Improving INFORM calculation method on permanent magnet synchronous machines

Transcription

1 IMTC 27 - IEEE Instrumentation and Measurement Technology Conference Warsaw, Poland, May 1-3, 27 Improving INFORM calculation method on permanent magnet synchronous machines A. Zentail and T. Daboczi2 ThyssenKrupp Nothelfer Kft. and also with Department of Measurement and Information Systems, Budapest University of Technology and Economics, Magyar tudosok krt Budapest, Hungary Phone: , Fax: , zentai@mit.bme.hu. 2Department of Measurement and Information Systems, Budapest University of Technology and Economics, Magyar tudosok krt Budapest, Hungary Phone: , Fax: , daboczi@mit.bme.hu. Abstract - This paper reports advances in sensorless rotor position estimation in motor control of electronic power assisted steering systems (EPAS). A systematic calculation error was discovered in the INFORM [1] - a saliency based sensorless rotor position estimation method, - when it was applied to permanent magnet synchronous machines (PMSMs). A solution was found to correct the angle error of the measurement which was introduced by the PMSM. Keywords - Sensorless rotor position estimation, INFORM, motor control, permanent magnet synchronous machines (PMSMs), field oriented control (FOC), electronic power assisted steering systems (EPAS). I. INTRODUCTION In EPAS electric machines are connected to the mechanical system to reduce driver's work by generating torque in the appropriate direction. Nowadays three phase permanent magnet synchronous machines (PMSMs) are used in vehicles. Automotive environment demands special requirements for motor control application, as e.g. high reliability, working with different, but usually low voltage level, providing high torque at high speeds with small size and high efficiency. Also the system cost plays an important role in automobile system design, because in high volume production every unnecessary part increases the overall cost dramatically. This paper focuses on sensorless rotor position estimation technique which enables the system designer to omit the rotor position sensor to reduce cost or increase the robustness of the system. The current control is based on the direction of the rotor magnet field so the rotor angle is one of the most important signal. System cost can be reduced by omitting a rotor angle sensor or the robustness can be improved by validating the angle sensor signal with a saliency based rotor angle measurement method. The improving method of INFORM calculation will be described in the following order: first motor models will be presented to understand the motor parameters, especially the machine inductivities in function of rotor angle [1]. It will be followed by a short description of a sensorless position estimation method called indirect flux detection by on line reactance measurement (INFORM) [1]. In the next section a systematic error of the INFORM method is described in case of applying it to PMSM. In the following sections a solution to the systematic error is presented and simulation results will be introduced and evaluated. Finally a conclusion will be presented. II. MODES OF PERMANENT MAGNET SYNCHRONOUS MACHINES PMSMs are controlled by field oriented control (FOC). Machines can be modeled in different coordinate systems. The most simple model is described in a coordinate system, where the two axes (d,q) are fixed to the rotor magnetic axis. Queer (q) component is perpendicular to rotor's magnetic field, it is used to generate torque. Direct (d) component is parallel with rotor's magnetic field and is used to decrease the effect of rotor magnetic field to stator windings (field weakening) [2], [3]. In this model the current and the voltage signals are not sinusoidal even if the rotor is rotating with a constant speed, because the coordinate system of this model rotates synchronously with the rotor. In one mechanical working point, where the torque and the rotor speed are constant all the currents and the voltages are constant. It is also possible to describe the machine in the coordinate system of the stator phase windings (u,v,w). This machine model is closer to the machine physical model. In this model voltage and current signals are sinusoidal, the most important parameter is the phase angle of the sinusoidal signals. The two machine models are equivalent. Mostly the d,q model is used, because it is easier to calculate with constant signals. To change from physical model to rotor oriented model it is required to convert 3 phase stator oriented reference frame (u,v,w) into magnetising (d) and torque producing (q) components. To change from stator oriented to rotor /7/$2. 27 IEEE 1

