A Novel Current Control Method Based Field Oriented Control for PMSM Drive

A.MaideenAbdhulkader Jeylani1, J.Kanakaraj

2, A.Mahaboob subahani

3

1Assistant Professor,Dept of EEE, Sri Krishna college of Engineering and

Technology, Coimbatore 2AssociateProfessor, Dept of EEE, PSG College of Technology, Coimbatore

3AssistantProfessor, Dept of EEE, PSG College of Technology, Coimbatore

Corresponding author mail ID: jeylania@skcet.ac.in1

Abstract---This paper presents a new Predictive Current Control (PCC) strategy using Field Oriented Control (FOC) for Permanent Magnet Synchronous Machines (PMSM), to improve the performance of the current loop. Compared with traditional FOC, Predictive control results in better dynamic performance and less current ripple.Based on the researches conducted, FOC and PCC have good Performance in PMSM drives. Hence a new method based on combined FOC-PCC is adopted in this paper. The main objectives of the FOC-PCC controller are current reference tracking, current amplitude limitation and torque by ampere ratio optimization which improves the quality of torque and speed control.The control scheme is based on a model including the inverter and PMSM and taking into account the discrete nature of the inverter leg states. It predicts the future evolution of the currents for each possible configuration of the inverter. The switching state which minimizes a given cost function is selected.The simulation has been implemented with MATLAB 2013a/SIMULINK for a 750 W PMSM with rated speed of 3000 rpm and rated current 4.8 A. The sampling time has been set to 20μs, and the DC link voltage is maintained at 180 V. The reference speed has been set to 3000 rpm and load torque is set to 2 Nm. The simulation results shows that the load current is 6 A with current ripple of 0.5 A. The current THD is restricted to 1.62%. The torque by current optimization is also achieved by reducing the d axis component of stator current to zero by using FOC-PCC control technique.

Keywords: Permanent Magnet Synchronous Motors, Predictive Current Control, Feld Oriented Control.

I.INTRODUCTION

Inverter-fed AC-machines are widely

used in industrial applications. When fast torque

responses and high-performance operation are required, Permanent Magnet Synchronous Machines (PMSM) are often used and high performance current controls are needed. Many studies have been performed for the development of such algorithms. Among them, methods called Predictive Current Control (PCC) show very good performances compared to classical methods such as Vector Control or Direct Torque Control (DTC). The technique introduced in [1–5], consists in predicting the future value of the load currents for all the voltage vectors the inverter can generate. Then the inverter configuration which minimizes a cost function is selected. So one and only one configuration is selected for application during the next sampling period. This approach is a direct approach since the control variable is directly the inverter switching states (Fig. 1); it is then noted Direct Predictive Control (DPC) in this paper. It is worth to note that this control scheme isquite different from DTC [6]. Indeed with DTC the appliedconfiguration is selected according to a table and there is no prediction of the future possibleload currents.

In FOC-PCC, a rotating dq frame oriented to rotor magnetic field axis is defined, hence each stator current component has a physical meaning. The imaginary component Iq is proportional to electric torque while real component Id is proportional to reactive power. The machine control is implemented as a current control scheme, where current references are generated by external speed loop. The model of machine is used for predicting the behavior of stator currents, and cost function is considered to reduce the error between reference and predicted currents.

This paper is organized as follows. Section II defines an appropriate model of PMSM for the model based predictive control design. Section III makes an overview Generalized Predictive algorithm for control of PMSM drive. Section IV deals with simulation and the results obtained from simulation are analyzed. Section V deals with hardware implementation of the

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predictive current control of VSI feeding RL load and the real time results are analyzed.

