Wide Speed Range V/f with Stabilizing Loops Control of Tooth-Wound IPMSM Drives

Ana Moldovan*, Sorin C. Agarlita*, Gheorghe D. Andreescu**, Senior Member, IEEE, Ion Boldea*, Life Fellow, IEEE *Dept. of Electrical Engineering, **Dept. of Automation and Applied Informatics

University Politehnica of Timisoara, 2 Vasile Parvan Blvd., 300223 Timisoara, Romania anamoldovan2003@yahoo.com, agasoryn@yahoo.com, daniel.andreescu@aut.upt.ro, boldea@lselinux.upt.ro

Abstract – Novel or modified sensorless control methods, credited with fast dynamic response, better drive efficiency and short computation time are just a few of nowadays main concerns. Therefore, this paper aims to theoretically characterize and digitally investigate through comprehensive Matlab/Simulink simulations three different V/f control strategies, with correction loops. The proposed control methods are all characterized by the missing of the vector current control standard speed and current controllers and they all use the Maximum Torque per Ampere condition (MTPA); coordinate transformations are not necessary. The most important claims of these new control strategies are fast dynamic speed and torque response, low computation effort and the bypassing of initial rotor position problem. To prove the previous claims, a fractionary winding interior permanent magnet synchronous motor (IPMSM) 42Vdc prototype was made and its parameters were previously determined by standstill and load performance laboratory tests. Preliminary test results with proposed method three are available at this point.

Index terms – sensorless control, V/f control, stabilizing loop, fast dynamic, MTPA, IPMSM.

I. INTRODUCTION

n introduction to Interior Permanent Magnet Synchronous Motors (IPMSMs), to their characteristics

such as increased efficiency, high torque density, reluctance torque contribution, their rugged construction, simple maintenance as well as the exposition of their drawbacks is briefly presented in the beginning of the paper.

During the last two decades, permanent magnet synchronous machines have been increasingly used in many industrial drives [1], as high performance variable speed motors. This happened mainly because of the machine qualities exposed above and its capability of operating above base speed (in case of high saliency, the speed domain at constant power goes above 3/1).

Due to the absence of brushes and commutation, the AC permanent magnet (PM) machines are considered the most attractive from all the PMs machines [2]. The change from the field flux corresponding to a dc field winding to the permanent magnet flux increases the machine torque and power density and the efficiency is improved. Because of the low torque pulsations, the PM machines are characterized by low vibration and noise [3]. The recent increasing of NdFeB PMs cost, their demagnetization at raised temperatures, the start from a known initial position, are some of the main permanent magnet electric machines disadvantages. The use of an IPMSM for electric drive applications requires the initial rotor position information [4-6], provided in general by

an encoder or a resolver. Position sensors have their disadvantages like higher cost of the drive, the machine size is increased (in case of small power drives), while the system reliability may also be decreased. Therefore, many papers have as their main focus to eliminate position sensors and to obtain high performance control for an IPMSM drive. Consequently, sensorless control methods such as motion-sensorless field oriented control (FOC) and direct torque and flux control (DTFC) drives are used more and more [7-12] and they are widely applied, using proportional-integral (PI) speed and current controllers and voltage decoupling schemes. Sensorless FOC and DTFC for general sensorless AC drives, even for the speed control range in the 20/1-100/1 range are used when fast dynamic speed and torque response is required, in spite of rather sophisticated software and hardware schemes for control.

This paper focuses on the development of three modified V/f control strategies, each of them with different correction loops. The first V/f control method uses the magnetic energy error through a PI controller, to correct the voltage vector amplitude, while the torque error is used through a second PI controller for the voltage vector phase angle correction. During the second control strategy the same torque loop is implemented to correct the voltage vector phase angle, but the amplitude is adjusted using the reactive power error, again through a PI regulator. The third V/f control strategy presents only one stabilizing loop, based on the MTPA operating condition, used to correct the voltage vector amplitude. The output of a high pass filter (HPF) applied on the calculated active power is integrated and added to the reference position, for damping speed and torque oscillations. When the machine is operating under the MTPA condition, we can easily calculate the current vector angle.

