V/f Control Strategy with Constant Power Factor for SPMSM Drives, with Experiments

Cristina-Elena Coman*, Sorin-Cristian Agarliţă** and Gheorghe-Daniel Andreescu*, Senior Member, IEEE *Department of Automation and Applied Informatics, **Department of Electrical Engineering,

“Politehnica” University of Timisoara, Timisoara, Romania E-mails: cristina.coman@aut.upt.ro, sorin.agarlita@et.upt.ro, daniel.andreescu@aut.upt.ro

Abstract—A simplified sensorless V/f control for surface permanent magnet synchronous motor (SPMSM) drives with two stabilizing feedback corrections is developed. The stabilizing corrections are the voltage-vector speed correction based on the active power variation, and the voltage amplitude correction based on power factor angle regulation loop. The dq axis inductances are experimentally determined and the iron losses are taken into account with validation based on close results between simulation and experiment. The proposed scalar V/f control structure, with real-time implementation on DSP, is experimentally compared with standard Field Oriented Control (FOC) strategy, that uses position encoder, proving good dynamics.

I. INTRODUCTION Sensorless control methods are control strategies for

electric drives without rotor position/speed transducers, mainly used in order to:

• enhance reliability and performance per cost factor; • avoid accurate mounting and calibration of

mechanical sensors; • decrease costs, mass and volume; • eliminate disturbances induced by direct

measurement, sensor failures and sensor vibrations that create problems at very high speed.

Sensorless techniques are based on estimations of rotor position/speed by measuring electrical quantities, like stator phase currents and/or inverter DC-link voltage/current.

A good contribution for scalar V/f control of PMSM drives is brought by [1]. The voltage magnitude is controlled to maintain a constant stator flux linkage in the PMSM by measuring only two phase currents. The instantaneous active power variation is extracted using a high pass filter (HPF) in order to correct the voltage frequency reference, yielding the speed stabilizing [1], [2]. The same voltage frequency correction is used in [3] and, in addition, the reactive and active powers are employed to correct de voltage amplitude.

Others PMSM V/f controls use a single current sensor: a DC-link current sensor [4], or a phase current sensor [5]. In [5], also a power factor angle loop with optimized reference for voltage amplitude correction is employed.

Although sensorless control methods are preferred for their low costs, sometimes high performances are more important and thus, the best control methods are still vector control methods with motion sensor. The main vector control strategies are Field Oriented Control (FOC) and Direct Torque Control (DTC) [6]. A comparison study between them for PMSMs is outlined in [7] to establish the main advantages and drawbacks for each control.

To minimize torque ripples of PMSM drives, a robust current control loop using a complex adaptive internal model is discussed in [8].

In order to operate under Maximum Torque per Ampere (MTPA) conditions [9], [10], the following directions must be considered: motor parameters variations need a proper understanding [11], identification [12], [13] and modeling [14], [15], [16].

The present paper develops the V/f control of SPMSM drives with two stabilizing feedback corrections [2], with the following contributions: real-time implementation on DSP, experimental SPMSM parameter identification and validation based on close results between simulation and experiment, and experimental comparison with standard FOC (vector control with position encoder). The proposed V/f control structure proves good dynamic performance.

II. SURFACE PMSM MODEL AND CONTROL METHODS

A. SPMSM Mathematical Model The PMSM model in dq rotor reference is given by:

λ

= + λωd s d rd

qvt

-dd

R i (1)

λ

= + + ω λq s q rq

dvddt

R i (2)

λ = λ +PM d dd L i ; λ =q q qL i (3)

1 5 ⎡ ⎤= λ + −⎣ ⎦e PM q d q d qT . p i ( L L )i i (4)

ω = − − ω ω = ωm e L m m rJd / dt T T B , / p (5)

θ = ωr rd / dt , (6)

where (vd, vq), (id, iq) are the stator voltage and current components, Rs is the stator resistance, Ld, Lq are dq axis inductances, ωr, θr are the electrical rotor speed and position, ωm is the mechanical rotor speed, (λd, λq) are the stator flux components, λPM is the PM flux, Te is the electromagnetic torque, TL is the load torque, J is the motor inertia, B is the viscous friction coefficient and p is the number of pole pairs.

