Indirect Field Orientation for Induction Motors without Speed Sensor C. C. de Azevedol, C.B. Jacobinal, L.A.S. Ribeiro2, A.M.N. Lima1 and A.C. Oliveira1j2 UFPB/CCT/DEE/LEIAM - Campus II - Caixa Postal 10105 58.109-970 Campina Grande, PB, Brazil. Fax: +55-83-3101015 - jacobina@dee.ufpb.br 2CEFET-MA - Sdo Luis. MA. Abstract: This article investigates a modified indirect field oriented control strategy that employs a direct estimation of the frequency of the rotor flux vector. The estimate of the frequency of the rotor flux vector is obtained from the directly measurable stator currents and voltages, and is completely independent of the rotor resistance. The proposed scheme can be used in applications where there is no need for speed control or simply to insure the independency of rotor resistance. Experimental results are presented and demonstrate the performance, correctness and feasibility of the proposed methodology. are presented. II. INDUCTION MOTOR MODEL For the purposes of the present investigation tion machine is described by the induc- I. INTRODUCTION The indirect field oriented control (IFOC) technique is very useful for implementing high performance induction motor drive systems [l-4]. In the IFOC technique the shaft speed, that is usually measured, and the slip speed, that is calculated based on the machine parameters, are added to define the angular frequency of the rotor flux vector. Then, the standard IFOC technique is essentially a feedforward scheme which has the drawbacks of being dependent of the parameters that vary with the temperature and the level of magnetic excitation of the motor and also requires the measurement of the shaft speed. The use adaptive schemes for compensating the parameter changes was proposed in [5-71. This article investigates a technique that uses a direct estimation of the frequency of the rotor flux vector to obtain an IFOC independent of the speed machine and the rotor resistance. This scheme is suited for high performance indirect field oriented controller and can be used in applications where there is no need for speed control or simply to insure the independency of rotor resistance. The estimate of the angular frequency of the rotor flux vector is obtained from the measurable stator variables (voltages and currents). The proposed scheme keeps the IFOC tuned even when the rotor resistance changes. Moreover, there is no special test signal being used and the machine is supplied with three-phase sinusoidal pulse width modulated voltage waveforms. Several model are presented to estimated the rotor flux frequency. Experimental and simulation results We - Z) = J,n$wI. + F,w,. (6) The superscript a indicates the use of a generic reference frame and the variables and parameters used in the above expressions are defined as follows: i) v, = w:~ + jws,, iz = i & + ji &, i, = irad + ji&, 4: = 4 $ + j4 & and 4, = Cd + M, are the stator voltage, the stator current, the rotor current, the stator flux and the rotor flux vectors, respectively; ii) w,, w,, T, and Tl are the angular shaft speed, the angular speed of the dq coordinate system, the electromagnetic torque and the load torque, respectively and iii) P, Jm, F,, r,, r,, I,, 1, and 1, are the number of pole pairs, the moment of inertia, the viscous friction coefficient, the stator resistance, the rotor resistance, the self inductance of the stator, the self inductance of the rotor and the mutual inductance between stator and rotor, respectively. III. MODIFIED INDIRECT FIELD ORIENTED CONTROL The equations of the standard indirect field oriented control are defined from the equations that link the rotor flux vector to stator current vector. This relationship, in a reference frame aligned with the rotor flux vector, is given by 0-7803-7404-5/02/$17.00 (c) 2002 IEEE 809
where the superscript e indicates the use of the rotor flux reference frame, r, is the rotor time constant (7, = IF/r,), W,l = w, -w, is the slip frequency and w, is the angular frequency of the rotor flux vector with respect to the stator. In the indirect field oriented strategy, the torque control is achieved through is,, while the rotor flux is controlled by izd. The reference values of izd, is, are given by.e* a sd = a.e* s* = 1 1, T,* P 1% is; (11) In the standard indirect field oriented control, the estimate of the frequency of the rotor flux vector w, is determined by adding the slip frequency, calculated by to the shaft speed w,. In the proposed scheme the estimate of the frequency of the rotor flux vector w, is obtained directly without calculating w,~ as an intermediate step. This alternative makes the IFOC more robust to parameter variations since, as it will be shown in the following, the estimate of the frequency of the rotor flux vector is no longer dependent on the rotor resistance. Figure 1 shows the block diagram of the modified IFOC as