IM loading machine

Encoder

IPMSM Prototype

Fig. 1. IPMSM-laboratory prototype

A

424978-1-4673-1653-8/12/$31.00 '2012 IEEE

Using the machine equations in d, q coordinates, we determine the voltage vector angle. The difference between the afore mentioned angles is exactly the power factor angle, which can be also estimated from the active and reactive power. The error between the calculated and estimated values of the power factor angle corrects the voltage vector amplitude through a PI regulator.

All three V/f control strategies, with stabilizing loops are characterized by the absence of the usual speed and current controllers and by the absence of coordinate transformation.

In order to obtain high performance control and to design fast and efficient controllers, accurate knowledge of machine parameters is mandatory.

As mentioned before, the machine prototype used for the experimental setup is a fractionary winding IPMSM (Fig.1) and both standstill and load performance testing have been initially conducted to determine the machine parameters.

The paper is organized as follows: Section II, The IPMSM Structure and Experimental

Analysis are illustrated; Section III, V/f with Magnetic Energy Balance for Voltage Amplitude Correction Loop and Torque Balance for Voltage Phase Angle Correction is exposed; Section IV, deals with V/f with Reactive Power Balance for Voltage Amplitude Correction Loop and Torque Balance for Voltage Phase Angle Correction; In Section V, The Proposed V/f Control with Voltage Amplitude Correction and Active Power Calculation is presented; Finally, during Section VI, Discussion and Conclusion are highlighted.

II. IPMSM STRUCTURE AND EXPERIMENTAL ANALYSIS

Experimental analysis has the scope to provide the machine parameters (Table I) which are necessary for further system simulations and experimental tests.

In order to obtain high performance drive systems and to design fast and efficient controllers, accurate knowledge of machine parameters is of a great importance [13], [14].

There are three essential parameters that have to be well known and they are: “d” and “q” axis inductances and the permanent magnet flux linkage. Therefore, a comprehensive measurement procedure will be described during this section. First, the IPM machine mathematical model is written and its structure and vector diagram (Fig. 2.) are shown afterwards.

ωΨ= ⋅ + + ⋅ ⋅Ψss s s r s

dV R I jdt

; (1)

( )Ψ = ⋅ + Ψ + ⋅ ⋅s d d PM q qL I j L I ; (2)

( )( )32

= ⋅ ⋅ Ψ + − ⋅ ⋅e PM d q d qT p L L I I ; (3)

Where sV , sI , Ψs are the stator voltage, current and flux vector; dL , qL are dq axes inductances; ΨPM is the permanent magnet flux linkage; sR is the stator resistance; ω r is the electrical rotor speed and p is the number of pole pairs.

a) b)

Fig. 2. Vector diagrams for IPMSM, Ld<Lq: a) IPMSM structure; b) IPMSM vector diagram;

There are several methods presented in literature for the estimation of electromagnetic excited SM [13], [15], [16], but most of them cannot be applied to PMSM, if we take into account that the PM excitation cannot be disabled or require rather expensive and complicated equipment.

The mathematical machine model embedded in system simulations and experiments needs precise parameters, if accurate results are expected [17]. Further on, several tests for model parameters estimation will be embedded in a quick, inexpensive and practical guide for IPMSM drive experimental characterization.

The torque is not measured directly; it is estimated from the measured currents. The measurement procedure consists of several tests which were chosen in order to allow the machine parameters estimation in a wide area of variation. It has to be mentioned that the thermal and acoustic behavior were not considered.

A. Standstill measurements First, the phase resistance was measured, as it is used

further on for other parameter determination. There are a few easy ways to estimate the resistance, like: a precision Ohmmeter a RLC bridge or a multimeter.

Supposing that the motor is symmetrical, we can consider that each phase has the same impedance Fig. 3. The resistance measurement has been done by supplying the machine from a dc voltage source (4).

DCech

VRI

= (4)

With the above described method, we obtained R=0.138 Ω, but when supplied by an inverter, the voltage drops within the latter and along the cables should be considered, increasing the equivalent resistance to R=0.2 Ω.

A static test with locked rotor, in order to prevent any induced voltage caused by the magnetic field movement was performed to estimate the inductances along d, q axes (Fig.4).

Fig. 3. The phase resistance measurement scheme

425

Fig. 4. “d, q” inductance estimation scheme While supplying the machine from an autotransformer as in

Fig. 4., the rotor “d” axis aligns itself along phase “a” axis. This way, Ld can be obtained from the equivalent impedance.

