Direct Flux Vector Control of Axial Flux IPM Motors for in-Wheel Traction Solutions

R. Bojoi, Senior Member IEEE, G. Pellegrino, Member IEEE, A. Cavagnino, Senior Member IEEE, P. Guglielmi, Member IEEE

Politecnico di Torino, Dipartimento di Ingegneria Elettrica, Corso Duca degli Abruzzi 24, 10129 Torino, Italy radu.bojoi@polito.it, gianmario.pellegrino@polito.it, andrea.cavagnino@polito.it, paolo.guglielmi@polito.it

Abstract-The paper describes a Direct-Flux Vector Control

(DFVC) scheme suitable for synchronous Permanent Magnet (PM) drives employed in applications that require motor flux-weakening operation, as happens for traction drives. The proposed controller operates in stator flux reference frame and can be easily adapted for Surface-mounted PM (SPM) and Interior PM (IPM) motors. The stator flux is directly controlled by the direct component of the voltage vector, while the torque is controlled by regulating the quadrature current component. The DFVC scheme has been used for an Axial Flux IPM (AFIPM) designed as a wheel motor for light traction application. Experimental results are provided for an 1.2 kW AFIPM prototype, demonstrating good steady-state and transient performance, as well as maximum torque production under current and voltage limitations.

I. INTRODUCTION

The Axial Flux Permanent Magnet (AFPM) motors are considered today as an interesting and feasible solution for traction drives [1-3]. Due to its flat shape, the AFPM machine can be directly mounted inside the wheel or can be directly connected to the wheel, obtaining the so-called “wheel motor” [1]. For this reason, the mechanical differential and even the reduction gear can be removed.

The traction applications usually require a large constant torque from zero to the base speed ωb. Above the base speed up to the maximum speed ωmax, a constant power operation is required. Depending on the specific vehicle design, the ratio between the base speed and the maximum speed is usually in the range 1:2 to 1:4.

Different AFPM motors solutions have been proposed in the literature as wheel motors [1-6]. Among these solutions, the AFPM motor using interior magnets (AFIPM) is more suitable as wheel motor due to its robustness and flux-weakening capability [6].

The AFIPM motor needs a suitable control strategy to fulfill the requirements imposed to a wheel motor. At low speed, Maximum Torque Per Ampere (MTPA) operation is needed to maximize the motor efficiency, while at high speed operation maximum torque capability (with limited current and limited voltage) must be obtained.

The literature reports many vector control schemes for IPM motors requiring flux-weakening operation [7-10]. Most of them are based on current control implemented in rotor frame. The flux-weakening operation is obtained using proper techniques. Some proposed schemes are based on the motor model and for this reason they are sensitive to motor parameters detuning [7]. To overcome this problem, a flux-

weakening scheme using a closed-loop voltage control was proposed in [8,9]; although good results are obtained at steady-state operation, fast DC link variations (e.g. during motor braking) may produce instability and the current control is lost.

In contrast with the vector control schemes based on rotor flux orientation, the Direct Flux Vector Control (DFVC) approach is implemented in (ds,qs) stator flux frame [10]. The stator flux is directly controlled by the ds-axis component of the stator voltage vector, while the torque is controlled by regulating the qs-axis component of the stator current vector. The direct flux control approach makes the DFVC particularly convenient for machines requiring deep flux-weakening operation, as happens for AFIPM machines employed as wheel motors.

The paper presents a DFVC scheme for an AFIPM machine designed as a wheel motor in light traction applications. Maximum torque capability and control stability are obtained at high speed with higher robustness against motor parameter detuning than the vector control schemes implemented in rotor frame.

The paper is organized as follows. First, the AFIPM motor model is analyzed. Then, the DFVC is described, emphasizing the most important parts. Finally, experimental results for a 1.2 kW AFIPM motor are shown, demonstrating the DFVC feasibility for the considered application.

