**Open Access**-
**Authors :**Ranjan Kumar, Rajendra Murmu -
**Paper ID :**IJERTCONV8IS16026 -
**Volume & Issue :**NCSMSD – 2020 (Volume 8 – Issue 16) -
**Published (First Online):**18-10-2020 -
**ISSN (Online) :**2278-0181 -
**Publisher Name :**IJERT -
**License:**This work is licensed under a Creative Commons Attribution 4.0 International License

#### Performance Analysis of Permanent Magnet Synchronous Motor

Ranjan Kumar

Department of Electrical Engineering, BIT Sindri, India

Rajendra Murmu

Dept. of Electrical Engineering BIT sindri, India

Abstract The permanent magnet synchronous motors (PMSM) became more plausible being used in traction applications due to their high torque to weight ratio properties and extensive flux weakening properties to extend the constant power region to obtain maximum speed of PMSM drives. This paper presents the close loop control technique which is field oriented control (FOC) for a salient pole PMSM drives using a proportional- integral-derivative (PID) controller as a speed controller. An imposing model of FOC with flux weakening control is submitted to inspect the performance of PMSM drives on top of a extensive range of speed which includes both constant torque region and constant power region. A space vector pulse width modulated (SVPWM) three phase voltage source inverter (VSI) fed PMSM drive is simulated in MATLAB/Simulink. The maximum speed which happens in flux weakening zone is detected that it depends on the PMSM motor parameters. It is ahead condescended by the result obtained from simulation of PMSM drive under examination.

Keywords FOC, PMSM, Field-Weakening region, SVPWM

INTRODUCTION

The permanent magnet synchronous motors (PMSM) presently get too plausible due to their transcendent properties like high torque to weight ratio, high flux density, high power factor, low noise, smaller volume and size, longer life, and superior dynamic performance. The PMSMs are widely used with the current controlled voltage source inverter (VSI) for industrial and traction applications because of their excellent properties. In industrial applications, servo motors demand constant torque region and in traction applications, both constant torque and constant power region are necessary. Due to these properties, PMSM drive is also chartered for aircraft and vehicular applications where its high credibility is a most crucial feature.

In the close loop speed control, PMSM uses two advanced execution speed control techniques. These are vector control, also known as field oriented control, and direct torque control. These two control techniques are invented for asynchronous motor drives which are also suitable for PMSM control. The DTC chooses a appropriate voltage based on a predetermined switching table to get the desire torque. But, due to its initial execution and poor speed operation, this technique is not used these days. Now, FOC is used due to their wonderful dynamic performance for PMSM. In FOC, stator current is splitted into flux generating (d-axis current) and torque generating (q-axis current) component for getting the disunited control of PMSM drives.

In the literature, papers have dealt with direct torque control and field oriented control with flux weakening control

for PMSM drives. Poonam Jayal and G. Bhuvaneswari [1] have experimentally presented the control of PMSM drive using FOC and field weakening control. They investigated the PMSM drive from few hundred speed to 3500 rpm speed. They used PI controller as speed controller which give satisfactory results. Dongyun Lu and Narayan C. kar proposed extensive groupage and overviews of flux weakening control Strategy for PMSMs. Several control algorithms have been examined in this paper with advantage and disadvantage that help explorer to select suitable flux weakening control algorithm for traction applications. S. Dwivedi and Bhim Singh [3] presents a comparative idea with verification of two close loop control techniques which are vector control (FOC) and direct torque control (DTC). They investigated these two techniques for PMSM drives experimentally and observed that DTC gives best control strategies for control of speed of PMSM drive. J. O. Estima and A. J. Marques [4] presents a comparative work regarding PMSM drives for without any fault and fault operating conditions. During inverter faults condition, the stator phase current stops being sinusoidal and directing to beating torque which affects machine performance but power factor improve. V. R. Jevremovic [5] has proposed a simple but robust closed-loop flux weakening regulator for PMSM. The important features of this regulator is that it is single gain and it is independent of motor parameters. it operates satisfactory in both regions and provides expansion of PMSM speed range.

Leopold Sepulchre [6] has presented a control algorithm for flux weakening strategy in d-q frame for PMSM drive which enables to drive these machines without depending upon the speed of drives. A algorithm is proposed to figure out the current references in the stator reference frame for salient poles PMSM.