The same experiment can be repeated for “q” axis, but this time the rotor should be locked.

To simplify the modeling and all the calculations for control, an average value for both inductances Ld=1.14e-3 H and Lq=1.286e-3 H was considered, while the permanent magnet flux linkage was considered constant, 0.02Ψ =PM Wb , even if in reality, it slightly depends on temperature.

B. Load performance testing The IPMSM prototype was verified on a laboratory test-rig.

It was controlled using vector control and both speed and current regulators were implemented through „Matlab/ Simulink” Package. Experiments were carried out on the test-bench using DSpace 1103 and Control Desk interface.

To verify that the machine can produce the required torque at a specified speed, it was run as a generator. An induction motor drive held the speed constant at an imposed value while the IPMSM prototype was in torque control mode. Using the existing experimental bench, experiments have been conducted to determine the motor efficiency and the results are depicted in Fig. 5.

0.5 1 1.5 2 2.5 3

0.4

0.5

0.6

0.7

0.8

0.9

1

Torque [Nm]

Eff

icie

ncy

600 [rpm]

1200 [rpm]

1800 [rpm]

Fig. 5. Efficiency versus torque for different speed values As results show, the IPMSM has a better efficiency at high speeds, where η=83,2 %, for 1800 rpm and 0.5 Nm load, than at lower speeds, where η=38,8 % for 600 rpm and 3Nm.The rather small specific volume of the machine (as required in automotive applications) explains the moderate efficiency, besides partial loading.

III. V/F WITH MAGNETIC ENERGY BALANCE FOR VOLTAGE AMPLITUDE CORRECTION LOOP AND TORQUE BALANCE FOR

VOLTAGE PHASE ANGLE CORRECTION

The core of the proposal consists in “driving to zero” through a close loop the Δ mW magnetic energy difference between its expressions in αβ (stator) and in dq (rotor)

coordinates, without any rotor position (or speed) estimation, to obtain the voltage amplitude correction, *ΔV .

The magnetic energy in dq coordinates is based on the prescribed “d” axis current, *

di , determined from MTPA condition. The ac machine magnetic energy in αβ coordinates αβmW is written in (5).

* *3 ( )2αβ β α α β= −∫mW V i V i dt (5)

With *αV , *

βV as the reference voltages and ,α βi i calculated from the measured ,a bi i currents.

In steady state, dq coordinates, the same magnetic energy may be expressed in quite a unique form by using the active flux (6) concept by which all ac machine models “loose” their magnetic saliency [18].

*Ψ = Ψ −ad S SqL I (6)

Where *2 *2= +S d qI i i is the stator current and SΨ is the stator flux vector. The active flux expression for IPMSM in rotor flux coordinates is expressed in (7).

*( )*Ψ = Ψ + −ad PM d q dL L i (7)

The dq formula for the steady state stored magnetic energy mdqW is written in (8).

* * 23 *( )2

= Ψ +amdq d d q sW i L i ; (8)

To avoid rotor position estimation we need to “fix” the desired longitudinal current *

di , (10) such that to consider the maximum torque per current condition (9) below base speed for up to full torque. *2 * 22 ( ) /( )⋅ + ⋅Ψ −d d PM d q si i L L = i ; (9)

2

* 21 1 1 24 2 4

⎛ ⎞Ψ Ψ= − ⋅ − ⋅ ⋅ + ⋅⎜ ⎟⎜ ⎟− −⎝ ⎠

PM PMd s

d q d q

i IL L L L

(10)

A similar stabilizing loop for voltage phase angle correction γΔ in the V/f control is proposed around the αβ (11) and dq torque formula (12), which is basically the same in active flux coordinates, for all ac machines:

13 * ( * * )2eT p i iαβ α β β α= Ψ − Ψ ; (11)

*1

3 * * *2

aedq d qT p i= Ψ ; * 2 *2

q S di i i= − (12)

To estimate αΨ and βΨ , the voltage model is used:

**( * )1 S

T V R isTα α αΨ = −

+; **( * )

1 ST V R isTβ β βΨ = −

+; (13)

With *di and

adΨ reference values, as described above, the

torque stabilizing loop is simply described by (14) and (15): e e edqT T TαβΔ = − (14)

* *( * ( ))1 *

pie SMi e

ii

kT k sign T

T sγΔ = −Δ + Δ

+ (15)

The general control scheme is drawn in Fig.6. and digital simulation results for the imposed requirements are presented in Fig.8. The PI regulators structure is shown in Fig.7.