proposed in this paper. Note that there is no need for speed measurement nor slip calculation since the angular frequency of rotor flux vector is directly provided by the Frequency Estimation block. The models employed for estimating the frequency of the rotor flux vector are discussed in the next section. IV. ROTOR FREQUENCY ESTIMATION MODELS Reference models based on stator variables have been employed in adaptation laws designed for compensating the changes of the rotor time constant [5,6]. On the other hand, these reference models have also been employed in an adaptive scheme that keeps the indirect field oriented controller permanently tuned without any speed measurement [8]. In this paper the use of reference models based on stator variables is proposed for estimating the angular speed of the rotor flux vector w,. In the present case, w, is estimated only by using measurable stator variables (voltages and currents), independently of the rotor resistance and thus avoiding the use of a speed sensor for torque control applications. Indeed, the estimation of w, as proposed in this paper is not included as a part of any adaptive scheme. In this paper, four different types of reference models for estimating w, have been studied. A. d-axis voltage The reference d-axis voltage is given by vugei = r,i~~ - w,al,i~~ (12) where o = 1 - l&/(1,1,) is the leakage factor. From this equation and considering that ved = US:, where vzd represents the measured voltage, an estimate of the frequency of the rotor flux vector i3, can be calculated by B. q-axis voltage model The reference q-axis voltage is given by (13) (14 From this equation and considering that us, = vi;, where us, represents the measured voltage, an estimate of the frequency of the rotor flux vector i3, can be calculated by C. Reactive power model The reference reactive power is given by (15) Q* = w, (I&;) + d&,*) ) (16) while the actual reactive power can be determined the current and voltage measurements by from (17) From these equations and considering that Q = Q*, an estimate of the frequency of the rotor flux vector i3, can be calculated by D. Active power model The actual active power can be calculated from the current and voltage measurements by while the reference active power is given by (19) P* = rs((isz) + (isi) ) + w,(l, - Ols)i~~i~t. (20) From these equations and considering that P E P*, an estimate of the frequency of the rotor flux vector i3, can be calculated by 810
IFOC...................................................e* e* cu^e Vsq e e vsd vsq Fig. 1. Block diagram of the modified IFOC scheme The above reference models can be used for implementing the Frequency Estimation block as shown in Fig. 1. Note that all these models do not require the measurement of the shaft speed and consequently it is not necessary to use any electromechanical sensing device. Another key point is that the changes of the rotor resistance do not affect the value provided by the Frequency Estimation block w, [check (13), (15), (18) or (al)]. V. SIMULATION RESULTS The performance of all the proposed reference models was studied by numerical simulation. However, only selected results for the q-axis voltage model, see equation (15), will be presented in this paper. The performance improvement of the modified IFOC scheme is referred to the behavior of the standard IFOC implementation. Figure 2 shows the transient behavior of the standard IFOC with respect to changes in the torque reference and the rotor resistance. The motor is supplied with an ideal three-phase voltage source and without any closed-loop for speed control. The reference magnetic excitation is kept constant at 4: = 0.197Wb. The changes in the reference torque are defined as: T,* = 0.15N.m for t < 2s and for t > 4s and T,* = 0.075N.m for 2s 5 t 5 4s. The changes in the rotor resistance occurs for t > 6s when the rotor resistance is increased of 50%. Figure 3 shows the transient behavior of the proposed IFOC scheme under the same conditions. Before the change of rotor resistance both the standard IFOC and the modified IFOC exhibits the same transient performance. After the change of the rotor resistance, the modified IFOC remains tuned. However, the standard IFOC presents a detuned behavior when the rotor flux and the electromagnetic torque are reduced. The simulation results indicate that it is possible to operate the machine with the proposed scheme at low speed (5% of the rated speed). VI. EXPERIMENTAL RESULTS The experimental tests were conducted by using an ac drive available in our laboratory. The motor is a 1/3Hp four pole induction motor supplied with a three phase transistor inverter. The drive system in controlled through a PC-Pentium equipped with dedicated plug-in boards. The parameters of the motor used in the simulation and experimental tests are r, = 26.80, 1, = 0.521H, 1; = 0.521H, lh = 0.498H, rc = 26.80. Similarly as it was done in the simulation study, the performance of the proposed scheme (using the q-axis voltage model) is referred to the standard IFOC implementation. Figure 4 shows a first experimental test result illustrating the transient performance of the standard IFOC. In this test the behavior of the IFOC is evaluated with respect to steps in the reference electromagnetic torque. The magnetic excitation is kept constant at 4: = 0.197Wb and the profile of the electromagnetic torque is defined by 811