2 oriented reference frame Clarke (1) and Park (2) transformations are used, where io, id are real and imaginary currents in a stator oriented complex reference frame, (8r is the angle between stator phase flux direction and rotor magnetic flux direction (d) and id, iq are currents in the rotor oriented reference frame [4] [5]. Clarke transformation (1) changes from stator oriented 3 axis reference frame (u,v,w) to stator oriented orthogonal 2 axis frame (a,3). Park transformation (2) rotates stator oriented reference frame (a,3), which results rotating reference frame (d,q) which rotates synchronously to rotor. 2 j.2. ia= Ee {iu 1j.47 +i i3 W e 4 - < i, =3 {itl U) + iv ei 3 + iw ei 3 } 3 itu+iv +iw iu (1) 2 iv +iu /3- consist of two components: a constant offset and a sinusoidal part (6), where, is the constant part amplitude and r is the angle dependent amplitude of the phase inductivity. The amplitude of the sinusoidal part depends on the difference between d and q. (If d and q are the same, than the phase inductivities have only the constant part and the sinusoidal parts vanis.) Rt, Rv, Rw remain constant, and the induced voltages of the permanent magnets are sinusoidal (without having a constant offset). 'did Ud = Rs * id + d -dt-q gel * iq Uq = Rs? q +q diq+d gel td +Wel Kgen Wel = np Wmech (4) (5) lid iq = COSO +ssl*o = -sin OrU * y +Cos Or *it r+* (2) u (98r) v (98r), + r sin (2.r) c + r sin 2(8r + 3) (6) If machine's star point is not connected then currents in u,v and w windings can be calculated using (3), where it, iv, iw are the phase currents, as it can be seen in Fig. 1. iu +iv +iw = (3) + w (9r) = c + r sin 2(8r + <) Rc ~, 6acef 'q 'qi Ud Fig. 1. Motor phase currents A machine model in rotor oriented (d,q) reference frame can be seen in Fig. 2. This machine model is described with (4), where Ud, Uq are voltage inputs, id, iq are the currents in d and q loops, R, is the resistance d and q are the inductances in the direct axis and the quer axis, Kgen is the generator constant, Wel is the rotor electrical speed. Wel can be calculated with (5), where Wmech is the rotor mechanical speed and np is the number of rotor magnetic pole pairs. The d,q model can be transformed to u,v,w model with the inverse of the previously mentioned Park and Clarke transformations. The phase inductivities in u,v,w model (u,v,w), Fig. 2. Motor model in rotor oriented reference frame III. INFORM CACUATION In PMSM type of machines rotor position information (angle between rotor permanent magnet axis and magnetic axis of phase u winding) is essential in motor control application, because without knowing the exact rotor position the required torque cannot be generated [6]. Motor control uses 2