This paper presents a complete modeling and implementing of FOC for PMSM drive and also utilizing flux weakening control to obtain speed above base speed. Drive design is tested using MATLAB/SIMULINK for FOC implemented PMSM drive in constant torque and flux weakening regions.

MODELING AND FOC OF PMSM DRIVE

The air-gap flux in a PMSM is constant until no current is provided through the stator side in d-axis. With the help of d- axis stator current, the air gap flux magnitude can be modified to achieve maximum speed of PMSM drive in constant power regions.

Mathematical Modeling of the PMSM

The mathematical modeling of PMSM is derived by supposing no saturation, sinusoidal electromotive force, zero constant and varriable losses. The stator voltage equations for a PMSM in the synchronously revolving reference frame (d-q reference frame) are as follows:

disd

FLUX WEAKENING STRATEGY OF PMSM

The advanced PMSM drives become too plausible in industrial and traction applications day by day. Therefore enhancing the speed range of PMSM drive is necessary and this is done only with the help of flux weakening control strategy.

Limitations of Flux-weakening Control

Vsd = isdRs + Ls

Vsq = isqRs + Ls

dt

disq dt

– Lsweisq (1)

+ Lsweisd + mwe (2)

The voltage limit Vmax that the voltage source inverter ( VSI ) can able to supply the PMSM as input is extented by DC link voltage and space vector PWM (SVPWM) strategy. The maximum stator current Imax is also decided by the VSI rating and machine thermal ratings. Let Vmax and Imax are the maximum inverter output per phase

Where, Vsd and Vsq are direct(d) and quadrature(q) axis stator voltage components. isd and isq are d-q axis stator current components. Rs and Ls are stator per phase resistance and

voltage and current respectively. Therefore, the limits of voltage and current which also limitation on maximum attainable speed of PMSM drive are given as follows:

inductance. we is electrical rotor speed. m is permanent magnet flux linkage

The torque evolved by the PMSM is given as:

2 2

i

i

+ i

+ i

sd sq

v

v

+ v

+ v

2 2

sd sq

2

I

I

max

V

V

2

max

(5)

(6)

Here, Vmax = 0.577 Vdc ( for space vector PWM )

3 P

Te 2 2 misq

Where,

kT isq

(3)

Description of Flux Weakening Control

The flux weakening control is carried out by introducing negative d-axis current into stator to reduce the

P = Number of pole KT = torque constant

The evolved torque is equilibration through load torque, accelerating torque and damping torque of the system and this mechnical equation can be showed as:

dw

rotor flux. Due to this negative current, q-axis component of stator current reduces inevitably. Thus electromagnetic torque get reduced. The block diagram of Flux-weakening control of PMSM is demonstrated in the figure 2.

This control strategy is introduced by the introduction of outer external loop. In the flux weakening control, if the voltage exceed the limitation of voltage ( Vmax =

where,

Te TL

J m Bw

dt m

(4)

0.577Vdc ) then the flux Weakening controller feels the error of the voltage and inject negative d-axis current. At the speed below reference speed below reference speed, the output voltage magnitude of the current regulation is generally less

Te = Electromagnetic Torque TL = Load Torque

J = Moment of inertia

B = Damping Coefficient

wm = Mechanical Rotor speed in rad/sec

than Vmax. Therefore, the flux weakening algorithm is not operated.

The maximum speed that a PMSM can be achieved at no load, in the flux weakening zone, is calculated from equations (1) and (2) is given by :

v2 i R 2

Field-oriented control strategy of PMSM

w (max) sn sn sn

(7)

mn 1 L i

The determination of the position of field flux is the origin of FOC. In Field oriented control, the stator current is transmuted to synchronously revolving reference frame i.e. d- q reference frame. The stator current is splitted into two components id and iq. The d-axis component (id) is responsive for flux production while q-axis current (iq) is responsible for torque production. The idea of splitting the stator current is utilised to control the flux and torque for speed control similar as dc motor. Therefore, when this FOC technique is carried out, it permits an substantive control of the produced torque and field flux to achieve better dynamic performance. The block diagram of Field-oriented controlled PMSM is demonstrated in the figure 1.

sn sn

where, wmn is the per unit speed, vsn is the per unit stator phase voltage, Rsn and Lsn are the per unit per phase resistance and inductance respectively.

