils on the solenoid and ism the maximum current through the armature winding. It was made the optimal designing of an experimental model by means of Matlab environment having the power of 2,5 kW for rotor 1 and 1,7 kW for rotor 2, the model being in fabrication. The principal parameters of the model are given in Table I.

Table I: Parameters and machine dimensions Frequency (f) 50 Hz Outer diameter (Do) 260 mm Number of poles - rotor 1 (2p1) 14 poles Inner diameter (Di ) 156 mm Number of poles - rotor 2 (2p2) 10 poles Slot depth (hss) 21 mm Current density (Js) 4.33 A/mm2 Axial length of stator core (hcs) 72 mm Air-gap length (g) 2 mm Axial length of rotor core (hcr) 15 mm Pole-arc-ratio rotor 1 (αi1) 1 Magnet axial length (hPM) 5 mm Pole-arc-ratio rotor 2 (αi2) 0.6944 Permanent magnet material NeFeB

Vector control strategy and dynamic simulation We assume that the stator windings are connected in series and the objective of the dynamic simulation is to evaluate the dynamic and steady state operation of the dual vector control algorithm using two frequencies modulation operation. Fig. 4 illustrates vector control strategy.

Iαβ

θ2

T2

θ1

*2T

*1T

T1

Feed Forward +

+

+

+

βαI ,1

*2qi

*1qi

βαI ,2

Feed Forward

Torque control 2

Torque control 1

+

+

*,1 βαi

*,2 βαi

θ1-θ2

Unplug- ging

rotor 1 rotor 2

+

- *

, βαI

abc/αβ

Power battery

PI Controller

V*Inverter

ICE Control ICE

T1

ω1

θ1 rotor 1 rotor 2

T2

ω2

Stator

θ2

Fig. 4: The proposed dual vector control strategy The classic vector control with two-frequencies is made after the currents id1, id2, iq1, iq2 corresponding to the spinning systems with pulsations ω1 and ω2. In this case, the stator windings are in series and for control we can use the voltage V* and a single current. Because we don’t have the possibility to control the four components of the currents, we propose a solution in which are controlled the torque components iq1, iq2, and components id1, id2 we let to vary freely because in cases when the longitudinal and the transversal inductivity are equal (Ld = Lq) the components id1 and id2 don’ have any effect upon the torque. In fig. 5 is presenting the fluxes of the permanent magnets (ψPM1 and ψPM2) and the emf induced voltages (ue1 and ue2) in the coordinate system (α, β). The projections of these measures on the two axes have the expressions:

,sin,cos 11PM111PM1 θψψθψψ PMβPMα ⋅−=⋅−= ,sin,cos 22PM222PM2 θψψθψψ PMβPMα ⋅−=⋅−= (6)

,coscos,sinsin 11111e111111e1 θψωθuuθψωθuu PMePMβPMePMα ⋅⋅=⋅=⋅⋅−=⋅−= (7)

.coscos,sinsin 22222e222222e2 θψωθuuθψωθuu PMePMβPMePMα ⋅⋅=⋅=⋅⋅−=⋅−= (8)

d1

β

α

d2

q2

q1

ψPM1

ψPM2

uePM2

uePM1

θ1

θ2

Fig. 5: The phase diagram of the permanent magnets’ fluxes and the emf induced voltages The resulting voltages by the two axes have the matrix expression:

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −−=⎟⎟

⎠

⎞⎜⎜⎝

⎛

22

11

21

21

coscossinsin

PM

PM

βe

αe

ψωψω

θθθθ

uu . (9)

The electromagnetic torques developed T1 and T2 have the expressions:

( ) ( ) ,cossin23,cossin

23

222222111111 θiψθiψpTθiψθiψpT βPMαPMβPMαPM ⋅⋅+⋅⋅−=⋅⋅+⋅⋅−= (10)

where from are deducted the currents iα and iβ:

( )⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

⋅⎟⎟⎠

⎞⎜⎜⎝

⎛−−

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛

22

2

11

1

12

12

21

23

23

sinsincoscos

sin1

PM

PM

β

α

ψp

T

ψp

T

θθθθ

θθii . (11)

From the previous equations is found that the machine can be driven by a single inverter by the

currents *αi and *

βi produced by the voltage V*. Due to the term ( )21sin1θθ −

it’s very difficult to

follow the prescribed current that can vary within (-∞, +∞). Currents limitations are introduced while the sinus is monitored by its sign given by the difference (θ1 - θ2). By this, the solution becomes easier to implement and is avoided the division. When the speeds become closer, ω1 is equaled with ω2 (fig. 6a), the systems are rotated until θ1-θ2=900 (-900) (fig. 6b). In this way the machines are decoupled and can be charged.

θ1 - θ2

d1

d2

q2 q1

*1qi

*2qi

*2qi

q2

d2 q1

*1qi

θ1-θ2=900(-900)

d1

a) b) Fig. 6: a) systems d1-q1 and d2-q2 rotating at ω1 = ω2;

b) systems d1-q1 and d2-q2 rotating at ω1 = ω2 and θ1 - θ2 = 900 (-900) The dual vector control strategy is illustrated in fig. 7 via a dedicate Matlab Simulink Code, for the dual torque control mode.