The electromagnetic torque (4) has two components: the magnetic torque 1.5pλPMiq, and the reluctance torque driven by the difference between Ld and Lq. For SPMSM, the magnetic torque is available only because Ld=Lq=Ls, and therefore the reluctance torque is equal to zero.

– 147 –

8th IEEE International Symposium on Applied Computational Intelligence and Informatics • May 23–25, 2013 • Timisoara, Romania

978-1-4673-6400-3/13/$31.00 ©2013 IEEE

B. PMSM Inductances Identification and Iron Loss Resistance Calculation

The dq axis inductances of the SPMSM tested prototype are determined after performing dc current decay tests at standstill, with the rotor aligned along d axis, and along q axis, respectively. The electrical diagram of the test is illustrated in Fig. 1. The current decay occurs in the phases B and C, which are actually connected in series, while in the phase A different value of constant current (icc) is injected.

The dq inductances are calculated with the expression:

, (2 ) / (2 )= ⋅ ⋅ + ⋅∫ ∫d q s D contL R idt V dt I , (7)

where: Rs - phase resistance; i - decay current, VD - diode voltage drop, Icont - the direct current before the decay. The dependencies (λd - λPM) =Ldid and λq =Lqiq are illustrated in Fig. 2 a,b. The cross coupling is visible for both axis.

Other parameters of the SPMSM are listed in Table I. The SPMSM model is further enhanced by taking into

consideration the core losses. A traditional approach is used, which considers only two components, i.e., the hysteresis losses and eddy current losses (8).

Figure 1. DC current decay test at standstill for dq inductance

identifications

Figure 2. (λd - λPM)(id) and λq(iq) dependencies

TABLE I. SPMSM PARAMETERS

Parameter Value Rated power 400 W Rated current 1 A Rated phase voltage 220 V Number of pole pairs p=2 Stator phase resistance R=16.5 Ω Stator inductance Ld=Lq=Ls Ls=90 mH Rated speed nn=1500 rpm Inertia of rotor J = 2.5∙10-3 Kgm2

Viscous friction coefficient B = 3·10-3 Nms/rad

2 2 2= λ + λiron h s e sP k f k f , (8)

where Piron are the core losses, kh and ke are the hysteresis and the eddy currents coefficients, f is the frequency and λs is the peak stator flux.

The iron losses are usually modeled as a resistance connected in parallel with the induced emf. The resistance is calculated based on:

2 23

2ω λ

= siron

ironR

P. (9)

By introducing (8) in (9), it is obtained:

26π=

+irone h

Rk k / f

. (10)

For a given λs=constant, kh and ke can be identified by linear fitting having at least two measurements. In this case kh=0.47 and ke=0.005.

The equivalent circuit of the SPMSM for the q-axis is presented in Fig. 3.

Figure 3. q-axis equivalent circuit of PMSM

C. Sensorless V/f Control System The proposed V/f control structure for SPMSM drives

contains a basic V/f scalar control with two added stabilizing feedback corrections, i.e., voltage vector speed correction Δωr and voltage amplitude correction ΔV [2].

The control structure is presented in Fig. 4, containing the following main parts: the basic V/f control (the upper part of the figure), the voltage vector speed correction (Δωr) using active power variation extracted by a high pass filter (HPF), the voltage amplitude correction (ΔV) using a PI controller for the power factor angle loop with a low pass filter (LPF) on the angle reference.

The electric frequency fe* is the control system

reference. At ramp startup, under no load conditions, the voltage amplitude command V1

* is determined from (1, 2):

V1* = λPM ·|ωr

*|, (11)

C.-E. Coman et al. • V/f Control Strategy with Constant Power Factor for SPMSM Drives, with Experiments

– 148 –

V1c* ωr

*

P, Q, φComput.

