Voltage Vector Controller For Rotor Field-oriented Control Of Im Based On Motional Electromotive Force

Voltage Vector Controller for Rotor Field-Oriented Control of Induction Motor Based on Motional Electromotive Force Ming MENG School of Electrical Engineering, North China Electric Power University No. 619 Yonghua North Road Baoding 071003, China

Abstract- According to the principle of electromechanical energy conversion and reference frame transformation theory, it is demonstrated that rotor field orientation decouples not only flux linkage and torque but also rotor transformer electromotive force (TEMF) and rotor motion electromotive force (MEMF). The rotor MEMF is controlled in field-oriented control (FOC), direct torque control (DTC) and direct self control (DSC). The control of torque and speed in variable-frequency induction motor drives can be achieved by control of rotor MEMF. Moreover, a voltage vector controller for rotor field-oriented control of induction motor based on control of MEMF is presented and it can achieve not only constant torque control but also constant power control. The results of simulation show that the proposed control scheme has good dynamic performance and an effective new way for the high performance speed control of induction motors is provided.

I.

INTRODUCTION

Induction motors with squirrel-cage rotors are the workhorse of industry due to their reliability, low cost and rugged construction. However, compared with DC motors, induction motors are more difficult in speed control and not suitable for high dynamic performance applications because of their complex inherent nonlinear dynamics. So induction motors commonly run at essentially constant speed, whereas dc motors are preferred for variable-speed drives. The situation has changed dramatically with the advent of field-oriented control (FOC) or vector control theory [1] and the advances in power electronics and modern microcomputers [2]. Field-oriented control techniques incorporating fast microprocessors have made induction motors attractive candidates for high performance drives. Induction motors have competed with and will replace dc motors in high-performance control areas. As the flux and torque control variables of DC motors are inherently physically decoupled by commutators and brushes, DC motor drives can have very good dynamic behavior. Based on this principle, the field-oriented control made induction motor drives similar to separately excited DC motor drives in the independent control of flux and torque by means of coordinate transformation and rotor flux vector orientation [1]. The oriented field may be rotor flux, airgap flux, stator This work was supported by the PhD Teacher Research Foundation of North China Electric Power University.

flux and even arbitrary flux [3]. The vector control can be realized through current vector or voltage vector. Induction motors may be fed by current-source inverter (CSI) or voltage-source inverter (VSI) [4]. After field-oriented control, direct torque control (DTC) [5] and direct self control (DSC) [6] were developed and applied to induction motors high performance drives successfully. On the other hand, the principle of electromechanical energy conversion is the basic principle of electromechanical energy converter which transforms electrical into mechanical energy. Induction motor is classed as a very complex and important electromechanical device [7]. FOC, DTC and DSC put too much emphasis on decoupling flux and torque control. Although the principle of electromechanical energy conversion is an important tool for rotating electrical machine analysis, it is rarely used to analyze induction motors’ FOC. In this paper, based on the principle of electromechanical energy conversion and coordinate transformation theory, it is demonstrated that the function of TEMF and MEMF in the process of electromechanical energy conversion is decoupled by transformation from phase reference frame to two-phase orthogonal reference frame and rotor field orientation decouples not only flux linkage and torque but also rotor TEMF and rotor MEMF. The rotor MEMF is controlled in FOC, DTC and DSC. The control of torque and speed in variable-frequency induction motor drives can be achieved by control of rotor MEMF. In addition, a voltage vector controller for rotor field-oriented control of induction motor based on control of MEMF is proposed and it can achieve not only constant torque control but also constant power control. The performance of the proposed scheme is investigated in simulation using MATLAB/SIMULINK at different operating condition. It is found that the presented control technique provides good dynamic performance and the analysis is valid. An effective new way for the high performance speed control of induction motors is given. The rest of this paper is organized as follows. Firstly, the MEMF control principles are described in Section II. In SectionIII, the voltage vector controller for rotor FOC of induction motor based on control of rotor MEMF is developed. SectionIV represents and analyzes the simulation results using MATLAB/SIMULINK. Finally, the conclusions are given for the whole paper.

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II. A.