II. AFIPM MOTOR MODELING

A. AFIPM motor structure description The AFIPM motor considered in this paper uses a novel

design initially proposed in [5] and experimental validated for steady-state operations in [6]. The prototype basic structure is shown in Fig.1a. The machine is arranged by one rotor sandwiched between two stators. Each stator core is one-side slotted wound core realized by taped wound laminations, where the slots are radially positioned. The axially magnetized permanent magnets find accommodation in a stainless steel rotor disc; above the two PMs sides are fixed two rings realized with Soft Magnetic Composite (SMC) material. For each rotor pole pitch, two gaps (flux barriers) are opened in these rings. In this way, the main poles and the leakage pole are created (Fig.1b and Fig.2). The main poles allow to easily modifying the no-load quasi-sinusoidal airgap flux density waveform, whereas the leakage poles introduce a suitable saliency in the machine.

978-1-4244-5226-2/10/$26.00 ©2010 IEEE 2224

β ds

qs

q λ δ d

ϑ

α

ω

Fig. 3. Definition of the

reference frames.

(a) overall motor structure.

Stator 1 Stator 2

Flux Barrier Leakage Pole

Permanent magnet Stainless Steel Disc

Main Pole

(b) pole pitch unfolded axial section at the average radius.

Fig. 1. AFIPM motor structure.

MagnetLeakage Pole

Main Pole

Stainless Steel Disc

Fig. 2. AFIPM motor structure: view of the rotor poles (left side)

and of the rotor disk without poles (right side). As a consequence, the flux barrier position and their

dimensions can be designed in a such a way that the Ld and Lq stator inductances can satisfy the conditions to deliver the request torque in the whole flux weakening region [5].

B. Motor Model The machine stator vectors (voltage, current and flux) are

called v , i and λ , respectively. The adopted vector reference frames are defined in Fig. 3 for a generic radial IPM machine as follows: stationary frame (α,β), rotor frame (d,q) and stator flux frame (ds,qs). The subscript “s” used for the machine vectors will refer to the stator flux reference frame.

The AFIPM voltage equation and the electromagnetic torque expression in stationary reference frame are:

dt

diRv s

αβαβαβ

λ+⋅= (1)

( )αββα ⋅λ−⋅λ⋅⋅= iipTe 23 (2)

where Rs is the stator resistance, p is the pole-pairs number.

The motor model must be completed with the current-to-flux relation, also known as the magnetic model.

For motors employing internal permanent magnets, it is more convenient to define their magnetic models in rotor frame as

[ ] ( )( )⎥⎦

⎤⎢⎣

⎡λλ

=⎥⎦

⎤⎢⎣

⎡λ+⎥

⎦

⎤⎢⎣

⎡⋅=λ

qdq

qddm

q

ddq ii

iiii

L,,

0 (3)

where λm is the flux linkage due to the magnets. As demonstrated in [11,12], a realistic magnetic model

should take into account the cross-saturation. To investigate the impact of cross-saturation and also the magnetic saturation, the AFIPM motor model has been experimentally identified using the procedure described in [11]. In Fig. 4 the variations of λd(id,0), λd(id,5A), λq(0,iq) and λq(-5A,iq) are reported for ∈di [-5,0] (A) and ∈qi [0,5] (A).

As shown in Fig.4, the impact of cross-saturation is quite small and can been neglected. For this reason, the magnetic model (3) can be written in the simplified form as

⎥⎦

⎤⎢⎣

⎡λ+⎥

⎦

⎤⎢⎣

⎡⋅⎥

⎦

⎤⎢⎣

⎡=λ

000 m

q

d

q

ddq i

iL

L (4)

where Ld is the motor d-axis inductance, while Lq is motor the q-axis inductance.

If the rotor position is ϑ (Fig. 3), then the magnetic model in stationary reference frame can be obtained as

( ) ( ) ( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎦

⎤⎢⎣

⎡λ+⎥

⎦

⎤⎢⎣

⎡⋅ϑ⋅⎥

⎦

⎤⎢⎣

⎡⋅ϑ−=λ⋅ϑ−=λ

β

ααβ 00

0 m

q

ddq i

iA

LL

AA (5)

where ( ) ( ) ( )( ) ( )⎥⎦

⎤⎢⎣

⎡ϑϑ−ϑϑ

=ϑcossinsincos

A .

Fig. 4. Measured stator flux-linkage components

versus stator currents in rotor frame.