Block

λPMV1

* V* V0

*

θv*

Δωr

PI

P

ΔV

ΔP

φ-

vs*

is

fe*

ωv*

INV

LPF

HPF

-

2π |ωr*|

∫

φ*

φ

φf*

Vdc

PMSM

Load

VSI

Kω/ωr*

dvqv

αβ

Figure 4. Proposed V/f control structure with two stabilizing feedback

corrections for SPMSM drives

where ωr* is the electrical speed reference. The voltage

offset V0* is added for a prompt start-up. The voltage

vector position θv* is obtained by integrating the voltage

vector speed ωv*. The operator dvqv to αβ transforms the

voltage vector vs*(V*, θv

*) in polar coordinate into vs*(vα*,

vβ*) in αβ stator reference (Fig. 5). The voltage vector speed correction is added to

prevent the synchronism losing [1], [2]. For steady state operation, the voltage vector position in

dq rotor reference (θvd) is constant, therefore the voltage vector speed ωv = ωr because ωvd = 0 (Fig. 5). In order to compensate the rotor speed variation, which appears in transient state operation, the corrected voltage vector speed reference ωv

* takes the form

* *ω = ω + Δωv r r , (12) where Δωr is the transient rotor speed variation.

The rotor speed variation Δωr is active only in transient state, and because it is not available for measurement (the absence of position/speed encoder), Δωr is estimated using the active power variation ΔP [1], [2]. For a step load torque, the rotor speed decreases and because the voltage amplitude is initially constant (the voltage amplitude correction is not so fast), the rotor speed correction Δωr is obtained from active power variation ΔP based on (1-6):

/ω ωΔω = ⋅Δ ⋅ ω− = Δr e rK T K P , (13)

where Kω=20 is a gain experimentally obtained.

The instantaneous active power P is calculated using the measured stator currents and reference stator voltages:

( )* *3 / 2 α α β β= +P v i v i . (14)

The active power variation ΔP is extracted from P using a 1st order high pass filter (HPF), with experimentally chosen time constant T=0.2 s.

The voltage amplitude correction ΔV is based on the power factor angle regulation loop. V/f control uses the voltage vector reference frame dvqv with the dv axis oriented along the voltage vector vs. The electromagnetic torque Te is controlled by the current vector ϕ= j

s si I e using the voltage amplitude V, where φ is the angle between voltage and current vectors, i.e., the power factor angle (Fig. 5).

A PI controller is used for the power factor angle regulation loop, with the voltage amplitude correction ΔV as output. The time constant Ti= Ls/Rs ≈0.005 is chosen close to the electrical time constant, and the proportional constant kp=0.2 is chosen to avoid chattering and to obtain a desired bandwidth.

d

q

isvs

φθv

λPM

α

θr

θvd

dv

Figure 5. Correlation between dvqv frame, dq frame and stator frame

The power factor angle is given by

( )φ 2 ,= atan Q P , (15)

where Q is the instantaneous reactive power, computed as

( )* *3 / 2 β α α β= −Q v i v i . (16)

D. FOC Strategy In order to compare the performance of the proposed

sensorless V/f control with two stabilizing corrections, a Field Oriented Control (FOC) standard strategy with measured position from an encoder is used.

The FOC structure is presented in Fig. 6, where PIω is the speed controller, and PIid, PIiq are the current controllers, all tuned by using Kessler methods [17].

III. EXPERIMENTAL AND SIMULATION RESULTS Simulations and experiments use the Matlab/Simulink

environment with 100 µs sampling period, employing the proposed sensorless V/f control structure (Fig. 4) and FOC structure (Fig. 6) for SPMSM drives.

Experiments are implemented on the dSPACE 1103 real-time platform. The test rig consists of a SPMSM mechanically coupled with an induction machine (load), two Danfoss VLT 5000 voltage source inverters (VSI), three current sensors (only two are used), and an incremental encoder as a witness only.

For the proposed sensorless V/f control structure, simulations and experiments are performed and compared (Fig.7-10) for the speed profile (ωr

*) shown in Fig. 7. The test comprises: acceleration (9000 rpm/s2) from zero to rated speed; rated torque loading, unloading; deceleration at half rated speed; rated torque loading, unloading; and finally deceleration down to zero speed.

