ࡱ> CEBSWt7 <bjbjUU r7|7|8lDJx<Jn,Ldzzz+++++++$\- |/l,,g zz(,g g g @zz+g +g g %r*T&+z@ IJ %C++$>,0n,Q+V0~0+"g JJA Sensorless Vector Control System - Saturation in Iron Analysis D. Vukadinovic and M. Smajo Faculty of Electrical Engineering Mechanical Engineering and Naval Architecture/Department of Power Engineering, Split, Croatia dvukad@fesb.hr AbstractDue to saturation impact in iron and thermal changes of stator and rotor windings induction motor (IM) is especially non-linear system. This non-linear system control can be solved by using theory of adaptive control with observer theory application. In this paper is analyzed IM sensorless vector control system based on MRAS (Model Reference Adaptive System). Estimation of rotor flux, rotor speed and stator resistance identification is based on known stator voltages and currents. In this paper has been analyzed saturation of mutual inductance in the low speed region and impact of changes of stator and rotor resistance. Mutual inductance Lm is chosen by method described in reference [3]. I. Introduction With the development of microelectronic circuits (DSP, FPGA, dSPACE, etc.) high-speed performances are now realized using vector control of IM drives. In these systems is intensively researched IM rotor speed estimation using measurement stator currents and voltages. However, most of proposed sensorless vector control systems (without speed and flux measurement) have problem based on IM parameter changes due to saturation in iron and thermal changes of stator and rotor resistance. Rotor speed estimation and knowledge of IM parameters at same time is very important. In the last two decades, various IM sensorless vector control systems have been proposed. Most of the actual researches are based on MRAS theory, Luenberger observer or stochastic methods, such as Extended Kalman Filter technique [6]. The researched sensorless IM vector control systems are based on an adaptive control with using theory of observers. II. Rotor flux and speed observer The analyzed sensorless induction motor vector control is shown in Fig. 1 [1]. The control system is established in synchronously rotating d,q reference frame. The angular frequency of this frame (s* is at the same time reference value of first harmonic angular frequency of supply voltage vector. The observed vector control system is based on two-axis control; d- component of stator current vector  EMBED Equation.3  that is reference value of rotor flux, and q- component of stator current vector  EMBED Equation.3  that is reference value of IM electromagnetic torque. The reference value of angular frequency (s* and reference values of the stator voltage vector components  EMBED Equation.3  and  EMBED Equation.3  are formed by using set reference value of rotor speed (* and reference value of rotor flux  EMBED Equation.3 . The modern microelectronics and power electronics circuits enable "copying" of first harmonic supply voltage  EMBED Equation.3  from electronics circuits to IM stator, and actual stator voltage vector and reference voltage vector are equal ( EMBED Equation.3 ). Also, their angular frequencies are equal ( EMBED Equation.3 ).  EMBED Visio.Drawing.6  Figure1. Sensorless vector control system The feedback signals in the control system are measured components of stator current vector isd and isq and estimated rotor speed  EMBED Equation.3 . The components of the stator current vector are given by transformation of measured phase currents in original a,b,c reference frame. For rotor speed estimation  EMBED Equation.3  and forming angular velocity (s* has been used the method based on rotor flux adaptive control with observer theory application. For rotor flux estimation can be used space-vector voltage equation of stator or voltage equation of rotor. The well-known space-vector voltage equation of stator is expressed as:  EMBED Equation.3 , (1) and estimated rotor flux is:  EMBED Equation.3 . (2) On the other hand, rotor flux vector can be estimated using space-vector voltage equation of rotor winding which being expressed by stator current vector has the form:  EMBED Equation.3 , (3) where  EMBED Equation.3  and  EMBED Equation.3 . The equations (1) and (2) describe the voltage model, and equation (3) describes the current model [1]. The input values for rotor flux estimation using (1), (2) and (3) are stator supply vector  EMBED Equation.3 , angular frequency (s and measurement stator current vector  EMBED Equation.3 . The stator and rotor resistances Rs and Rr are thermal dependent. It is supposed that relative changes of stator and rotor resistance are equal. The stator and rotor leakage inductance Ls( and Lr( have constant (unsaturated) values, because in observed vector control system stator and rotor currents dont reach especially large values (Is<2Isn)[3]. Mutual inductance Lm varies rapid during saturation in iron. This effect is especially expressed in low speed region and cannot be neglected. Thus, rotor flux position in reference d,q frame has been described with three vectors (Fig. 2): rotor flux vector is estimated by using voltage model  EMBED Equation.3  current model  EMBED Equation.3 and actual rotor flux EMBED Equation.3 .  