Design of Position Detection Strategy of Sensorless Permanent Magnet Motors at Standstill Using Transient Finite Element Analysis W. N. Fu 1, and S. L. Ho 1, and Zheng Zhang 2, Fellow, IEEE 1 The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 2 Great Lakes Electric, Stevensville, MI 49127, USA Sensorless control of permanent magnet (PM) motors at standstill and low speed is very challenging to implement. A methodology to design and optimize the position detection strategy of PM motors using transient finite element analysis (FEA) of magnetic field is presented. It addresses effects arising from both the iron core saturation and the transient characteristics of signals. A combined inductance which is sensitive to the rotor position throughout the complete cycle is proposed for the realization of position detection. The advantage of the proposed novel algorithm is that the rotor s position at low speeds down to standstill can be easily and robustly detected. A two-phase PM motor with salient structure is used to serve as an example to demonstrate the method. Index Terms Electric motor, initial rotor position, low-speed, magnetic field, permanent magnet, sensorless control, standstill. P I. INTRODUCTION ERMANENT MAGNET (PM) motors are being widely used by virtue of their high efficiency and simple structure. Usually a sensor is incorporated in high precision applications for detecting the mechanical positions of the rotor. Obviously, it is undesirable to have a position sensor as it increases the cost and complexity as well as compromising the reliability of the drive system. It would be highly desirable if a robust sensorless control method can be easily implemented. Hitherto, the back emf of the stator windings can be used to detect the position of the rotor at high speed and hence no external position sensor might be needed. At standstill and low speeds, the back emf is either zero or too small to be processed reliably. To overcome this difficulty, some researchers propose to detect the rotor s position by injecting special signals into the windings [1-5]. The exploitation of such special signals and the evaluation of their effectiveness are usually supported by extensively experimentation. Studies based on circuit analysis methods using coordinate transformation to the d-q axes have been presented [6-8]. The major disadvantages of using such methodology are that the effects of iron material saturation and the transient nature of the signals cannot be accounted for readily. In this paper a novel methodology for detecting the position and the magnetic polarity of PM motors at low speeds down to standstill is presented. A combined inductance based on the induced back emf and current is proposed to increase the rotor position detection accuracy. The proposed finite element analysis (FEA) can quickly evaluate the effectiveness of the detection method and address all the complicated interreaction effects among saturation, transient behaviour as well as the time and space high-order harmonics [9-10]. A twophase PM motor having salient structures is proposed for the implementation of the sensorless control algorithm. With the proposed methodology, the position of the rotor can be detected easily and robustly. It does not require three-phase to two-phase coordinate transformation either. II. ROTOR POSITION DETECTION AT STANDSTILL To detect the rotor position of the motor, the magnetic structure of the machine should have anisotropic properties. Fig. 1(a) shows the motor being studied. Its salient pole structure ensures the magnetic reluctances in the direct axis (i.e. the d axis, which is the magnetization direction of the PM in the rotor) and quadrature axis (the q axis, which lags the d axis by 90 and in this paper all angles are expressed in electrical degrees) are different. It has four poles. Its PM material s magnetic coercivity is 738113 A/m and its relative permeability is 0.999971. Its polarization can be observed in Fig. 1(b). The stator has two phases and each slot has 60 conductors. The winding axes of phase A and phase B are electrically perpendicular to each other. (a) Plan view (b) The flux produced by PM Fig. 1. The PM motor being studied (θ = 0 ) A. Basic Relationship between Rotor Position and EMF The basic mechanism to detect the position of the rotor is to inject a high-frequency carrier voltage into phase A and then measure the induced emf in phase B. When the phase A s axis