3 TABE I. PWM patterns of INFORM pulses Measured 1 Pulse 1 Phase connected to (PWM %) 1 Inductivity ] symbol U V W tu(v,w) U+ UDC () GND () GND () _V,W( ) U- GND () UDC () UDC () _V(,W) V+ GND () UDC () GND () _l_,w(v) V- UDC () GND () UDC () _W(,V) W+ GND () GND () UDC () _l_,v(w) w- UDC () UDC () GND () Fig. 3. Motor model in stator oriented reference frame V wv U Fig. 4. Phase windings orientation Pulse Width Modulation (PWM) changing the duty cycle of the power MOSFETs to apply the appropriate voltage level to the phase windings. It is assumed, that the machine inductivity is changing as a function of rotor position. To measure the inductivity six different PWM pulses should be generated. Three if one of the three phases is connected to UDC and the other two is connected to GND. Other three if two of the three phases is connected to UDC and one is connected to GND. PWM patterns for different INFORM pulse types can be seen in Table I. Because of the symmetry of the inductivity measurement the six different pulses are the excitation signals for the identification of three different resultant inductivities of the machine phases. This three inductivity values are varying as a function of rotor position. Each of them has a constant part and a sinusoidally varying component, but their sinusoidal components phase which depends on rotor position are shifted with ±2w/3 radian as it can be seen in Fig. 5. Resultant inductivity of the machine phases can be calculated from current answer to the voltage pulses using (7) or (8), where Au is the measurement signal amplitude, Ait is the current answer, At is the measurement pulse with. To estimate rotor position using inductivity change of the stator phases a specially designed electrical machine is needed. Inductivity varies as a function of rotor position almost in every type of PMSM. But if this property of the machine is not emphasized during design period, inductivity change can not be measured in automotive environment. In the test environment inductivity variation is 3% and approximately sinusoidal as a function of rotor position (9), where is the resultant inductivity of the machine phases, o is the average constant part of the inductivity, q -d is the amplitude of the sinusoidal part of the inductivity, (r is the rotor angle, is the phase offset. Main disadvantage of this method is that inductivity varies two times faster than the rotor angle. This phenomenon can result 7 rad (18) failure in position estimation. Main goal of research was to improve an existing position detection algorithm. (9r) - -RsAt ln(1 _2Au -3RAi Au r.,ai/at o + (q -d) sin(29r + ) IV. ANGE ERROR A. Introduction to the angle error problem In [1] the INFORM algorithm assumes that the resultant inductivity of the three phase of PMSM have sinusoidal inductivity. We will show that this assumption is not appropriate and leads to noticeable errors. We will also show how this error can be corrected. There is a problem if the previously mentioned INFORM method is used on PMSM. The angle calculation () results an error because in PMSM two sinusoidal phase inductivities are switched parallel and one serial in every measurement configuration as it can be seen in Fig. 6. This circuit results an inductivity which is not sinusoidal. (7) (8) (9) 3

4 15F X 1-/ C 5 u v Electrical angle (rad) w 8 Fig. 5. Phase inductivities (a,, v,,) of the machine or arg + V(W)e + ))+ () + W(U,V)e(J( 3 +2)) Fig. 6. Electric circuit of the inverter and motor windings angle with the standard equations the not sinusoidal inductivities result an angle error. The calculated and the reference rotor position is depicted in Fig. 8. The error signal is periodical, frequency of the error is three times faster than frequency of the INFORM angle signal.' Repeating the simulation with approximately 3% difference between q and d the error signal can be seen in Fig. 9. This parameter setting is common in PMSMs produced by ThyssenKrupp Presta, and results maximum ±4.3 error in the estimate of the angle. Resultant inductivities are depending on INFORM patterns. The resultant inductivity for different INFORM pulse patterns (Table I) are calculated according (11), (12) and (13). It can be seen that equations (11), (12) and (13) are transforming originally sinusoidal functions into functions which are not exactly sinusoidal u = 4 -Resultant inductivity for U+ pattern Sin function u(v,w) (9)r) = u (98r) + v(u,w)((9)r) = v((9)r) + w(u,v)(9)r) = w(9,r) v (98r)+w (98r) u (98r) w (98r) u (98r) v (98r) (1 1) (12) To see the difference between the resultant inductivity and a sinusoidal function the physical parameters of the machine are set to have extreme difference between d and q. The result can be seen in Fig. 7. The resultant inductivity has narrower high peaks and wider lower peaks than a sine function. The cause of this error is that the resultant inductivity value of two parallel inductance is closer to the smaller inductivity if they are not equal. As a result of simulating INFORM measurements with different pulse patterns on PMSM, three resultant inductivities can be determined. The three different resultant inductivities have the same shape, as it can be seen in Fig. 7, only the phase offset of them is different (±27/3). Calculating the INFORM 3 2 Fig. 7. Resultant inductivity (,, Electrical angle (rad) 8 (v,w) )of the machine compared with a sinus signal This error comes from the physical system, because the machine circuit nonlinearly transforms the sinusoidal phase inductivities. The difference comes from equations (11), (12) and (13), because the resultant inductivity of parallelly switched inductivities is not sinusoidal. B. New algorithm to eliminate systematic angle error With the six different INFORM patterns three different resultant inductivities are measured: u(v), v(u,w) w(u,v) The three independent measurements contain all information about the three phase inductivities: u, v, w. We propose a new method to eliminate the systematic error of the measurement method. From the measured inductivities of the machine (11), (12) and (13) the exact value of the phase induc- 1 INFORM angle signal has also two times higher frequency than the electric rotor angle signal of the machine. 4