PMSM DRIVE SYSTEM DESCRIPTION

The figure 1 shows the complete basic building block of field Oriented control of PMSM drive using Flux weakening control. The drive consists of PID controller as speed controller, space vector PWM (SVPWM), the PMSM and three phase VSI to supply the PMSM drive system. This system is functioning for constant torque and constant power zone.

figure 1 Block diagram of Field oriented controlled PMSM

In this close loop system, the time constant of system are designed such that the internal current loop responds faster than external speed loop. The figure 2 shows the block diagram of Flux-weakening controller for PMSM drive system. When speed is greater than rated speed, flux weakening controller operates and inject negative d-axis current which invariably reduces q-axis current. Hence electromagnetic torque reduces. The maximum speed that can a PMSM drive system attained is achieved in this region.

fig. 2. Block diagram of Flux-weakening control of PMSM

MAXIMUM ATTAINABLE SPEED IN FLUX WEAKENING REGION

The PMSM parameters utilised for simulation are given in table-I and are utilised for investigative calculation.

Base power (Pbase)

750 watts

No. of poles

2

Base speed

3000 rpm

Base torque (Tbase)

2.39 Nm

Base current ( Ibase )

2.19 A

Per phase stator resistance ( Rs )

0.6 Ohm

Per phase stator inductance ( Ls )

0.002 H

Inertia constant (J)

0.00015 kg-m2

Torque constant (KT)

0.59Nm/Arms

PM flux linkage ( pm )

0.8 Wb

Phase to phase supply voltage (VLL) (Ideal supply source)

230 Volts RMS

DC voltage (VDC)

321 Volts

Base power (Pbase)

750 watts

No. of poles

2

Base speed

3000 rpm

Base torque (Tbase)

2.39 Nm

Base current ( Ibase )

2.19 A

Per phase stator resistance ( Rs )

0.6 Ohm

Per phase stator inductance ( Ls )

0.002 H

Inertia constant (J)

0.00015 kg-m2

Torque constant (KT)

0.59Nm/Arms

PM flux linkage ( pm )

0.8 Wb

Phase to phase supply voltage (VLL) (Ideal supply source)

230 Volts RMS

DC voltage (VDC)

321 Volts

TABLE-I PARAMETERS OF PMSM MOTOR

From the above values, analytical calculation can be done as follows:

Base voltage (Vbase) = Pbase/3Ã—Ibase = 114.115 volts Base speed (wbase) = Pbase/Tbase= 313.81 rad/sec Base Impedance (Zbase) = Vbase/Ibase = 52.13 Ohms Base inductance (Lbase) = 0.166 H

Per unit phase resistance (Rsn) = Rs/Zbase = 0.0155 Per unit phase inductance (Lsn) = Ls/Lbase = 0.0126

Per phase stator voltage (Vs) = 0.577Vdc/1.414 = 130.97 Per unit stator voltage (Vsn) = Vs/Vbase = 1.147

After putting these values in equation (7), the maximum attainable speed by PMSM drive in field weakening region can be given as:

w(max) = 1.162

For a base speed of 3000 rpm, the utmost speed of the PMSM drive, in rpm, becomes

N = 1.162Ã—3000 = 3485 rpm

SIMULATION AND RESULTS

The accomplished model of field-oriented controlled PMSM drive system is developed in MATLAB/SIMULINK environment to emulate the deportment of the drive with PID controller. Figure 3 shows the simulated model of the field- oriented controlled PMSM drive system. The transient, steady state response and dynamic response above base speed for this PMSM drive have been investigated for several operational circumstances.

figure 3. MATLAB/Simulink Model of Field Oriented controlled PMSM drive

(i). Starting Response of the PMSM drive (below base speed)

Figure 4(a) demonstrates the simulated result of the rotor speed of Field oriented controlled (FOC) PMSM drive. From the figure, it is observed that the PMSM drive reaches at a speed of 2000 rpm standstill in 0.24 sec with load torque 0.4

p.u. without any undershoot or overshoot. figure 4(b) and 4(c) shows the simulated results of the three phase stator current and the torque during this Operating condition.