MotTorqRef

V_I_w

Scope

LoadTorque

1.5

LPF

1

0.2s+1ICESpeedRef

261

ICEModel

1

0.1s+1

ICEControl

PIcontroller

DualRotor

V

Tl1

Tl2

Ialpha beta

w1

w2

Tem2

Convertor

Vref V

Control

Tref1

w1

Tref2

w2

Ialpha_beta

Vref

Fig. 7: Simulink diagram of the AFPM drive

Figures 8 Show the Simulink diagram of the advanced dual torque controllers of the AFPM drive, respectively.

d, q - alfa , beta

Vref1

TrigonometricFunction

sin

Torq _c2

PIcontroller

Torq _C1

PIcontroller

Switch

Sign

ScopeTorque

ScopeI,V

Product

LPF 2

1

0.2s+1

LPF 1

1

0.2s+1

Integrator 1

1s

Integrator

1s

Ialpha _betaReg

PIcontroller

Goto 3

[Iq 2c]

Goto 2

[Iq1c]

Goto 1

[Iq 2]

Goto

[Iq1]

-K-

-K-

-K-

2

-K-

5

-K-

7

From 3

[Iq 2c]

From 2

[Iq 1c]

From 1

[Iq2]

From

[Iq1]

-u(1)*sin(u(4))+u(2)*cos(u(4))

u(1)*cos(u(3))+u(2)*cos(u(4))

-u(1)*sin(u(4))+u(2)*sin(u(3))

-u(1)*cos(u(4))+u(2)*cos(u(3))

-u(1)*sin(u(3))-u(2)*sin(u(4))

-u(1)*sin(u(3))+u(2)*cos(u(3))

Abs

|u|

Ialpha _beta5

w24

Tref 23

w12

Tref 11

Fig. 8: Detailed diagram of the control block The complete sets of parameters used in simulation are given in table II.

Table II: Dual vector control drive system parameters

Motor Parameters Phase Resistance 2.875 Ω Power (rotor 1) 2.5 kW Ialfa-beta Controller Phase inductance 8.50E-003H Power (rotor 2) 1.7 kW Ti 0.004 s Rotor 1 PM flux 0.125 Wb IGBT Inverter Ki 100 Rotor 2 PM flux 0.175 Wb VDC 560 V Limit H 500 V Pole pairs rotor 1 7 Control parameters Limit L -500 V Pole pairs rotor 2 5 ICE controller Torque Controller 1,2 Inertia rotor 1 0.018 kgm2 Ti 0.8 s Ti 0.02 s

Ki 0.5 Ki 0.1 Limit H 1 N⋅m Limit H 20 N⋅m

Inertia rotor 2 (including reduction of translating mass)

0.18 kgm2

Limit L -20 N⋅m Limit L -20 N⋅m The drive torque of the thermal motor in stationary regime is equal with the electromagnetic torque of rotor 1 (fig. 9b). In fig. 9a is presented the torque reference for the rotor 2 and the torque achieved by this, observing that is monitored the reference with quite high accuracy. The strongest oscillations that appear both in the torque of rotor 2 and the rotor 1 have place in the moment when the electric speeds of the two rotors become equal (fig. 10). The delay between the reference and the achieved value is due to the rank 1 filter with a time constant of 0.2 s.

The speed of rotor 1 reaches rapidly to the reference value imposed to the thermal motor and the speed of rotor 2 results depending on the torque reference (fig. 10). Equalizing the electric speeds, it appears an oscillation but passing is made quite easily. In the electric speeds’ equalizing area the current shows an increase. To be noticed also the current and voltage modulation, specific to the components that contain two frequencies (fig. 11). The variation forms of the two torque in the electric speeds equalizing area is presented in fig. 12. It is noticed that the pulsation frequency is reduced to equalizing the electric speeds. Fig. 13a shows the reference and the torque of the rotor 2 if the motor is operating also as generator. In fig. 13b is represented the torque of rotor 1 in this situation and in fig. 13c the speeds of the two rotors.

Reference

Achieved rotor 2 torque

Rotor 2 Torque [N⋅m]

Rotor 1 Torque [N⋅m] a)

b) Time [s]

Achieved rotor 1 torque

Fig. 9: a) Reference and achieved torque by rotor 2; b) achieved torque by rotor 1

Rotor 1 speed

Rotor 2 speed

Fig. 10: Rotor 1 and rotor 2 mechanical speed

[A]

[V]

Time [s]

Fig. 11: Voltages and currents in coordinates (α, β)

[rad/s]

Time [s]

[N⋅m]

Time [s]

[N⋅m]

Fig. 12: Torques’ variation (without signal filtering) around the electric speeds’ equalizing area

Reference

Rotor 2 torque

Rotor 1 torque

Rotor 2 speed

Rotor 1 speed

c)

a)

b)

Time [s]

Rotor 2 Torque [N⋅m]

Rotor 1 Torque [N⋅m]

[rad/s]

Fig. 13: a) reference and achieved torque by rotor 2 when operates both as motor and as generator; b) rotor 1 torque in this case; c) speeds of the 2 rotors in this case

Conclusion The single stator dual-rotors permanent magnet axial synchronous machine can be controlled by a single inverter and two frequencies, the two rotors being able to operate both as motor and as generator in a wide speed range, in the same sense or in different senses. By simulation is shown that the rotors reach at a certain moment in the situation of equality of the electric speeds, the power transfer between generator and motor being made directly without the inverter, and the transitory regime due to this equality is exceeded without important torque oscillations and speed. It is found also that passing from one operation regime into another (motor-generator or reverse) is made rapidly and easier.

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