426

eT αβ

edqT

mW αβ

mdqW

Teε

dVmWε

dθ {

Fig. 6. V/f with stabilizing loops – control scheme

dV

1⋅−

sK Tz

mW αβ

m dqW

Fig. 7. PI regulator structure. Simulation results (Fig. 8.) have been conducted at 1500

rpm speed and a proportional with speed, 2Nm load torque.

a) 0 0.5 1 1.5 2 2.5 30

500

1000

1500

spee

d [rpm

]

0,17 0.2

1500

2 2.2

1500

1515

w ref

w enc

b) 0 0.5 1 1.5 2 2.5 3

0

1

2

torq

ue [N

m]

Te est

Te ref

c) 0 0.5 1 1.5 2 2.5 3

-15

-10

-5

0

id ref

[A]

d) 0 0.5 1 1.5 2 2.5 3-50

-22

0

22

50

Iab

[A]

e) 0 0.5 1 1.5 2 2.5 3

-20

0

20

Udq

[V

] Uq

Ud

f) 0 0.5 1 1.5 2 2.5 3

0

20

40

60

Idq

[A] Id

Iq

g) 0 0.5 1 1.5 2 2.5 30

10

20

2730

V [V]

V

V ref

h) 0 0.5 1 1.5 2 2.5 3

-2

0

2

thet

a[ra

d]

2.9

3

3.1

th refth est

Fig. 8. Digital simulation results for V/f with magnetic energy and torque stabilizing loops: a) speed; b) torque; c) Id

* reference current; d) α, β current; e) d, q voltage; f) d, q current; g) voltage vector amplitude; h) voltage vector

phase angle A rather fast acceleration of the machine from zero speed

up to 1500 rpm, in 170 ms and a slight difference between the reference and the actual motor speed is visible in Fig. 8a. The real speed oscillates around the target with about ±5 rpm, during transients; when the unloading 150 ms slope occurs, the speed increases with 15 rpm and afterwards it stabilizes in about 220 ms. The realized torque oscillates with less than ±0.1 Nm around the reference (Fig. 8b) and the current decreases from 21A to 19A when the unloading is applied, as it can be noticed in Fig. 8d. It should be noted that the negative imposed *

di (Fig.8c) is not realized (Fig.8f), yet. The corrected voltage vector amplitude and its reference

value is shown in Fig. 8g., while the 0.1 rad (5.73 electrical degrees) difference between the reference and estimated phase angle is visible in Fig. 8h.

IV. V/F WITH REACTIVE POWER BALANCE FOR VOLTAGE AMPLITUDE CORRECTION LOOP AND TORQUE BALANCE FOR

VOLTAGE PHASE ANGLE CORRECTION

The core of the second proposal consists in driving to zero through a close loop the reactive power difference between its expressions in α, β and d, q coordinates, without using any rotor position (or speed) estimation, to obtain the voltage amplitude correction, *VΔ . The MTPA condition, is again considered to impose *

di current (10) for d, q reactive power calculation. The ac machine reactive power in α, β coordinates, Qαβ, is :

* *3 ( )2

Q V i V iαβ β α α β= − (16)

With *Vα , *Vβ as the reference voltages and ,i iα β calculated from the measured ,a bi i . In steady state, d, q coordinates, the same reactive power may be expressed in quite a unique form by using the active flux concept

adΨ (6) [18]. For active flux

estimation (7), stator flux estimation is crucial, thus a combined voltage/current model observer is used [18].

The dq formula for the steady state reactive power Qdq:

* * * 23 * *( )2

adq r d d q sQ i L iω= Ψ + ; (17)

The torque stabilizing loop has the same structure as exposed during the previous section, thus the torque error

427

(14) and the voltage phase correction (15) are easily calculated. The corresponding control scheme has the same structure with the one in Fig. 6, though the magnetic energy is now replaced by the reactive power correction loop.