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III. DFVC STRATEGY

A. Motor Model in Stator Flux Reference Frame The voltage model and the electromagnetic torque referred

to the stator flux reference frame are

⎥⎥⎦

⎤

⎢⎢⎣

⎡δ+ω⋅λ+⎥

⎦

⎤⎢⎣

⎡λ+⋅=

dtd

dtdiRv dqssdqs

0

0 (6)

( ) qsTqse ikipT ⋅=⋅λ⋅⋅= 23 (7)

where ω is the rotor speed and δ is the load angle defined as stator flux position respect to the rotor d-axis (Fig.1).

From (6) it immediately results that the stator flux vector magnitude λ can be directly regulated by the ds-axis voltage, while the load angle (and consequently the torque) can be controlled through the qs-axis voltage. However, (7) shows that the regulation of the qs-axis current is straightforward for torque regulation. In this case, the (ds,qs) voltage model must have the qs-axis current as state variable instead of the load angle that was used in [13].

As demonstrated in [7], the voltage model in (ds,qs) frame becomes

( ) ( ) ( ) ( )λ⋅ω−⋅λδ+⋅−⋅δ+⋅−=⋅

+⋅−=λ

qsdssdsqssqs

d

dsdss

vbiRvaiRdt

diL

viRdtd

, (8)

( ) ( ) ( )qd LLa −⋅=δ 121 (9)

( ) ( ) ( ) ( ) δ⋅λλ+δ⋅−−=λδ cos2cos1, mqd LLb (10) It can be noted from (8) that there is a cross-coupling

between flux and torque current regulation channels only when a flux variation is required. Moreover, the control is stable only if ( ) 0, ≥λδb . Otherwise, an increase of qs-axis voltage will produce a decrease of the iqs current (and torque) and the control is lost. The loss of stability can be avoided by limiting the load angle, as it will be discussed later.

B. DFVC Scheme The whole AFIPM control scheme is shown in Fig.5. The

main blocks are: DFVC, the Stator Flux Observer (SFO) and the speed computation block. The DFVC uses an outer speed loop that provides a reference torque value, but the reference torque can also be generated in an open-loop fashion.

AFIPM

vdc + -

αβi

*ω + PWM PI

*αβv

δϑ ˆ,ˆs

Stator Flux Observer

λ̂

*eT

vdc -

DT

iabc

Speed computation

ω

ϑ

DFVC

*abcv

dtvαβ

2 3

2 3

2 3

dtabcv

Fig. 5. AFIPM control scheme.

The SFO is shown in Fig. 6; it is based on the magnetic model (5) at low speed (current model) and on the stator back-EMF integration (voltage model) at high speed. The crossover angular frequency ωco between low-speed and high speed models coincides with the observer gain g (rad/s). The SFO provides the stator flux magnitude, the stator flux position and also the load angle.

The inverter non-linearity effects (mainly the dead-time effects) are compensated using an error vector dtvαβ [14] that is subtracted from the reference stator voltage vector in (α,β) frame, as shown in Fig. 6. This error vector is computed by applying the Clarke transformation on the phase voltage errors (computed by the DT block) that depend on the sign and the values of the measured phase currents [14].

The DFVC block is shown in Fig. 7. It is implemented in stator flux reference frame and contains two inner control loops that regulate the stator flux and the qs-axis stator current. Both loops use Proportional-Integral (PI) controllers. The flux and current regulation take into account the inverter voltage and current limits, as well as the load angle limitation.

(1) Maximum voltage limitation Below the base speed, the reference flux is computed

according to the Maximum Torque Per Ampere (MTPA) profile using as input the required torque, as shown in Fig. 8a. The MTPA block has been implemented as a 64 points Look-Up Table (LUT) according to preliminary calibration tests using torque measurements. If no off-line motor identification is available, analytical MTPA curves can be used [10], at the expense of a higher ampere per torque ratio.

∫

Rs

*αβv

αβi

+ - -

αβλˆ

+ - g

αβλ~

ϑ

x λ̂

sϑ̂

αβ dq

dqiαβ

dq

dqλ~

dtvαβ

-

Magnetic model (4)

Magnetic model (5)

x∠

Fig. 6. Stator flux observer.

αβi

*eT

PI

PI

αβ dq

dqαβ

sϑ̂

*dsv

*qsv

iqs

*qsi

vdc

+

Max torque current

computation iqs,max

1−Tk

22

21 uu −

-

Vs,max

*αβv

u1 u2

Reference flux generation

*λ

λ̂

δ̂

ids

iqs Flux

controller

qs –axis current controller

Max voltage

+

-

Fig. 7. DFVC scheme.

