 Open Access
 Authors : Ranjan Kumar, Rajendra Murmu
 Paper ID : IJERTCONV8IS16026
 Volume & Issue : NCSMSD – 2020 (Volume 8 – Issue 16)
 Published (First Online): 18102020
 ISSN (Online) : 22780181
 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 integralderivative (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, FieldWeakening 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 (daxis current) and torque generating (qaxis 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 closedloop 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 dq 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 airgap flux in a PMSM is constant until no current is provided through the stator side in daxis. 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 (dq 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 Fluxweakening 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 dq 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 daxis 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, qaxis component of stator current reduces inevitably. Thus electromagnetic torque get reduced. The block diagram of Fluxweakening 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 daxis 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

Fieldoriented 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 daxis component (id) is responsive for flux production while qaxis 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 Fieldoriented 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 Fluxweakening controller for PMSM drive system. When speed is greater than rated speed, flux weakening controller operates and inject negative daxis current which invariably reduces qaxis 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 Fluxweakening control of PMSM

MAXIMUM ATTAINABLE SPEED IN FLUX WEAKENING REGION
The PMSM parameters utilised for simulation are given in tableI 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 kgm2
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 kgm2
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
TABLEI 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 fieldoriented 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 proportionalintegralderivative 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.
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