Fig 1. Direct Predictive Control Principle

II. MODELING OF PMSM

The use of space vector facilitates the derivation of Voltage equation of PMSM with compact expression. The space vector of three phase voltage and currents are expressed in (1)&(2) as

𝑉𝑠 =2

3∗ 𝑉𝑎 𝑡 + 𝑎𝑉𝑏 𝑡 + 𝑎2𝑉𝑐 𝑡 (1)

𝐼𝑠 =2

3∗ 𝐼𝑎 𝑡 + 𝑎𝐼𝑏 𝑡 + 𝑎2𝐼𝑐 𝑡 (2)

Where Va(t), Vb(t), Vc(t) represents the

terminal line to neutral voltage for each phase

respectively and a= 𝑒−𝑗2𝜋/3. With surface mounted PMSM is

considered, the space vector of stator flux is described in (3)

𝜑𝑠 = 𝐿𝑠 𝐼𝑠 + 𝜑𝑚𝑔 𝑒𝑗𝜃𝑒 (3) Where 𝜑𝑚𝑔 is the amplitude of flux

induced by the permanent magnets,𝜃𝑒is the electrical angle of rotor and Ls is the sum of leakage and mutual inductance.

The stator voltage equation in space vector form can be written according to voltage law in (4)

𝑉𝑠 = 𝑅𝑠 𝐼𝑠 +𝑑

𝑑𝑡𝜑𝑠 (4)

Where 𝑉𝑠 is space vector of stator

voltage, 𝑅𝑠 𝐼𝑠 is the voltage drop on resistors of

the stator and 𝑑

𝑑𝑡𝜑𝑠 is the induced emf due to

change of magnetic flux. Substituting equation (3) in (4) we get

𝑉𝑠 = 𝑅𝑠 𝐼𝑠 + 𝐿𝑠𝑑

𝑑𝑡𝐼𝑠 + 𝑗 𝜔𝑒 𝜑𝑚𝑔 𝑒𝑗𝜃𝑒 (5)

To change the reference frame to d-q reference frame, as shown in figure 2 it is equivalent to rotate the α-β reference frame clockwise by 𝜃𝑒.

Hence 𝑉𝑠 ′ = 𝑉𝑠 𝑒−𝑗𝜃𝑒 , 𝐼𝑠 ′ = 𝐼𝑠 𝑒−𝑗𝜃𝑒

where𝑉𝑠 ′&𝐼𝑠 ′ represents space vectors referred to synchronous d-q reference frame. Therefore the equation (5) in d-q reference axis becomes,

𝑉𝑠 ′

= 𝑅𝑠 𝐼𝑠 ′ + 𝐿𝑠𝑑

𝑑𝑡𝐼𝑠 ′ + 𝑗 𝜔𝑒 𝐿𝑠 𝐼𝑠 ′

+ 𝑗 𝜔𝑒 𝜑𝑚𝑔 (6)

Fig 2.Vector Diagram of Electrical Variables of

PMSM

The stator voltage equation can be written in d-q coordinates

𝑉𝑑 = 𝑅𝑠 𝑖𝑑 + 𝐿𝑠𝑑

𝑑𝑡𝑖𝑑 − 𝜔𝑒 𝐿𝑠 𝑖𝑞(7)

𝑉𝑞 = 𝑅𝑠 𝑖𝑞 + 𝐿𝑠𝑑

𝑑𝑡𝑖𝑞 + 𝜔𝑒 𝐿𝑠 𝑖𝑑 + 𝜔𝑒 𝜑𝑚𝑔 (8)

The torque produced by machine

depends on flux magnitude and the magnitude of quadrature component of stator current vector.

𝑇𝑒 =3

2∗ 𝑝 ∗ 𝜑𝑚𝑔 ∗ 𝑖𝑞 (9)

And the mechanical rotor dynamics are described by

𝑑

𝑑𝑡𝜔𝑚 =

1

𝐽∗ 𝑇𝑒 − 𝑇𝑙 −

𝐵

𝐽∗ 𝜔𝑚 (10)

Where 𝜔𝑚 is the rotor shaft mechanical

speed, J is rotor inertia, B is friction coefficient and Tl is load torque.