4(a)Speed

5(c) Torque

figure 5. Response of the PMSM drive above base speed

(iii) Steady State Response of the PMSM Drive (Below Base speed)

4(b)Current

4(c) Torque

figure 4. Transient response of the PMSM drive below base speed

(ii) Dynamic Response of the PMSM Drive (Above Base Speed)

Figure 6 demonstrates the simulated results of the speed of the speed of the PMSM drive, the three phase stator current and the torque for steady state Operation with load torque 0.4 p.u.

6(a) Speed

Figure 5(a) demonstrates the simulated result of the utmost attainable speed of the PMSM drive with flux- weakening control. For this, the reference speed is modified to 3490 rpm. Then, the motor reaches at its maximum attainable speed of 3490 rpm in 1.05 sec at load torque 0.4 p.u. with slight overshoot. Since this Operation performed under flux- weakening region, the electromagnetic torque capability reduces but machine delivers its constant power.

5(a) Speed

5(b) Current

6(b) Current

6(c) orque

Figure 6. Steady state response of the PMSM drive

VI. CONCLUSIONS

The Permanent Magnet Synchronous Motor drives gaining more and more popularity in the varriable speed field due to their enhanced controllability, high torque to weight ratio, and better dynamic performance. This paper presents an attempt to unfold the excellent performance of PMSM drive which is controlled by field oriented control (FOC) technique using field weakening control for wide speed Operation. In this work, a proportional-integral-derivative controller (PID) is proposed as speed controller to improve the speed performance of PMSM drives. The PMSM drive has been examined under different operational circumstances such as starting, steady state and by changing reference speed for a broad range of speed operation. The performance of the

proposed control is inspected through MATLAB/SIMULATION which showed that the drive is working nicely in the constant torque and constant power zones.

REFERENCES

Poonam Jayaland G. BhuvaneswariPerfomance Analysis and control of permanent magnet synchronous motor drive over a wide speed range ( 978-1-5386-1379-5/17/$31.00 Â©2017 IEEE).

Dongyun Lu and N.C.Kar, "A review of flux-weakening control in permanent magnet synchronous machines," 2010 IEEE Vehicle Power and Propulsion Conference, Lille, 2010, pp. 1-6.

S. Dwivedi and B. Singh, "Vector Control vs Direct Torque Control comparative evaluation for PMSM drive," 2010 Joint International Conference on Power Electronics, Drives and Energy Systems & 2010 Power India, New Delhi, 2010, pp. 1-8.

Jorge O. Estimaand A. J. Marques Cardoso Performance Analysis of Permanent Magnet Synchronous Motor Drives Under Inverter Fault Conditions(Proceedings of the 2008 International Conference on Electrical Machines Paper ID 890).

V. R. Jevremovic and D. P. Marcetic, "Closed-loop flux-weakening for permanent magnet synchronous motors," 2008 4th IET Conference on Power Electronics, Machines and Drives, York, 2008, pp. 717-721.

L. Sepulchre, M. Fadel, M. Pietrzak-David and G. Porte, "Flux- weakening strategy for high speed PMSM for vehicle application," 2016 International Conference on Electrical Systems for Aircraft, Railway, Ship Propulsion and Road Vehicles & International Transportation Electrification Conference (ESARS-ITEC), Toulouse, 2016,pp.1-7.

G. L. S. N. V. A. V. Kumar and A. K. Jain, "Robust design and analysis with wide speed operation of surface mounted PMSM drive," 2014 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), Mumbai, 2014, pp. 1-6.

M. Zordan, P. Vas, M. Rashed, S. Bolognani and M. Zigliotto, "Field- weakening in vector controlled and DTC PMSM drives, a comparative analysis," 2000 Eighth International Conference on Power Electronics and Variable Speed Drives (IEE Conf. Publ. No. 475), London, 2000, pp.493-499.

Thomas M.Jahnsand VaheCaliskan Uncontrolled Generator Operation of Interior PM Synchronous Machines Following High-Speed Inverter Shutdown (IEEE transactions on industry applications, vol.35, no.6, november/december 1999 paperid 13472).

J.H. Song, J.M. Kim and S.K. Sul, "A new robust SPMSM control to parameter variations in flux weakening region," Industrial Electronics, Control, and Instrumentation, 1996., Proceedings of the 1996 IEEE IECON 22nd International Conference on, vol.2, no., Aug, pp.1193- 1198, 1996.