EMBED Visio.Drawing.6 Figure 2. Position of rotor flux vector  EMBED Equation.3  in stationary reference frame (,( and synchronously rotating reference frame d,q So, it is necessary to find such method of adaptive control that rotor flux vectors given from the current model and from the voltage model are just equal to actual rotor flux vector. In this paper has been proposed rotor-flux-based estimator with the current model as a reference model. The d- axis of synchronously rotating d,q frame is aligned with the flux vector  EMBED Equation.3 . The rotor flux vector  EMBED Equation.3  being estimated using the voltage model is output value of adaptive model. By solving the difference in rotor flux vectors given from the voltage and current model  EMBED Equation.3  EMBED Equation.3 , is possible to estimate rotor speed  EMBED Equation.3 . Also, verification of tuned stator and rotor resistance and mutual inductance is possible. Rotor flux vector described using current model is reference vector controlled by the components of reference stator current vector  EMBED Equation.3  and  EMBED Equation.3  in condition  EMBED Equation.3 = const. ( EMBED Equation.3 ). By introducing this type of control, equation (3) can be expressed as:  EMBED Equation.3 . (4) If equation (4) is described in scalar mode then d- component of rotor flux vector  EMBED Equation.3  ( EMBED Equation.3 ) and angular velocity of d,q reference frame  EMBED Equation.3  become:  EMBED Equation.3 , (5)  EMBED Equation.3 . (6) Because of the errors of estimated rotor speed  EMBED Equation.3  and motor parameters Lm and Tr the actual angle  EMBED Equation.3  is not the flux angle. This is a common problem of all vector control systems. The used signs indicate: * reference value, v vector estimated from the voltage model, c vector estimated from the current model, ^ estimated value. To calculate the fluxes from the voltage model of (1) and (2) a numerical integrating process is needed. However, it is difficult to maintain the vector control system stability during numerical integration process due to IM parameter changes. In order to overcome this problem, the current model using observer theory modifies the voltage model as follows [1]:  EMBED Equation.3 , (7)  EMBED Equation.3 , (8) where 1/Tc is the gain of the flux observer. The quality of rotor flux and speed estimation is strongly dependent on gain 1/Tc. By the simulation program it is shown that Tc must be equal to small positive value. In this paper Tc=0,048 [ms]. Stator and rotor fluxes are estimated by (7) and (8) of the adaptive model. If all IM parameters in the simulation are properly tuned then vectors  EMBED Equation.3  and  EMBED Equation.3 are absolutely equal in dynamic state as well as in the stationary state. When there is an estimation error of motor parameters (parameters in observer, especially mutual inductance Lm), than vectors  EMBED Equation.3  and  EMBED Equation.3  are different just in dynamic state, but in stationary state are equal. For the adequate rotor speed estimation is used the following equation [5]:  EMBED Equation.3 , (9) that, essentially, present proportional integrator (PI) controller with rotor flux component  EMBED Equation.3  as an input value and it must converge to zero. The output of PI speed controller is estimated rotor speed  EMBED Equation.3 . The constant value K( is the proportional gain and, T( is the integral gain of rotor speed PI controller. The rotor speed estimator is shown in Fig. 3.  