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𝜔𝑒 = 𝑝 ∗ 𝜔𝑚 (11) Where p is number of pole pairs

III.PREDICTIVE CURRENTCONTROL

A. Discrete Model of PMSM

The model of the machine is used for

Predicting the behavior of stator currents, and the cost function must consider the error between the reference currents and predicted currents. By using Euler’s approximation for stator current derivatives for a sampling period Ts, 𝑑

𝑑𝑡𝑖 = (𝑖 𝑘 + 1 − 𝑖(𝑘))/𝑇𝑠 (12)

Substituting (12) in (7) & (8) we get,

𝑖𝑑 𝑘 + 1

= 1 −𝑅𝑠𝑇𝑠

𝐿𝑠 𝑖𝑑 𝑘 + 𝑇𝑠 𝜔𝑒 𝑖𝑞 𝑘

+𝑇𝑠

𝐿𝑠𝑉𝑑 (13)

𝑖𝑞 𝑘 + 1

= 1 −𝑅𝑠𝑇𝑠

𝐿𝑠 𝑖𝑞 𝑘 − 𝑇𝑠 𝜔𝑒 𝑖𝑑 𝑘 +

𝑇𝑠

𝐿𝑠𝑉𝑑

− 𝜑𝑚𝑔 𝜔𝑒 𝑇𝑠 14 These equations allow the prediction of stator currents to be calculated for each of the seven voltage vectors generated by inverter. B. Control Scheme The control scheme for FOC of PMSM using predictive current control is shown in fig 1. Here a PI controller is used for speed control and generates reference for the torque producing current iq*. A Predictive current controller is used for tracking this current. In the predictive scheme, the discrete time model of the machine is used for predicting the stator current components for seven different voltage vectors generated by inverter. The voltage vector that minimizes a cost function is selected and applied during a whole sampling interval. The objectives of the predictive current control are

Torque current reference tracking

Torque by ampere optimization

Current magnitude limitation

The objectives are specified in coat function as follows

(15)

(16) The first term represents the minimization of reactive power allowing torque by ampere optimization, The second term is defined for tracking the torque producing current and the last term is for limiting the amplitude of stator currents. The algorithm for the predictive current control is shown in the following flowchart.

Fig 3. Flowchart for Predictive Control

IV. SIMULATION AND RESULTS

The simulation has been implemented

with MATLAB 2013a/SIMULINK for a 750 W PMSM with rated speed of 3000 rpm and rated current 4.8 A. The sampling time has been set to 20μs, and the DC link voltage is maintained at 180 V.

The specification of the PMSM used for the simulation is also listed as Table I.

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The simulation has been carried for a total period of 0.1 seconds. A load torque of 2 Nm is applied to the motor at 0.01 seconds. The set speed is 3000 rpm up to 0.05s. Speed reversal takes place at 0.05 s and the new speed is -2000 rpm. The stator current response to these changes is shown in figure 3 and the speed and torque variations are shown in figure 4. It can be seen from the results that all the objectives of the control are achieved during the tests. Fast tracking of torque producing current iq* is achieved while id* current is nearly zero. More over both the d and q components are decoupled. When the stator and rotor fluxes are 90 degree apart, then the produced electromechanical torque in rotor is maximum.

For this id=0, and iq=𝐼𝑠 . This is also achieved in the simulation, there by optimizing torque by current ratio. The current ripple is limited to 0.5 A with THD =1.62%.

Fig 4.Stator Current Waveforms

(a)

(b)

(c)

Fig 5. (A)Speed, (B)Torqueand (C)dq Current Waveforms

V. HARDWARE IMPLEMENTATION

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-100

-80

-60

-40

-20

0

20

40

60

80

Time

curr

ent(

A)

Motor 3-phase currents (A)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Time

Speed(r

pm

)

Speed (RPM)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-35

-30

-25

-20

-15

-10

-5

0

5

10

Time

Torq

ue(N

m)

TORQUE

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-100

-80

-60

-40

-20

0

20

40

Time

Id,I

q(A

)

Id=0, Iq

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PCC for three leg Voltage Source

Inverter feeding 3 phase RL load with R=50 Ω/phase and L=10 mH/phase is tested in hardware as a trial before implementing PMSM in hardware.Semikron 20 kW three leg inverter module is used andthe control logic is designed using Simulink and dSPACE 1104 kit. The load current is sensed using LEM current sensors LA 55P. . The sampling frequency is set to 20 kHz.The hardware setup is shown in figure 6.