MEMF CONTROL PRINCIPLES

Decoupling TEMF and MEMF

The reference frame transformation and field orientation are the elements of FOC. In the analysis of AC motor vector control, the commonly used reference frames are three-phase stationary coordinate, two-phase synchronously rotating coordinate and field-oriented coordinate [8]. In three-phase stationary coordinate, the induction motor voltage equation may be expressed in matrix form as [7] u = Ri + L

di ∂ L + ωr i. dt ∂θ

(1)

Where u is voltage vector, i is current vector, R is resistance matrix, L is inductance matrix, ș is electrical angle between A phase axis and a phase axis, Ȧr=dș/dt is rotor electrical frequency, Ldi/dt is TEMF vector and ˜L/˜șȦri is MEMF vector. If equation (1) is multiplied by iT, the power balance equation is obtained as di 1 ∂L 1 ∂L iN u 䰉 iN Ri 䯷 䯴 i L + iT ω r i䯵 + i T ωr i . dt 2 ∂θ 2  ∂θ

Input Ohmic  

 T

electrical power

T

loss power

T

Stored magnetic power

which are reactive powers and the latter, namely MEMFs, produce active powers. Equation (3), (4), (5) and (6) show that the function of TEMF and MEMF in electromechanical energy conversion is decoupled by transformation from three-phase stationary coordinate to two-phase synchronously rotating coordinate. In rotor field-oriented coordinate, equation (5) and (6) may be expressed as repectively [2]

Ouput mechanical power

(2)

B.

usq = Rsisq + pψ sq + ωsψ sd

(4)

0 = Rrird + pψ rd − ωslψ rq

(5)

0 = Rr irq + pψ rq + ωslψ rd .

(6)

Where usd is d-axis stator voltage, usq is q-axis stator voltage, isd is d-axis stator current, isq is q-axis stator current, ird is d-axis rotor current, irq is q-axis rotor current, ȥsd is d-axis stator flux, ȥsq is q-axis stator flux, ȥrd is d-axis rotor flux, ȥrq is q-axis rotor flux, Rs is stator resistance, Rr is rotor resistance, Ȧs is synchronous speed, p is differential operator and Ȧsl=Ȧs-Ȧr is slip frequency. pȥsd, pȥsq, pȥrd and pȥrq are all TEMFs. Ȧsȥsd, Ȧsȥsq, Ȧslȥrd and Ȧslȥrq are all MEMFs. The former, namely TEMFs, produce stored magnetic powers

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0 = Rrirq + ωslψ r .

(8)

Modeling

The rotor MEMF is defined as er=Ȧslȥr. So in rotor field-oriented coordinate, the induction motor voltage equations can be expressed as

As follows from (2), the stored magnetic power, which is reactive power, is all of the sum of the powers defined as the products of the current by the TEMF, and half the sum of the powers defined as the products of the current by the MEMF. The mechanical power, which is active power, is equal to half the sum of the powers defined as the products of the current and the MEMF. Therefore, we may conclude that electromechanical energy conversion involves only the MEMF, whereas the TEMF does not contribute to this conversion [9]. The above analyses show that the function of TEMF and MEMF in electromechanical energy conversion is not decoupled. In two-phase synchronously rotating coordinate, the induction motor voltage equation may be expressed as [2] (3)

(7)

Equation (7) and (8) show that rotor TEMF and rotor MEMF are decoupled by rotor field-orientation in two-phase synchronously rotating coordinate. Hence, the rotor field orientation decouples not only flux and torque but also TEMF and MEMF in rotor.

usd =

usd = Rsisd + pψ sd − ωsψ sq

0 = Rr ird + pψ r

Rs (1 + Tr p) σ L (1 + Tr p) p ψr + s ψr Lm Lm

(9)

σ LsTr L + m pψ r − ωs er Lr Lm usq =

σ LT p RsTr er + s r er Lm Lm

+ ωs (

σ Ls (1 + Tr p) Lm

ψr =

Lm isd 1 + Tr p

isq = er

(10)

L + m )ψ r Lr

Tr . Lm

(11)

(12)

Where Lm is magnetizing inductance, Ls is stator self-inductance, Lr is rotor self-inductance, ı=1-L2m/LsLr is leakage factor and Tr=Lr/Rr is rotor time constant. The electromagnetic torque can be expressed as

Te = np

ψr Rr

er .

(13)

Where np is number of pole pairs. C.

Control Principles of Rotor MEMF

As for rotor field-oriented control of induction motor, it is found that control of rotor-oriented flux and rotor MEMF can control torque and speed from equations (11), (12) and (13). Similar conclusion can be obtained for DTC and DSC. The basic principles of DTC and DSC are that the magnitude and rotating speed of stator flux space vector are controlled by

2007 Second IEEE Conference on Industrial Electronics and Applications

III. VOLTAGE VECTOR CONTROLLER In the conventional vector control, the flux and torque are controlled respectively and the speed controller generates torque command or torque current command. As above-mentioned the control of torque and speed in variable-frequency induction motor drives can be achieved by control of rotor oriented flux and rotor MEMF. According to above principle the rotor field-oriented control of induction motor based on motional electromotive force is presented in this paper. The main difference between the proposed vector control method and the conventional method is that the speed controller generates the rotor MEMF command. A.

Decoupling Voltage

er

e r*

ω*

ω

σ L sTr

÷

ω sl*

ωs

Lm Ls Lm

ψr*

usq*

R sT r Lm

×

θ

×

Rs Lm

ψr

ψr

usd*

er

us is

ωm

Fig. 1. The control system of direct rotor field-oriented based on control of REMF.