EMBED Visio.Drawing.6  Figure 3. The rotor speed estimator Therefore, taking into account that there is rotor flux component  EMBED Equation.3  in negative feedback control loop of the PI controller of rotor speed (Fig. 1) it will really converge to zero. Fig. 3 and 4 depict the analyzed rotor flux and speed observer. The stator resistance depends indirect on rotor speed estimation during estimation of vector rotor flux components. Their actual value varies with inner temperature of IM. Thus, it is necessary to know exactly the value of stator resistance for stability and speed control accuracy. For rotor resistance estimation is used equation as follows [1]:  EMBED Equation.3 , (10) where  EMBED Equation.3  is the identification gain and must be set equal to a small positive value. The gain  EMBED Equation.3  defines convergence speed of rotor resistance from initial value to actual value. It was obtained by trial and error procedure ( EMBED Equation.3 =2). The described procedure of rotor flux estimation, rotor resistance identification is represented in Fig. 4.  EMBED Visio.Drawing.6  Figure 4. Stator flux and rotor resistance estimator It is proposed that relative changes of rotor resistance are equal to relative changes of stator resistance. Process of stator resistance identification and rotor speed estimation is simultaneously. III. Simulation results The input parameters of simulation program are IM parameters (appendix) and command variables (* and isd*. The run-up of unloaded IM has been simulated to rotor speed of 6,28 [s-1] (stator frequency is then fs=1 [Hz]). If desired condition is constant value of rotor speed ((=6,28 [s-1]) at applied step load, vector control systems must increase stator frequency fs. Fig. 5 shows static characteristic of electromagnetic torque in mode  EMBED Equation.3  at frequencies of stator voltage supply at fs = 1 [Hz] and fs = 4,06 [Hz].  Figure 5. IM torque-speed characteristic by condition  EMBED Equation.3  and frequencies of supply voltage fs = 1 Hz and fs = 4,06 Hz It is shown in Fig. 5 that for rotor speed at 6,28 [s-1] and stator voltage frequency at 4,06 [Hz] corresponds electromagnetic torque of 12,32 [Nm] (1,2 Mtn ). Thus, it is expected stator frequency increasing in dynamic state. To illustrate this effect motor was loaded in time t=159 [ms] with load torque 20 % higher than nominal torque value (Mt=1,2 Mtn). The actual speed and estimated rotor speed are shown in Fig. 6. This result has been reached with saturated mutual inductance (Lm = 0,23 [H]).  Figure 6. Actual and estimated rotor speed by step load torque at 1,2 Mtn Frequency of stator voltage has been reached at 4,06 [Hz]. This is the same value defined by torque-speed characteristic in Fig. 5. Fig. 6 is correct at the active load torque only. IV. Conclusion In this paper the sensorless vector control system is based on the current model as the reference model and voltage model as the adaptive model. Proposed rotor flux and rotor speed estimation algorithm is simpler than conventional MRAS algorithm that inversely defines adaptive and reference model. The analyzed vector control system is based on rotor speed estimation by solving an error in estimated q- component of rotor flux and by stator resistance estimation by solving an error in estimated d- component of rotor flux. The rotor flux and rotor speed estimation strongly depend on the observer gain 1/Tc. The researchers, in this paper, have been shown that mutual inductance Lm saturation strongly depends on quality of rotor speed estimation. Unsaturated value of mutual inductance Lm in analyzed observer gives bad rotor speed estimation, and the vector control system becomes unstable. By determining mutual inductance in the way described in reference [3] actual speed is practically in conformity with the estimated rotor speed. Appendix IM Parameters Pn 1,5 [kW] Mn 10,5 [Nm] nn 1391 [r/min] Rs 4,293 [(] Rr 3,866 [(] Ls( 0,0182 [H] Lr( 0,0219 [H] Lm 0,4058 [H] p 2 J 0,035 [kgm2] References [1] M. Tsuji, S. Chen, K. Izumi, E. Yamada: A Sensorless Vector Control System for Induction Motors Using q-Axis Flux with Stator Resistance Identification, IEEE Transactions on Industrial Electronics, Vol. 48, No. 1, February 2001. [2] D. Vukadinovic: State Variable Estimation in Vector Controlled Induction Motor, Master's Thesis, Faculty of Electric and Computer Science, Zagreb, 2002. [3] M. Smajo, D. Vukadinovic: Impact of Saturation Effect in Iron on Asynchronous Motor Characteristics, Proceedings of 9th International DAAAM Symposium, pp. 449-450, Cluj - Napoca, Romania, 1998. [4] Smajo, M., Dynamic Characteristics of Electric Motor Drive with Squirrel Cage Induction Motor supplied from Indirect Voltage and Frequency Converter (in Croatian), Zagreb, Doctoral Dissertation, 1989. [5] P. Vas: Artificial-Intelligence-Based Electrical Machines and Drives, Oxford University Press Inc., New York, 1999. [6] B. K. Bose: Power Electronics and Variable Frequency Drives, Institute of Electrical and Electronics Engineers, Inc., New York, 1997. 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