As in previous section, tests have been conducted at 1500 rpm speed and a proportional with speed, 2Nm load torque was applied; the machine unloading is also applied at 2s and the simulation results are shown in Fig. 9.

As it can be seen from Fig. 9a., the machine accelerates from zero speed up to the prescribed value in about 170ms; the actual speed oscillates around the reference one with ±5rpm and when the machine unloading occurs, the speed increases with 20 rpm. A proportional with speed 2Nm torque is prescribed for the motor loading and an 150 ms slope was applied for the machine unloading, at 2s (Fig. 9b). The realized torque oscillates during transients with less than ±0.1Nm around the prescribed waveform.

a) 0 0.5 1 1.5 2 2.5 30

500

1000

1500

spee

d [rpm

]

2 2.2

1500

1520w enc

w ref

b) 0 0.5 1 1.5 2 2.5 3

0

1

2

torq

ue [Nm

]

Te est

Te ref

c) 0 0.5 1 1.5 2 2.5 3-4

-3

-2

-1

0

idref

[A]

d) 0 0.5 1 1.5 2 2.5 3-50

-20

0

20

50

Iab

[A]

e) 0 0.5 1 1.5 2 2.5 3

-20

0

20

Udq

[V]

Uq

Ud

f) 0 0.5 1 1.5 2 2.5 3

0

20

40

Idq

[A]

Id

Iq

g) 0 0.5 1 1.5 2 2.5 30

10

20

30

V [V]

V

V ref

h)0 0.5 1 1.5 2 2.5 3

-2

0

2

thet

a[ra

d]

-2

0

1.62.1

th ref

th est

Fig. 9. Digital simulation results for V/f with reactive power and torque stabilizing loops: a) speed; b) torque; c) Id

* reference current; d) α, β current; e) d, q voltage; f) d, q current; g) voltage vector amplitude; h)

voltage vector phase angle;

When the load is cancelled, the current values decrease from 20 A to 17 A which can be easily observed from Fig. 9d. Again, we can see from Fig. 9f that the prescribed negative di* as shown in Fig. 9c) is not realized, yet.

The corrected voltage vector amplitude and its reference value is shown in Fig. 9g, while the 0.5 rad (28.66 electrical degrees) difference between the reference and estimated angle waveforms is drawn in Fig. 9h.

V. THE PROPOSED V/F CONTROL WITH VOLTAGE AMPLITUDE CORRECTION AND ACTIVE POWER CALCULATION

The V/f control strategy proposed during this section is slightly different from the above described control methods, especially because it does not use the active flux concept.

First of all, we will use the MTPA condition to prescribe the stator current vector angle (18), while the analytical machine model in (19) and (20) is used to determine the voltage vector angle (21). The difference between the two angles is *ϕ (23) and it will be used, further on, for voltage amplitude correction. The angles mentioned above are shown in Fig. 10., [21].

To obtain the estimated value of the angle, ϕ , we need to know the active and the reactive power (26), (27). The error between *ϕ and ϕ is the input of a PI controller used further on to correct the voltage vector amplitude (25).

d djX I0E

SI

dI

qISV

S SR I

q qjX I

q

d

δ

ϕΨ

PMΨ

Fig. 10. IPMSM Phasor diagram (Ld<Lq, Id<0).

428

2 2 2PM PM q d

q d s

- + 8 (L -L )asin

4 (L -L ) Is

MTPA

Iλ λ⎛ ⎞+ ⋅ ⋅⎜ ⎟Ψ = Ψ =⎜ ⎟⋅ ⋅⎝ ⎠

(18)

The general scheme for voltage vector amplitude correction is drawn in Fig. 11.

*Vα

*Vβ

iα

iβ

ω

ϕεMTPAϕ

Pϕtan r

a

Pa

P

⎛ ⎞⎜ ⎟⎝ ⎠

aP

rP

MTPAΨ

sI MTPAδ δ

Fig. 11. Voltage vector amplitude correction scheme *Vα

*Vβ

iα

iβ

*ωθω

dωdP

02⋅π⋅ f

1TsT+

Fig. 12. Voltage phase correction [20]

( ) ( ) ( )0cos sin sδ⋅ = − ⋅ ⋅ Ψ + ⋅ ⋅ ΨS d S S SV E X I R I co (19)