Figure 6. FOC structure for SPMSM

– 149 –

8th IEEE International Symposium on Applied Computational Intelligence and Informatics • May 23–25, 2013 • Timisoara, Romania

0 5 10 15 200

200

400

600

800

1000

1200

1400

1600

time (s)

Spee

d (rp

m)

ω*ωVF-loopsωEncoder

ωSimulation

2 4 6 8

145015001550

Figure 7. Simulation vs. experiment: Investigated speed profile (ω*), including speed variation due to rated torque loading and unloading

Figure 8. Simulation vs. experiment: electromagnetic torque

Figure 9. Simulation vs. experiment: magnetizing current variation

Figure 10. Simulation vs. experiment: power factor angle variation

Figure 11. Experimental speed responses for speed profile ω*,

V/f control vs. FOC

Figure 12. Experimental electromagnetic torque for V/f control vs. FOC

Figure 13. Experimental magnetizing current for V/f control vs. FOC

Figure 14. Experimental power factor angle variation for V/f control vs.

FOC

C.-E. Coman et al. • V/f Control Strategy with Constant Power Factor for SPMSM Drives, with Experiments

– 150 –

In Fig. 7, a rather surprising agreement is obtained between simulations and experimental results, which highlights good dynamic performance, and induces the validation of the proposed SPMSM model. The torque response and power factor angle variation are illustrated in Fig. 8 and 10 respectively. The magnetizing current (Fig. 9) is obtained using position information from the encoder, which is used only as a witness, in order to survey the actual behavior of the machine.

In order to quantify the proposed sensorless V/f control performance, a standard vector control with position transducer (FOC from Fig. 6) is implemented for comparison. Experimental results for both control strategies are illustrated and compared (Fig. 11-14).

Fig. 11 shows experimental speed responses of both strategies with small overshoots. A compromise between good speed reference tracking capability and good disturbance rejection must be taken into account for the FOC speed controller tuning. Even if the V/f control presents less speed overshoot, the FOC strategy is capable to handle higher acceleration demands.

Similar profiles of the electromagnetic torque for both strategies are seen in Fig. 12. In both cases, the developed torque is estimated based on the iq current obtained with position information from the encoder.

The magnetizing current is illustrated in Fig. 13. While FOC succeeds in maintaining id=0 during the entire test, V/f control presents id variation, but after a while, it settles somewhere close to zero in steady state. This fact is expected because a constant power factor regulation is adopted for V/f control.

In Fig. 14, the power factor angle variation is observed. Under rated load operation, both strategies settle to a very low value of φ: 6.6 degrees for FOC and respectively 3.5 degrees for V/f control during steady state.

CONCLUSION A simplified sensorless scalar V/f control for SPMSM

drives with two stabilizing feedback corrections is developed, implemented and experimental tested. The stabilizing corrections are: the voltage-vector speed correction based on the active power variation, and the voltage amplitude correction based on power factor angle regulation loop.

For a better modeling of the SPMSM, dq axis inductances are experimentally identified and the iron losses are taken into account. The comparison between the simulation and experimental results employing V/f control presents small errors and therefore SPMSM accurate modeling is validated.

The proposed scalar V/f control strategy proves good dynamic performance in terms of fast reference tracking and prompt disturbance rejection. An optimal constant power factor angle reference of 3.5 degrees is experimentally chosen.

Evaluation of experimental results between the proposed scalar V/f control and the standard FOC using position encoder proves appropriate dynamic results.

The proposed sensorless V/f control strategy is suitable for low cost PMSM drives and high speed applications.

ACKNOWLEDGMENT 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 Program Human Resources Development (POSDRU) 2007-2013, and also by the strategic grant POSDRU 107/1.5/S/77265 (2010).

REFERENCES [1] P. D. C. Perera, F. Blaabjerg, J. K. Pedersen, and P. Thøgersen, “A

sensorless, stable V/f control method for permanent-magnet synchronous motor drives,” IEEE Trans. on Ind. Appl., vol. 39, no. 3, pp. 783-791, May/June 2003.

[2] G.-D. Andreescu, C.-E. Coman, A. Moldovan, and I. Boldea, “Stable V/f control system with unity power factor for PMSM drives,” Proc. 13th Int. Conf. Optimization of Electrical and Electronic Equipment (OPTIM 2012), pp. 432-438, May 2012.