coincides with either the d axis or the q axis, there will be no induced back emf (Fig. 2(a)). When the rotor s d axis is not aligned with the axis of phase A, the magnetic field set up by the high frequency injected current is distorted due to the salient structure of the rotor (Fig. 2(b)). Consequently a corresponding emf will be induced in phase B. To illustrate this phenomena, assuming the coercive force H c of the PM is zero, a voltage v A = sin (2π 0.1t) V is applied to phase A and the rotor is rotating at a very slow speed of 1 /s. The calculated emf waveforms in phases A and B are shown in Fig. 3, where the waveform with bigger amplitude is the induced emf e A in phase A and the one with smaller amplitude is the induced emf e B in phase B. One notes that when the rotor s positions θ are 45, 135, 225 and 315, the values of the induced back emf in phase B will have the largest amplitude. current i A, emf e A and e B are calculated (Figs. 4-5). Figs. 6 and 7 shows the amplitude of e B and the steady-state amplitude i A versus the rotor position, respectively. Fig. 4. Induced emf when θ = 45 and f = 10 3 Hz at standstill (e A e B <0) Fig. 5. Current in phase A when θ = 45 and f = 10 3 Hz at standstill (a) θ = 0 (b) θ = 45 Fig. 2. Magnetic flux distribution produced by the currents in stator Back emf in phase A Back emf in phase B Fig. 6. The amplitudes of the induced emf of phase B vs rotor position Rotor position (degree) Fig. 3. Induced emf for rotor position detection when the rotor rotates slowly B. When Rotor Position 0 θ < 45 From Fig. 3, one notes that when the rotor position θ increases from 0 to 45, the emf e B in phase B will increase gradually. To evaluate the feasibility of the proposed technique further, the coercive force H c of the PM is set to its original value so that the effects of iron saturation and real current value in phase A can also be taken into account. A voltage v A = V m sin (2πft) with V m = 1 V and f = 1000 Hz is applied to phase A, which simulates the real implementation situation. When the rotor is resting at different positions, the Fig. 7. The amplitudes of the current of phase A vs rotor position The equivalent self inductance of phase A and the equivalent mutual inductance between phase A and phase B can be calculated by ea eb LA = and M =, (1) 2πfiA 2πfiA respectively. Their values versus the rotor position are shown in Figs. 8 and 9, respectively. One notes that because i A changes with the position, the largest amplitude of e B occurs at
30, instead of 45. However, M reaches the maximum at an angle of 45. Because of the symmetrical waveform of M and L A, it is better to use M and L A rather than e B and i A as the position indicators. One notes that near 45, M is not very sensitive to the rotor positions. Fortunately, near this position L A is very sensitive to the position. Hence a combined inductance is introduced: LCombined = w1 M + dsignw2 ( LA LAverage ) (2) where L Average is the average of L A. When 0 θ < 45 and 135 θ < 180, d sign =+1; when 45 θ < 135, d sign =-1. w 1 = 0.43 and w 2 = 0.57 are the weightings which are determined by: w = M M + L L, (3) w ( ) [( ) ( ) ] max max A max ( L L ) [( M ) + ( L L ) ] 1 Average =. (4) 2 A Average max max A Average Fig. 10 shows the relationship of L Combined versus rotor position. One notes that the combined inductance is now sensitive to the rotor position throughout the complete cycle, thereby increasing the accuracy of the position detection algorithm. C. When Rotor Position 45 θ < 90 The values of L Combined are the same for the positions at θ and at 90 - θ (θ < 45 ), (Fig. 10). Hence the values of L A are used to indentify whether the rotor position is at 0 θ < 45 or 45 θ < 90 (Fig. 9). D. When Rotor Position 90 θ < 180 When the positions are at θ and 90 + θ (θ < 90 ), the amplitudes of L Combined are the same; the amplitudes of L A are also the same. However, when 0 θ < 90, e A e B < 0; when 90 θ < 180, e A e B > 0. Therefore this signal is used to identify whether the rotor position is between 0 to 90 or between 90 to 180. max Fig. 9. Equivalent self inductance of phase A vs rotor position Fig. 10. Combined inductance E. The Effect of the Load Current When the supply voltage is applied to the windings, load currents will flow and change the saturation condition which in turn changes the value of the inductances. As a typical example, Figs. 11 and 12 show the calculated mutual inductance and self inductance when different i A are applied at the position 22.5. In practical applications all the parameters at different rotor positions are computed and a look-up table is used to determine the rotor s position. Fig. 11. Equivalent mutual inductance vs load current i A at the position 22.5 Fig. 8. Equivalent mutual inductance vs rotor position Fig. 12. Equivalent self inductance vs load current i A at the position 22.5