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As the speed increases, the steady-state required motor voltage increases and for this reason the MTPA condition cannot be fulfilled anymore due to the limited available voltage. The voltage limitation condition is given by ( ) ( ) 2

max,22

sqssdss ViRiR ≤ωλ++ (11)

where Vs,max depends on the PWM strategy and on the instantaneous DC link voltage vdc.

From (11) it results that the voltage limitation operation is obtained by limiting the stator flux reference value with

ω

⋅−≅

ω

⋅−⋅−=λ qsssqssdsss iRViRiRV max,

22max

lim)(

(12)

where 3max, dcs vV = . The scheme from Fig.8a has the advantage that the flux-

weakening starting point is automatically selected according to the maximum DC link voltage and required qs-axis current. The voltage limitation acts also on the flux and current controllers outputs, as shown in Fig. 7.

(2) Maximum inverter current limitation The qs-axis reference current is computed from the required

torque according to (7). To limit the phase current to the maximum allowable inverter current Is,max (Fig.8b), the qs-axis maximum reference current is computed as

22max,max, dssqs iIi −≤ (13)

where ids is the ds-axis stator current component. The current limitation iqs,max is computed as a positive value

since the limitation operator from Fig. 7 limits both positive and negative values for the qs-axis reference current.

(3) Load angle limitation As shown by (8,10), the current regulation is stable only if

( ) 0, ≥λδb . From (10) it results that unstability is avoided by limiting the load angle δ at a maximum value δmax for which

( ) 0, =λδb . The motor operation with maximum load angle is also known as Maximum Torque Per Volt (MTPV) operation. For a conventional SPM machine (with no saliency), the MTPV operation is obtained for δmax=90°, while for IPM motor δmax>90°.

As shown in Fig.8b, the load angle limitation is performed using a PI controller that reduces the maximum allowed current (with no need of motor parameters) if the estimated load angle is higher than the specified δmax. The δmax set-point can be evaluated by means of the identified motor model or by finding the δmax value that obtains the best motor acceleration at no-load using the trial-and-error method.

MTPA

*eT

Eq. 12

*λ

Vs,max

iqs Flux-weakening block

λlim

(a)

22max, dss iI −

PI δ̂ maxδ

()abs +

-

+

-

iqs,max ids

MTPV controller

Inverter current limitation

(b)

Fig. 8. Voltage, current and load angle limitation schemes.

IV. EXPERIMENTAL RESULTS

The experimental tests have been performed using an 8-poles AFIPM motor prototype whose parameters are reported in the Appendix. The AFIPM motor (Fig.9a) is coupled with a large DC machine through a belt. The DC machine has been operated as a generator having a resistive load. The motor is fed by an industrial IGBT inverter (Fig. 9b) whose switching frequency is 10 kHz. The inverter is fed by a three-phase diode bridge rectifier with capacitive load. The line-to-line rectifier input voltage is 220Vrms. A braking chopper limits the DC link voltage during motor braking.

The control algorithm is synchronized with the PWM and it has been implemented on the dSpace DS1103 fast prototype board. During motor operation, the DS1103 board can save a large amount of data that can be visualized in Matlab format. The DS1103 board employs a special hardware interface for feedback acquisition, for PWM commands transmission and for hardware protection. The motor position is measured with a resolver through a resolver-to-digital converter. All control parameters are reported in Appendix.

(a) AFIPM prototype (b) Inverter and hardware interface

Fig. 9.Views of experimental setup.

A. Low Speed Operation The drive response to a 5Hz sinusoidal speed reference is

shown in Fig.10. The speed distortion is mainly caused by the mechanical coupler and the belt between the AFIPM shaft and the loading DC machine, and not due to the DVFC.

Fig. 10. Low speed operation with 5 Hz sinusoidal reference speed.

From top to bottom: (1) reference speed *ω (rpm), (2) rotor speed ω (rpm),

(3) observed stator flux λ̂ (Vs), (4) estimated torque Te (Nm), (4) ia (A).

