Optimization of self bearing induction motor drive

Optimization of self bearing induction motor drive Francisco E. C. Souza

Carlos Y. F. Silva

Andres O. Salazar

Dept. of Computation Engineering Dept. of Computation Engineering Dept. of Eletrotechnics Federal University of Federal University of Federal Institute of Education, Science Rio Grande do Norte Rio Grande do Norte and Technology of Rio Grande do Norte Natal, Brazil Natal, Brazil Mossoro, Brazil [email protected] [email protected] [email protected]

Werbet L. A. da Silva

Jossana Ferreira

Joao T. de Carvalho Neto

Dept. of Computation Engineering Federal University of Rio Grande do Norte Natal, Brazil [email protected]

School of Science & Technology Federal University of Rio Grande do Norte Natal, Brazil [email protected]

Dept. of Electronics Federal Institute of Education, Science and Technology of Rio Grande do Norte Natal, Brazil [email protected]

Abstract—The purpose of this paper is to perform the radial position control of a three-phase induction motor with split winding by the current control of only two phases. The third phase current is obtained by the sum of the two controlled currents. The objective is to reduce the number of components needed to drive the motor and reduce costs. This strategy was implemented in a prototype of 250 W that works in vertical position. The experimental tests showed similar results to the ones obtained with the three-phase control techniques. Index Terms—self-bearing, induction motor, split winding, radial position control

I. I NTRODUCTION The self-bearings motors do not have mechanical bearings, the rotor is supported by radial magnetic forces. The absence of mechanical bearing allows for a soft operation, without noise and mechanical wear. Then, periodic maintenance is not necessary and this kind of machine is suitable to work with high rotation speed. Previous works have studied the development of various types of self-bearings motors, such as induction self-bearing motors, reluctance self-bearing motors [1], brushless DC motors [2] and permanent magnet synchronous motors [3]. Some of them focused on three-phase induction self-bearing motors with split windings [4] due the robustness and ease of construction. The newest researches about these machines are focused on improving the rotor radial position control [5]. Despite all the advantages of self-bearings motors, the operation requires complex and costly control and drive structure. The three-phase induction self-bearing motors with split windings require six single-phase inverters, two position sensors, six current sensors, signal interface boards, power supplies and a digital signal processor. That support structure grows costlier as the machine size increases, the higher the machine power the greater the expense with peripheral devices. In this paper it is proposed a radial position control of a three-phase induction self-bearing motor with split winding by

by the current control of only two phases. This requires only four inverters, four current sensors and four current controllers. This strategy was successfully implemented and presented similar results to the three-phase control. II. C HARACTERISTICS OF SELF - BEARING MOTOR The self-bearing Induction motor is a device that holds two functions: electromagnetic torque and generation of rotor radial positioning forces. An usual way to accomplish the rotor radial position control is to add an extra winding to provide forces that keep the rotor centered. The three phase conventional stator winding is split into six parts, then each phase has two independent windings which are supplied by complementary currents. Consequently, there are six magnetic radial forces to be controlled. The rotor radial position determines the balance between the currents of the two windings at the same phase. Once the rotor is centered, both currents at the same phase are equal. Fig. 1 shows the produced magnetic field distribution of both phase A windings. The stator presents a four poles characteristic for all phases due to bearingless machine constructive aspects [6].

y

y

Ia

Ia A2

Ia A2

A1

F a2

Ia

F a1

A1

F a2

F a1

x

A1

A2

(a)

x

A1

A2

(b)

Fig. 1. Flux density distribution. (a) Centered rotor. (b) Displaced rotor.

Fig. 1(a) shows a representation of magnetic flux distribution with centered rotor. Fig. 1(b) presents a rotor displacement

situation. Once the air gap is varied, the decrease in reluctance causes an increase of flux density, meanwhile, the flux density is decreased at the opposite side, where the reluctance is → − → − increased. Hence, the force F a1 is bigger than F a2 in this example. III. M ACHINE DRIVE SYSTEM In order to control the magnetic forces in the air gap and consequently the rotor position, the stator is supposed to generate additional forces to counterbalance the rotor displacement forces. The self bearings with split windings use its own stator windings to generate the rotor positioning forces. That approach presents a cost to the system once it is necessary to control the current of the six windings. The former works about rotor positioning of split windings machines have considered the control of the three phases (six windings) for the rotor positioning, which implies in one inverter for each half winding (six inverters). This work realized an optimization of the motor drive by the use of just two phases instead of three to control the rotor radial position which reduces the number of inverters to four.