8 (b) Fig. 2. Rotor flux (a) and electromagnetic torque (b) for the standard IFOC Fig. 3. Rotor flux (a) and electromagnetic torque(b) for the IFOC with rotor flux frequency estimation based on the q-axis model. VII. CONCLUSION T,* = 0.15N.m for OS < t 5 3s T,* = 0.075N.m for 3s < t 5 6s and T,* = 0.15N.m for 6s < t 5 8s. Figure 7 shows an experimental test result illustrating the transient performance of the modified IFOC under the same operating condition. It can be seen that the modified IFOC presents a behavior as good as the standard IFOC. The implementation of the modified IFOC was based on the q-axis voltage model. Figures 6 and 7 show the results of a second test. In this test is investigated the behavior of the both IFOC strategies for change in the rotor resistance. The transient conditions are: 4: = 0.2Wb; T,* = 0.15N.m with an increase of 50% in the rotor resistance for t > 4s. The increase in the rotor resistance de-tunes the IFOC, since the electromagnetic torque has changed. This can also be observed indirectly by the difference in the rate of change of the shaft speed. These results show that the modified IFOC is completely independent of the change in the rotor resistance. This paper has demonstrated that it is feasible to use same reference models employed for adaptive laws that aims at keeping the IFOC permanently tuned for providing an accurate estimate of the frequency of the rotor flux vector. Consequently, the presented results demonstrate that it is possible to keep permanently tuned the IFOC without using any adaptive scheme. It is worth noting that in the proposed scheme the estimate of the frequency of the rotor flux vector is obtained from the directly measurable stator currents and voltages, is completely independent of the rotor resistance and does not rely on any signal injection technique. The proposed technique is simple but provides a high performance torque control solution. The proposed scheme can be used in applications where there is no need for speed control or simply to insure the independency of rotor resistance. The experimental results have demonstrated the correctness and feasibility of the proposed methodology. 812
(b) (b) Fig. 4. Stator currents ied (a) and i& (b) and shaft speed (c) wt for the standard IFOC for a torque transient. Fig. 5. Stator currents ied (a) and i& (b) and shaft speed wt (c) for the proposed IFOC for a torque transient. REFERENCES [l] R. D. Lorenz, T. A. Lipo, and D. W. Novotny. Motion control with induction motors. Proceedigns of IEEE: especial issue on power electronic and motion control, 82(8):1215-1240, Aug. 1994. [2] R. W. de Doncker and D. W. Novotny. The Universal Field Oriented Controller. IEEE Trans. on Industry Applications, 30(1):92-100, Jan./Feb. 1994. [3] H. Kubota and K. Matsuse. Speed sensorless fieldoriented control of induction motor with rotor resistance adaptation. IEEE Trans. on Industry Applications, 30(5):1219-1224, Sep./Ott. 1994. [4] S. Peresada, A. Tilli, and A. Tonielli. Indirect fieldoriented control of induction motor: New design leads to improved performance and efficiency. In Conf. Rec. IECON 98, pages 1609-1614. IEEE, 1998. [5] T. M. Rowan, R. J. Kerkman, and D. Leggate. A Sim- 813
(b) (b) Fig. 6. Stator currents ied (a) and i& (b) and shaft speed wt (c) for the standard IFOC for a change in the rotor resistance. Fig. 7. Stator currents ied (a) and i& (b) and shaft speed wt (c) for the proposed IFOC for a change in the rotor resistance. ple On-Line Adaption for Indirect Field Orientation of an Induction Machine. IEEE Trans. on Industry Applications, 27(4):720-727, Jul./Aug. 1991. [6] L. A. de S. R i b eiro, C.B. Jacobina, A. M. N. Lima, and A. C. Oliveira. Parameter Sensitivity of MRAC Models Employed in IFO-Controlled AC Motor Drive. IEEE Trans. on Industrial Electronics, 44(4):536-545, Aug. 1997. [7] G. Yang and T. Chin. Adaptive-speed identification scheme for a vector-controlled speed sensorless inverterinduction motor drive. IEEE Trans. on Industry Applications, 29(4):820-825, Jul/Aug 1993. [8] C.B. Jacobina, J. Bione de M. Fl., F. Salvadori, A.M.N. Lima, and L.A.S. Ribeiro. A simple indirect field oriented control of induction machines without speed measurement. In Conf. Rec. IAS 97, pages 1809-1813, Roma - Italy, October 2000. IEEE - Industry Application Society. 814