III. MAGNET POLARITY DETECTION AT STANDSTILL A. Basic Polarity Detection Method The magnetic polarity is detected by sequentially injecting two impulse voltages with opposite signs into the windings as shown in Fig. 13. The voltage impulses applied to phases A and B are governed by the rule that the magnetic fields produced by these voltages should be along the d axis. Because the rotor s position has been determined already, the space vector angle of the voltage can be easily calculated. In the two sequences of impulse voltages applied, one impulse voltage will reduce the saturation of the iron core while the other impulse voltage will increase saturation. Figs. 13 and 14 show the applied voltages and the calculated currents, respectively. One notes that the two applied voltage impulses should be coordinated so as to allow the current to decay to zero before the next voltage impulse is applied. (2) According to M, L A and the load current, determine the rotor position θ. Step 2: Inject two impulse voltages with opposite signs into the windings sequentially to determine whether 0 θ < 180 or 180 θ < 360. Fig. 15. A series of voltage pulses is applied to the winding at standstill Fig. 16. The current responding to the series of voltage pulses at standstill Fig. 13. A pair of voltage pulses is applied to the windings at standstill Fig. 14. The current responding to the pair of voltage pulses at standstill B. Determination of the Magnitude of the Voltage Impulses Obviously, the magnitude of the applied voltage impulses should be sufficiently large to change the saturation condition of the magnetic materials. To determine the voltage s amplitude, a series of pairs of square-wave impulse voltages having gradually increasing amplitudes are applied to the windings as shown in Fig. 15. The calculated currents are shown in Fig. 16. From this figure the sensitivity of the current amplitude differences between the responses of the positive voltage and negative voltage to the amplitude of the voltage pulses can be observed clearly. C. Procedures to Detect the Rotor Position The procedures to detect the rotor position can be summarized in the following steps. Step 1: Inject a voltage v A = V m sin (2πft) into phase A. (1) If e A e B < 0, one has 0 θ < 90 ; if e A e B > 0, one has 90 θ < 180. IV. CONCLUSION To detect the position of the rotor at standstill and at low speeds by injecting a high-frequency carrier voltage into phase A, the full responses, which are the induced emf in phase B and the current in phase A, should be used to increase the accuracy of the calculation. When designing the injected signals and identifying the position of the rotor, one should take care of the iron materials saturation and the transient nature of the signals. It shows that the proposed transient finite element analysis of magnetic field can serve as a powerful tool for the design of a robust position detector for sensorless PM motor drives. REFERENCES [1] J. Holtz and H. Pan, Acquisition of rotor anisotropy signals in sensorless position control systems, IEEE Trans. on Ind. Appl., Vol. 40, No 5, pp 1379 1387, Sept./Oct. 2004. [2] P. L. Jansen and R.D. Lorenz, Transducerless position and velocity estimation in induction and salient AC machines, IEEE on Trans. Industry Application, Vol. 31, pp. 240 247, Mar./Apr. 1995. [3] J. Wisniewski and W. Koczara, Control of Axial Flux Permanent Magnet Motor by the PIPCRM method at standstill and at low speed, 13th Power Electronics and Motion Control Conference, 1-3 Sept. 2008, pp.2254-2260. [4] J. Persson, M. Markovic, Y. Perriard, A New Standstill Position Detection Technique for Nonsalient Permanent-Magnet Synchronous Motors Using the Magnetic Anisotropy Method, IEEE Trans. Magn. Vol.43, No.2, Part 1, Feb. 2007, pp.554-560. [5] Yen-Chuan Chang and Ying-Yu Tzou, A New Sensorless Starting Method for Brushless DC Motors without Reversing Rotation, IEEE Power Electronics Specialists Conference, 17-21 June 2007, pp.619-624.
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