Speed (rad/s)

means of stator voltage space vector and the aim to control of torque and speed of induction motor is achieved. From the standpoint of MEMF, the control of stator flux space vector has the same function as control rotor MEMF. Therefore, the rotor MEMF is controlled in DTC and DSC. In summary, the control of torque and speed in variable-frequency induction motor drives can be achieved by control of rotor oriented flux and rotor MEMF.

The combine of feed and feedforward can make control better [10]. The computer can make feedforward implement easily. From (9) and (10) the steady equations are obtained as usd =

Rs σLT ψ r − ωs s r er Lm Lm

(14)

usq =

RsTr L er + ωs s ψ r . Lm Lm

(15)

Control System

The proposed direct rotor field-oriented control system using voltage vector is shown in Fig.1. The rotor flux and rotor MEMF can be obtained through rotor flux current model. SIMULATIONS

In order to verify the validity and dynamic performance of the proposed control system based on rotor MEMF, the numerical simulations have been carried out using MATLAB/SIMULINK. The motor started with no-load. When the motor ran at steady angular speed 100rad/s the motor began to accelerate until its steady angular speed is 240rad/s in the field-weakening. The simulation results of rotor speed, torque and rotor MEMF are shown in Fig. 2 and Fig. 3 and Fig. 4. It can be seen from these simulation results that the proposed voltage vector controller based control of rotor MEMF has good dynamic performance and can achieve not only constant torque control with constant field but also constant power control with weakening field.

Time (s)

Fig. 3. Torque response.

Rotor MEMF (V)

IV.

Torque (Nm)

Equation (14) and (15) are the voltage feedforward decoupling equations. B.

Time (s)

Fig. 2. Speed response.

Time (s)

Fig. 4. Rotor MEMF response.

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V.

CONCLUSIONS

Based on the principle of electromechanical energy conversion and reference frame transformation theory, it is demonstrated that rotor field orientation decouples not only flux linkage and torque but also rotor transformer electromotive force (TEMF) and rotor motion electromotive force (MEMF). The rotor MEMF is controlled in field-oriented control (FOC), direct torque control (DTC) and direct self control (DSC). The voltage vector controller for rotor field-oriented control of induction motor based on control of MEMF is presented and it can achieve not only constant torque control but also constant power control. The theory analysis and simulation results show that the proposed control scheme has good dynamic performance. The control of torque and speed in variable-frequency induction motor drives can be achieved by control of rotor MEMF. An effective new way for the high performance speed control of induction motors is provided. APPENDIX Induction motor parameters used in simulation [11]

Rotor resistance Stator leakage inductance Rotor leakage inductance Magnetizing inductance Inertia

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37.3 460 60 300 183 0.087

KW V Hz Nm rad/s ȍ

ȍ mH mH mH kg.m2/s

REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9]

Power Voltage Frequency Maximum torque Rating speed Stator resistance

0.228 0.8 0.8 34.7 1.662

[10]

[11]

F. Blaschke, “The principle of field orientation as applied to the new TRANSVECTOR closed loop control system for rotating field machines,” Siemens Rev., vol. 34, pp. 217-220, 1972. B. K. Bose, Modern Power Electronics and VC Drives. New Jersey: Prentice-Hall, 2002. R. W. De Doncker and D. W. Novotny, “The universal field oriented controller,” IEEE Trans. Ind. Applicat., vol. 30, pp. 92-100, 1994. I. Boldea and S. A. Nasar, Vector Control of AC Drives. Boca Raton: CRC Press, 1992. I. Takahashi and T. Noguchi, “A new quick-response and high efficiency control strategy of an induction machine,” IEEE Trans. Ind. Applicat., vol. 22, pp. 820-827, 1986. M. Depenbrock, “Direct self-control (DSC) of inverter-fed induction machine,” IEEE Trans. Power Electron., vol. 3, pp. 420-429, 1988. S. A. Nasar, L. E. Unnewehr, Electromechanic and Electric Machines. New York: Wiley, 1983. P. Krause, Analysis of Electric Machinery. New York: McGraw-Hill, 1986. A. Ivanov-Smolensky. Electrical machines. Moscow: MIR Publishers, 1982. S. Tadakuma, S. Tanaka, H. Naitoh, K. Shimane, “Improvement of robustness of vector-controlled induction motors using feedforward and feedback control,” IEEE Trans. on Power Electronics, 12(2): 221-227, 1997. Le-Huy H. Comparison of field-oriented control and direct torque control for induction motor drives. Thirty-Fourth IAS Annual Meeting, 1999,2:1245-1252.

2007 Second IEEE Conference on Industrial Electronics and Applications