5 4 3 Reference angle -INFORM angle (no correction) method called INFORM [1] which will be used in an Electronic Power Assisted Steering System. There was a systematic error discovered on the estimation of angle signal. This -Corrected INFORM error -3 4) 4 6 Rotor electrical angle (rad) o ~~' Fig. 8. Reference rotor angle and INFORM angle on PMSM 5 INFORM angle error with 3% d and difference -5) Rotor electrical angle (rad) Fig.. Angle error eliminated CA 4 6 Rotor electrical angle (rad) error was analyzed and the theoretical background of the error was discovered. Also correction formulas was derived in analytical form to correct the error of the calculation. The correction formulas was tested with simulation and the result was analyzed. It was shown that the formulas correct the angle error of the calculation and the final angle signal is within calculation errors the same as the reference rotor angle. Fig. 9. The angle error signal tivities t, V and W can be calculated with (13). Using the result of (13) in further calculations the systematic error is eliminated. V. SIMUATION RESUTS The performance of the correction formulas (13) is tested with a simulation model. The simulation model includes motor control, IPM machine model, INFORM pulse pattern generation, inductivity measurement, correction formulas (13) and INFORM angle calculation (). The results of the simulation model is that the angle estimation with the proposed method does not contain the error which was described in Section IV as it can be seen in Fig.. VI. CONCUSION The aim of this research was to analyze and improve the properties of a saliency based rotor angle position estimation ACKNOWEDGMENT Financial, technical, support of ThyssenKrupp Research Institute Budapest is appreciated. [1] M. Schr6dl and M. ambeck, "Statistic properties of the INFORMmethod in highly dynamics sensorless PM motor control applications down to standstill," European Power Electronics and Drives, vol. 13, no. 3, pp , Mar. 23. [2] P. Vas, Sensorless Vector and Direct Torque Control. Oxford: Oxford University Press, [3] A. Zentai and T. Daboczi, "Improving motor current control using decoupling technique," in Proc. of the EUROCON 25. The International Conference on Computer as a tool, Belgrade, Serbia & Montenegro, Nov , 25, pp [4] The Matworks, Inc., Clarke Transformation (Embedded Target for Texas Instruments C2 DSPs), 25. [Online]. Available: clarketransformation.html [5] The Matworks, Inc., Park Transformation (Embedded Target for Texas Instruments C2 DSPs), 25. [Online]. Available: parktransformation.html [6] J. M. D. Murphy and F. G. Turnbull, Power Electronic Control of AC Motors. Oxford: Pergamon Press, 2. 5

6 u(v,w) v(u,v ) w(v,u) (-v(u,v ) u(v,w) -v(v,u) u(v v ) + v(u,w) v (v,u)) (3 u = 2 ~~~~~~~Den. (3 - = 2 u(v,w) v(u,w) w(v,) (-v(u,w) u(v,w) + v(u,w) w(v,u) + w(v,u) u(vdw))e Den. w -2 u(v,w) v(u,w) w(v,u) (v(u,w) u(v,w) + v(u,w) w(v,u)- w(v,u) tu(v,w))- Den. Den. = -+2 V(u,W) (v,u) u 2(vw) -2 w(v,u)2u(vw) v(u w) + v(u, w)2(v,w)2 + * * - +W(V, ) 1 (V,W) + (T,W) tw(, U) -2tt,W tt(rw t(v,t 6