B. Proposed two axes drive system In the proposed system, the radial force is produced only by the ∆ib and ∆ic components. A non-modulated current flows in the group A coils, which is the result of a composition of ib and ic currents. Therefore, there is no ∆ia variation to produce radial force in the machine’s rotor. Fig. 2 represents the current vector components in accordance to the system real orientation. Hence, it is necessary to obtain a transformation that produces ∆ib and ∆ic components from the radial force orthogonal axes provided by the radial position controller.

A. Three axes drive system The conventional method of implementing the rotor radial position control considers the magnetic force of the three phases (ABC). The rotor radial displacement is mapped according to the Cartesian plane, X and Y directions. The stator windings are set by placing the windings of phase A concurrent to X-axis, while the Y-axis is settled between phases B and C. With that configuration, it is possible to assign the X direction rotor forces restoration to the phase A and the Y direction to the combination of phases B and C. 1) X-axis control: Since only the phase A controls the X direction rotor displacement, it is necessary to manage the force of the two windings (A1 and A2) to move the rotor way back to the center. The currents in the two windings are complementary, one is increased in the winding that is located closer to the larger air gap position, meanwhile the other is decreased on the opposite winding. An increment of current, ∆ia , is added to the current of the winding that needs its magnetic forced enhanced, and is subtracted from the opposite winding. Once the rotor is centered, there is no need to generate repositioning forces and ∆ia is zero. 2) Y-axis control: There is a combination of the magnetic forces of phases B and C for the Y direction rotor positioning control. Increments of current ∆ib (phase B windings) and ∆ic (phase C windings) are generated in case of Y direction rotor displacement in order to provide the proper re-establishing forces to push the rotor back to the center. This method of repositioning the rotor in X and Y directions is efficient but comes with a high cost because the need of controlling the six windings demands six inverters in the power electronic interface.

Fig. 2. Axes transformation.

The decomposition of ∆ib and ∆ic in the orthogonal axis provides: 1 1 ∆ib − ∆ic (1) 2 2 √ √ 3 3 ∆iy = ∆ib + ∆ic (2) 2 2 Thus, ∆ib and ∆ic can be written in a matrix form as: √ #   "  3 ∆ib 1 ∆ix 3 √ = ∆ic −1 33 ∆iy ∆ix =

For the two-phase position control, the machine coil connection must be changed to preserve the phase A current characteristics (Ia ). Thus, the input terminals of the coils A1 and A2 are both connected to the machine neutral reference point. The new connection scheme is represented by Fig. 3. From the Kirchhoff’s current law: Ib + Ic = −Ia Since the currents of phases B (Ib ) and C (Ic ) are:

(3)

Fig. 3. Machine windings connection in a Two-phase mode.

Ib = Im cos(ωt −

2π ) 3

2π ) 3 The currents through the coils A1 and A2 are: Ic = Im cos(ωt +

Ia = Im cos(ωt)

(4) Fig. 5. Control Diagram.

(5) IV. R ESULTS (6)

Then, Ia , Ib and Ic compose the three-phase system necessary to generate a rotating magnetic field in the machine stator. Since the machine windings connections are modified, a simpler power supply circuit can be used to drive the motor. The new scheme is represented in Fig. 4.

The experimental trials have been divided into two parts. The first one refers to the current control, in which the behavior of the currents in phase A has no direct control. The second part refers to the rotor radial position control. A. Current control The project parameters of the current controller are: Kp = 150 and Ki = 1500. The response of the current controller to a sinusoidal input was verified by applying a non-modulated sinusoidal current as reference. The results are shown in Fig. 6, where the dashed lines are the references and the currents of phases B and C are outputs from the controller while the phase A current is consequence of phases B and C.

Fig. 4. Power supply circuitry.

The main difference between this new proposal and the original approach is the input of the coils A1 and A2 connected to the DC-link reference point. As a consequence of it, the proposed system uses less electronic devices as switches, drivers and sensors. The machine’s radial control is composed by the current and rotor’s gap control loop in a cascade mode (Fig. 5). There is no closed loop controller for the rotor speed. Two gap sensors feed the controller which is implemented in a Digital Signal Processor TMS320F28335. The rotor’s position given by the gap sensors is compared with the position reference. The results are used in two PID controllers that provide the currents reference to the axes transformation block. Then, the incremented ∆ib and ∆ic are modulated in the reference currents. The control signals sent to the inverters are generated by the currents controller block.

Fig. 6. Current Controller Response to a Sinusoidal Input.