[3] S. M. Sue and T.-W. Hung, “Minimum copper loss control for sensorless V/f controlled IPMSM drives,” Proc. Int. Symposium on Ind. Electron. (ISIE 2012), pp. 708-712, May 2012.

[4] M. Kiuchi, T. Ohnishi, H. Hagiwara, and Y. Yasuda, “V/f control of permanent magnet synchronous motors suitable for home appliances by DC-link peak current control method,” Proc. Int. Power Electronics Conf. (IPEC 2010), pp. 567-573, June 2010.

[5] A. Consoli, G. Scelba, G. Scarcella, and M. Cacciato, “An effective energy saving scalar control for industrial IPMSM drives,” IEEE Trans. Ind. Electron., early access article, 2013.

[6] C. Bian, S. Ren, and L. Ma, “Study on direct torque control of super high-speed PMSM,” Proc. IEEE Int. Conf. on Automation and Logistics, Jian, China, pp. 2711-2715, Aug. 2007.

[7] M. Aquirre, C. Calleja, A. Lopez-de-Heredia, J. Poza, A. Aranburu, and T. Nieva, “FOC and DTC comparison in PMSM for railway traction application,” Proc. 14th European Conf. on Power Electron. and Appl. (EPE 2011), pp. 1-10, Sept. 2011.

[8] Y. A.-R. I. Mohamed and E. F. El-Saadany, “A current control scheme with an adaptive internal model for robust current regulation and torque ripple minimization in PMSM vector drive,” Proc. IEEE Int. Electric Machines & Drives Conf. (IEMDC 2007), pp. 300-3005, May 2007.

[9] K.-W. Lee and S.B. Lee, “MTPA operating point tracking control scheme for vector controlled PMSM drives,” Proc. Int. Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM 2010), pp. 24-28, June 2010.

[10] C.-T. Pan and S.-M. Sue, “A linear maximum torque per ampere control for IPMSM drives over full-speed range,” IEEE Trans. on Energy Convers., vol. 20, no. 2, pp. 359-366, June 2005.

[11] R. Nalepa and T. Orlowska-Kowalska, “Optimum trajectory control of the current vector of a nonsalient-pole PMSM in the field-weakening region,” IEEE Trans. on Ind. Electron., vol. 59, no. 7, pp. 2867-2876, July 2012.

[12] Q. An and L. Sun, “On-line parameter identification for vector controlled PMSM drives using adaptive algorithm,” Proc. IEEE Vehicle Power and Propulsion Conference (VPPC 2008), Harbin, China, vol. 59, no. 7, pp. 1-6, Sept. 2008.

[13] S.-C. Yang and R.D. Lorenz, “Analysis of iron and magnet losses in surface-permanent-magnet machines resulting from injection-based self-sensing position estimation,” Proc. IEEE Energy Conversion Congress and Exposition (ECCE 2011), pp. 630-637, Sept. 2011.

[14] Z. Li and H. Li, “MTPA control of PMSM system considering saturation and cross-coupling,” Proc. 15th Int. Conf. on Electrical Machines and Systems (ICEMS 2012), pp. 1-5, Oct. 2012.

[15] N. Urasaki, T. Senjyu, and K. Uezato, “Relationship of parallel model and series model for PMSM including iron loss,” Proc. IEEE 32nd Annual Power Electronics Specialists Conf. (PESC 2001), vol. 2, pp. 788-793, 2001.

[16] N. Ishihara, M. Sanada, and S. Morimoto, “Structure of the PM synchronous motor for low iron loss characteristic in the high-speed region,” Proc. Int. Power Electronics Conf. (IPEC 2010), pp. 1317-1321, June 2010.

[17] S. Preitl, R.-E. Precup, A.-I. Stinean, C.-A. Dragos, and M.-B. Radac, “Extensions in symmetrical optimum design method. Advantages, applications and perspectives,” Proc. 6th IEEE Symposium on Applied Computational Intelligence and Informatics (SACI 2011), pp. 17-22, May 2011.

– 151 –

8th IEEE International Symposium on Applied Computational Intelligence and Informatics • May 23–25, 2013 • Timisoara, Romania