( ) ( ) ( )sin cos sinδ⋅ = ⋅ ⋅ Ψ + ⋅ ⋅ ΨS q S S SV X I R I ; 0 02 PME fπ λ= ⋅ ⋅ ⋅ (20)

q s s sasin((x *I *cos( )+R *I *sin( ))

sVΨ Ψ

=δ (21)

Where, [ ]20 d s s s

2

q s s s

-x *I *sin( )+R *I *cos( ))

+ *L *I *cos( )+R *I *sin( )s

EV

Ψ Ψ=

⎡ ⎤Ψ Ψ⎣ ⎦ω (22)

* ( )MTPA MTPAϕ ϕ δ= = + −Ψ (23)

tan⎛ ⎞

= ⎜ ⎟⎝ ⎠

r

a

Pa

Pϕ (24)

( )( )* 1P iV K K sϕΔ = Δ ⋅ + ⋅ (25)

( )32aP U I U Iα α β β= ⋅ ⋅ + ⋅ (26)

( )32rP U I U Iβ α α β= ⋅ ⋅ − ⋅ (27)

The aim of the second correction loop is to cancel the speed and torque oscillations and it consists of the active power (26), as the input of a high pass filter (HPF) [19-20]. The HPF (28) main role is to cut out the continuous component of the input signal. Its output is added to the reference speed in order to obtain the corrected speed, which integrated will give us the estimated voltage vector position (Fig.12).

HPFsH s= +α ; (28)

Digital simulations at 1500 rpm and 2 Nm proportional with speed, load torque (Fig. 13b) were implemented and their results are shown in Fig. 13. The machine accelerates from zero speed up to 1500 rpm in about 160 ms (Fig. 13a), though some oscillations of ± 36 rpm around the target are visible during transients. An 150 ms slope was also used for the machine unloading, at 2s.

a) 0 0.5 1 1.5 2 2.5 30

500

1000

1500

spee

d [rpm

]

0.16 0.2

1500

1540

2 2.152,2

1.5001520

1.570w enc

w ref

b) 0 0.5 1 1.5 2 2.5 3

0

1

2

torq

ue [Nm

]

0,15 0,21,8

2

2.07

te estte ref

c) 0 0.5 1 1.5 2 2.5 3

-20

0

20

Udq

[V] Uq

Ud

d) 0 0.5 1 1.5 2 2.5 3

-20

0

20

Iab

[A]

e) 0 0.5 1 1.5 2 2.5 3

-10

0

10

20

30

Idq

[A]

Id

Iq

f) 0 0.5 1 1.5 2 2.5 30

5

10

15

V [V]

17

17.1

V ref

V est

g) 0 0.5 1 1.5 2 2.5 3

-2

0

2

thet

a [rad

]

time [s]

2.3

2.7th est

th ref

Fig.13. Digital simulation results for V/f with voltage amplitude correction and active power calculation: a) speed; b) torque; c) d, q voltage; d) α, β

current; e) d, q current; f) voltage vector amplitude; g) voltage vector angle; The real torque oscillates with less than ±0.1 Nm around the reference. This time the negative dI was realized (Fig. 13e), though it was not followed by close loop regulation for this control method. Even if the control main goal was to eliminate the speed and torque oscillations, some pulsations still persist during transients. As Fig. 13c shows, after the machine unloading, the currents become three times smaller, as they decrease from 18A to 6A. In Fig. 13f, the reference

429

and the corrected voltage vector amplitudes are represented. The reference and the corrected phase angle are both plotted in Fig. 13g) and a 0.4 rad (almost 23 degrees) difference between them is shown during the zoom graph part.

All three proposed stabilizing loops methods produce fast speed response for wide speed range control, but still only the third one fulfils most requirements. Preliminary experimental work is shown next. The experiments have been performed at 300 rpm and a proportional with speed 0.5 Nm (25% TeN) torque.

a) 0 2 4 6 8 10-100

0

100

200

300

400

spee

d [rpm

]

270

300

330 w enc w ref

b) 0 2 4 6 8 10-5

0.5

5

Te[

Nm

]

c) 0 2 4 6 8 10

-2

0

2

thet

a [rad

]

-1.8

0

2

th ref

th est

d) 0 2 4 6 8 10-20

0

20

40

angl

e [d

eg]