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B. Load Rejection Behavior The drive load rejection has been tested below the base

speed (400 rpm) for step load transients of about 20 Nm from no-load, as shown in Fig. 11. It can be noted the good AFIPM torque response. As the speed is below the starting value of the flux-weakening range, the stator flux reference is generated according to the MTPA profile that minimizes the copper losses.

C. Flux-Weakening Operation The experimental results for motor speed reversal from

-900 rpm to +900 rpm for step speed reference value and inertial load are shown in Figs.12,13. It can be seen that the machine current is well limited at the maximum allowed value of 8A. During motor braking, the DC link voltage is limited at about 360V and has a sawtooth waveform with a 30V ripple due to the braking chopper operation. Since at flux-weakening operation the stator flux reference is dictated by the voltage limitation, the stator flux is varied to exploit all available voltage, as can be clearly seen in Figs.12,13. The DC link voltage increase during braking means also that DFVC gets more torque (and power) during braking respect to motoring operation (Figs. 12,13).

The AFIPM motor constant power operation is shown in Fig. 13. The AFIPM was operating at maximum speed (900 rpm) and no-load, when a step load transient was applied, followed by the load removal. It can be seen that the DFVC pulls-down the motor speed to limit the output power at about 1.3kW. The machine current was limited all the time to the maximum allowable current of 8A. The stator flux reference is adjusted according to the available voltage (the DC link voltage has a drop of about 20V) and also acccording to the required qs-axis current.

Fig. 11. Step load transients below base speed. From top to bottom:

(1) reference speed *ω (rpm), (2) rotor speed ω (rpm),

(3) observed stator flux λ̂ (Vs), (4) estimated torque Te (Nm), (4) ia (A).

Fig. 12. Speed reversal from –900 rpm to 900 rpm. From top to bottom:

(1) reference speed *ω (rpm), (2) rotor speed ω (rpm),

(3) observed stator flux λ̂ (Vs), (4) estimated torque Te (Nm), (4) ia (A).

Since the maximum current (8Apk) and speed (±900rpm) specifications do not include MTPV operation for the considered AFIPM prototype, the maximum load angle δmax has been limited on purpose at 70 degrees to demonstrate the feasibility of the load angle limitation strategy. The motor start-up from standstill to maximum speed (900 rpm) with δmax=70° is shown in Fig. 15. It can be seen that the MTPV limitation works very well. As a result, the torque is limited and also the machine current that will be below 8A.

Fig. 13. Speed reversal from –900 rpm to 900 rpm. From top to bottom:

(1) mechanical power Pmec (W) (2) observed stator flux λ̂ (Vs), (3) DC link voltage vdc (V).

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Fig. 14. High speed operation with load step transients.

From top to bottom: (1) reference speed *ω (rpm), (2) rotor speed ω (rpm),

(3) observed stator flux λ̂ (Vs), (4) estimated torque Te (Nm), (4) mechanical power Pmec (W), (5) DC link voltage vdc (V), (6) ia (A).

Fig. 15. Motor start-up with load angle limitation at 70 electrical degrees.

V. CONCLUSIONS

The paper deals with a DSFVC scheme strategy for AFIPM machine used as wheel-motor in light traction applications. This control strategy uses simple PI regulators implemented in the stator flux synchronous reference frame. While the stator flux is directly controlled by the ds-axis component of the stator voltage vector, the torque is regulated by controlling the qs-axis current component of the stator current vector. The DFVC guarantees maximum torque production under current and voltage constraints even under oscillatory

and highly variable DC link voltage. The DFVC stability at MTPV operation is obtained by a proper limitation of the load angle at a desired value. For the above presented features, the DFVC is a very good solution for IPM motors used for traction applications. Experimental results are provided for an 1.2 kW AFIPM motor prototype, showing good results for the entire speed range.

APPENDIX

A. AFIPM motor parameters Vrated= 200V, Irated= 5A, Rs= 5Ω@25°C, λm= 0.65Vs,

Ld= 84 mH, Lq= 105 mH, maximum speed ωmax=900 rpm, total inertia (motor+load) Jt=0.125 kgm2.

B. DFVC parameters Flux controller: kp,flux= 5000 s ki,flux= 500000 Current controller: kp,crt= 250 V/A ki,crt= 20000 V/A⋅s MTPV controller: kp,MTPV= 0.1 A/rad ki,MTPV=2000 A/rad⋅s

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