For this experiment there was not rotor radial position control. To avoid a random behavior, the machine’s rotor was fixed in the stator center. Fig. 7 shows the RMS values of the currents in Fig. 6. The RMS value of the reference is 0.707 A. In Table I is shown the RMS values of the current and the percentage error related to the value of the references.

Fig. 7. RMS values of the currents. TABLE I RMS VALUES AND ERROR OF THE CURRENTS . Currents (A) IB1 IB2 IC1 IC2 IA1 IA2

RMS value (A) 0.692 0.692 0.706 0.706 0.707 (average) 0.669 (average)

Error (%) 2.1 2.1 0.16 0.16 0 5.4

Fig. 9. Position Controller Response to the step variations on X-axis.

these two systems is almost insignificant. The effect appears as a disturbance which is quickly attenuated by the controllers. Fig. 10 presents the radial position of the rotor in steady state. It keeps oscillating around the references in the axis. This behavior produces a region called dispersion area around the stator center, showed in Fig. 11.

In order to verify the influence of indutance variations on the currents, the experiment was repeated with the rotor free to move radially. The results are shown in Fig. 8.

Fig. 10. X and Y Rotor position on steady state.

Fig. 8. Current Controller Response to a Sinusoidal Input (Free Rotor).

B. Positioning control The project parameters for the position controller are: Kp = 0.006, Kd = 8 · 10−6 and Ki = 4 · 10−3 . These values are used for both controllers: position controller for X and Y-axis. In order to verify the transient response, a step signal was applied to the position reference. In Fig. 9 is showed a step signal applied as reference for the X-axis position. Note that the X-axis position was not affected significantly. This is important because it means that the coupling between

Another test was performed using a radial load. The load was applied to the upper end of the rotor shaft, as is showed in Fig. 12, using a pulley and a mass held by a wire to apply a constant radial force in the machine rotor. The values of length 1(l1) and length 2(l2) are: l1 = 0.18 m and l2 = 0.3 m. Two different weights have been used in the tests: P1 = 296 gF and P2 = 439 gF. Fig. 13 presents the responses of the controller applying the radial loads P1 and P2 showed in Figs. 13(a) and 13(b) respectively. The system was able to respond satisfactorily in both situations, presenting stability and good response to the step variation of the position reference.

Fig. 11. Position of the rotor from the oscilloscope screen.

(a) 296 gf.

(b) 439 gf. Fig. 12. Radial load applied to the rotor shaft.

V. C ONCLUSION In this work, the radial position control of a three-phase induction motor with split winding using only two phases was successfully performed. The input of the coils A1 and A2 were connected to the DC-link reference point and the machine was supplied with two phases. The phase A current was obtained with no current controllers and the position control was able to compensate a radial load applied to the upper end of the rotor. The results showed a similar performance to the threephase control for the machine operation at frequencies close to the nominal (60 Hz) realized in previous works. This new approach brings to the system the advantage of using fewer components to drive the motor, reducing the experimental setup implementation cost. R EFERENCES [1] H. Wang, J. Bao, B. Xue and J. Liu, ”Control of suspending force in novel permanent-magnet-biased bearingless switched reluctance motor”,IEEE Transactions on Industrial Electronics, vol. 62, pp 4298-4306, IEEE 2015. [2] M. Ooshima and MA. Rahman, ”Control strategy of magnetic suspension and performances of a bearingless BLDC motor”, Electric Machines & Drives Conference (IEMDC), 2011 IEEE International, pp. 71-76, IEEE 2011. [3] N. Kurita, T. Ishikawa, N. Saito, T. Masuzawa and D. Timms ”A doublesided stator type axial self-bearing motor development for total artificial heart”,Electric Machines and Drives Conference (IEMDC), 2017 IEEE International, pp. 1-6, IEEE 2017.

Fig. 13. Position Controller Response with the radial load .

[4] J. Ferreira, J. A. de Paiva, A. O. Salazar, F. Castro, S. N. D. Lisboa, ”DSP utilization in radial positioning control of bearingless machine”, IEEE International Symposium on Industrial Electronics, ISIE’03, pp. 312-317, IEEE 2013. [5] L. P. dos Santos Jnior, Implementao de um sistema de controle inteligente de posio radial aplicado em uma mquina de induo como motormancal do tipo bobinado dividido,Thesis, Universidade Federal do Rio Grande do Norte, 2017. [6] A. Chiba, R. Miyatake, S. Hara, T. Fukao, ”Tranfer characteristics of radial force of induction-type bearingless motors with four-pole rotor circuits”, Int. Symp. Magnetic Bearing, pp.175-181, 1996.