ϕ

Ψ

ϕ tg Pδ

e) 0 2 4 6 8 10-4

-3

-2

-1

0

dV[V

]

f) 0 2 4 6 8 10

-5

0

5

dw[rad

/s]

g) 0 2 4 6 8 10

-20

0

20

Idq[

A]

-2-101Iq

Id

h)

-20

-10

0

10

20

Idq[

A]

Iq

Id

Fig.14. Experimental results for V/f with voltage amplitude correction and

active power calculation: a) speed; b) torque; c) voltage vector angle; d) current and voltage angles; e) voltage correction; f) speed correction; g) d, q

current; h) d, q current - steady state; As experiments show, the speed correction in Fig. 14f does

not manage to cancel the speed and torque oscillations. The machine accelerates in about 300 ms (Fig. 14a) and oscillates with ± 30 rpm around the target. The voltage correction is slowly stabilizing (Fig. 14e), while Fig. 14d shows that the estimated current vector angle is visibly oscillating, but manages to settle around the MTPA calculated value. This represents the moment when the current along d axis becomes negative (Fig. 14g). To prove that the negative Id current has been achieved, the Id, Iq currents during steady state operation are shown in Fig. 14h.

Still, from the experimental point of view, the machine fast response at full load torque is not solved yet.

VI. DISCUSSION AND CONCLUSION

This paper aims to find a sensorless control method for an IPMSM, which can provide fast speed and torque response, without the utilization of the standard current and speed regulators, without coordinate transformations and with less computation effort. Therefore, three different V/f with corrections control strategies have been investigated and their results were analyzed and discussed. The first two control methods use the active flux concept current, the MTPA condition and need a negative prescribed „d” current, which neither of them manages finally to realize, yet. The third V/f control method uses only the MTPA condition and the negative „d” current is realized, though it is not imposed. We have to admit that the analyzed V/f control methods still use PI controllers, with the statement that their presence affects only the correction of the variables.

0 0.05 0.1 0.15

0

500

1000

1500

time[s]

0 0.5 1 1.5 2 2.5 3

0

500

1000

1500

spee

d[rp

m]

time[s]

w ref w1

w ref

w2

w2w1

w3w3

Fig.15. Speed waveforms corresponding to all three proposed control

methods

430

The speed (1500 rpm) and proportional with speed torque (2 Nm) requirements were the same for each control strategy. During each of the proposed V/f control strategies, the machine accelerates rather fast, in about 160 – 170 ms.

Some fairly small speed and torque oscillations around the target signals are visible for the first two control strategies, but the third control method shows higher pulsations in speed response (Fig. 15.).

After the unloading occurs, the current values become lower with a few amperes for the first two control methods, but they decrease three times for the last proposed V/f with only one correction loop.

Preliminary experimental results show that the third V/f proposed control method manages to achieve a negative current along d axis, but it is not robust enough yet. More than that, machine fast dynamic response at full load torque has yet to be achieved.

TABLE I PARAMETERS OF THE IPMSM

Number of pole pairs (p) 4 Rated power (PN) 2 kW Rated speed (nN) 6000 rpm

Rated torque (TeN) 2 Nm Rated frequency (fn) 400 Hz

Rated phase to phase voltage (VS) 39 V(rms) Rated phase current (IS) 50 A(rms)

Stator resistance per phase (RS) 0.138 Ω d-axis inductance (Ld) 1.14 mH q-axis inductance (Lq) 1.286 mH

Rotor permanent magnet (λPM) 0.02 Wb Inertia of the rotating system (J) 40e-6 kg*m2

Viscous friction coefficient (Bm) 1e-6 Nms/rad

Windings connection Star connection

ACKNOWLEDGMENT

This work was partially supported by the strategic grant POSDRU 6/1.5/S/13, (2008) of the Ministry of Labour, Family and Social Protection, Romania, co-financed by the European Social Fund – Investing in People. This work was also supported by EU-FP7 EE-VERT Project (Grant agreement no. SCP7-GA-2008-218598-EE-VERT).

This work was partially supported by the strategic grant POSDRU/89/1.5/S/57649, Project ID 57649 (PERFORM-ERA), co-financed by the European Social Fund – Investing in People, within the Sectoral Operational Programme Human Resources Development 2007-2013.

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