Fig 6.Hardware Setup for Implementation of PCC

The Reference current is given in terms of α and β quantities through SINE and COS block in Simulink. The load currents are sensed through LEM current sensors and are given to dSPACE through ADC block. The output is firing pulses are through Master BIT IO ports. The following figure 7&8 shows the CONTROL DESK environment in closed loop control and the load current waveforms.

Fig 7.Matlab Simulink Control Logic

The waveforms of actual load currents in all the three phases are shown in fig 8.The following table shows the various set values of load currents and the measured values.

TABLE II SET CURRENT AND ACTUAL MEASURED CURRENT

Set Current A(peak) Actual Current A(peak)

0.3 A 0.28 A

0.25 A 0.242 A

0.2 A 0.196 A

Fig 8.Load Current Waveforms

VI. CONCLUSION

The aim of this paper was to give a simple and accurate method in PMSM drive. A new control technique based on conventional FOC is suggested. Also, the proposed control strategy uses predictive current control to estimate the required stator current accurately. Several numerical simulation using MATLAB have been carried out in steady-state and transient-state operation conditions. According to the results, the proposed technique is able to reduce torque ripple and its transient-states at mechanical torque variations. The advantages of the proposed method are torque to current optimization, fast response and low harmonic current.

VII. FUTURE WORK

This paper can be extended further by increasing the performance of the drive can be further improved by increasing the number of states of space vector of reference voltage. This

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will leads to reduction in the error between predicted and actual values. Moreover this drive can be applicable for HVAC applications and Hybrid Electric vehicles.

REFERENCES [1] A. Dehkordi, A. Gole, T. Maguire. Permanent Magnet Synchronous Machine Model for Real-Time Simulation. 2005. IPST’05, No. IPST05 - 159. [2] N. Farid, B. Sebti, et al. Performance analysis of field-oriented control and direct torque control for sensorless induction drives. 2007, 1–7. In Proc. IEEE, MED’07. [3] D. Fodorean, A. Djerdir, et al. Foc and dtc techniques for controlling a double excited synchronous machine. 2007, 258–1263. [4] C. French, P. Acarnley. Direct torque control of permanent magnet drives. 1996, 32(5): 1080–1088. IEEE Trans. Ind. Applicat. [5] L. Hoang. comparison of field-oriented control and direct torque control for induction motors. 1999, 1245 – 1252. In Proc. IEEE, IAS. [6] H. Moon, H. Kim, M. Young. A Discrete-Time Predictive Current Control for PMSM. 2003, 18(1): 464 –472. IEEE Trans. Power Electronics. [7] Patricio Cortes, Marian P. Kazmierkowski, Ralph M. Kennel, Daniel E. Quevedo , Jose Rodriguez, “Predictive Control in Power Electronics and Drives”, IEEE Trans Vol 55 No 12 Dec 2008. [8] Samir Kouro, Patricio Cortes, Rene Vargas, Ulrich Ammann, Jose Rodriguez, “Model Predictive Control – A simple and Powerful Method to control Power Electronics”, IEEE Trans Vol 56 No 6, June 2009. [9] Jose Rodriguez and Patricio Cortes, “ Predictive Control of Power Converters and Electrical Drives”, WILEY publication 2012. [10] Florent Morel, Xuefang Lin- Shi, Jean Marie Retif, Bruno Allard, Cyril Buttay, “A Comparative study of Predictive Current Control Schemes for a Permanent Magnet Synchronous Machine Drive”,IEEE Trans Vol 56 No 7 Jul 2009. [11] SaverioBolognani, Luca Peretti, Mauro Zigliotto, “Design and Implementation of Model Predictive control for Electric Motor Drive”,IEEE Trans Vol 56 no 6 June 2009.

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