2014 International Symposium on Power Electronics, Electrical Drives, Automation and Motion Comparison of carrier signal based approaches for sensorless wound rotor synchronous machines Alexander Rambetius, and Bernhard Piepenbreier, Senior Member, IEEE Chair of Electrical Drives and Machines, University of Erlangen-Nuremberg, Germany Email: [email protected] however fail at standstill and low speed. A common approach to overcome this limitation is the injection of a carrier signal. This carrier signal usually has got a higher frequency than the fundamental wave and is therefore often referred to as highfrequency (HF) signal. The conventional approaches for permanent magnet synchronous machines (PMSM) inject continuous HF-voltages into the stator and evaluate the resulting current response. In contrast to PMSMs WRSMs allow to use the rotor winding as the transmitter or as the receiver of the carrier signal, which results in the following possibilities for the transmission: • Stator Stator [7], [10], [16] • Rotor Stator [2], [5-6], [8-9], [12-13], [17-20] • Stator Rotor [10], [21] Furthermore it is possible to use the rotor as the transmitter and as the receiver. In this case the stator slots represent a position dependent saliency which can be evaluated. The stator teeth however saturate very quickly and consequently the rotor position estimation becomes complex. Therefore this approach is not addressed in this paper. A method to estimate the rotor speed by evaluating stator slotting harmonics in the rotor current can be found in [4]. The most intuitive approach of the aforementioned methods is to emulate a resolver by using the rotor as the transmitter and the stator as the receiver of the HF-signal. Since the rotor selfinductance is usually quite large this is not necessarily the approach to be favored since large rotor voltages might be necessary to create detectable stator currents [2]. If a rotating diode rectifier is used to inductively transmit the rotor power, the pulsation of this rectifier can be used as a carrier signal. The resulting current response can either be evaluated in the stator [5-6], [8] or in the rotor [22]. If the stator is used as the transmitter and as the receiver of the carrier signal (like for PMSM [23-25]) the rotor winding acts like a damper winding for the HF-signal and consequently the required saliency differs from the saliency which is necessary for sensorless control of PMSMs [10]. Recently HF-current control has been applied to PMSMs instead of HF-voltage injection [26-30]. If this approach is applied to WRSMs, the prerequisites chance compared to HFvoltage injection: Since the HF-current in the rotor can be controlled to zero, the rotor winding does not act like a damper winding anymore. Consequently a differential magnetic saliency regarding the inductances in the d- and q-axis is evaluated. The aim of this paper is to make the aforementioned approaches comparable in terms of signal-to-noise ratio and Abstract—Wound rotor synchronous machines enable a large variety of approaches for carrier signal based sensorless control since the rotor voltage serves as an additional input to the system and the rotor current as an additional, easy to measure, state variable. Consequently it is possible to use the rotor winding either as the transmitter or as the receiver of a carrier signal. In these cases the mutual inductance between the d-axis and the rotor winding is of major importance. Moreover a rotor saliency can be evaluated if the stator is used as the transmitter and as the receiver of the carrier signal. If voltage injection is used, the rotor winding acts like a damper winding for the carrier signal and consequently the evaluated saliency differs from the saliency which is utilized for sensorless control of permanent magnet synchronous machines. Carrier current control on the other hand offers the possibility to evaluate a magnetic saliency regarding the inductances in the d- and q-axis. This work provides a detailed review of the aforementioned approaches and analyses the prerequisites. In addition to this the different approaches are made comparable in terms of signal-to-noise ratio and cross saturation. This is done by introducing suitable intensity terms. With the help of identified parameters the most promising approach for the investigated machine is found. Experimental results confirm the validity of the comparison. Keywords—wound rotor synchronous machine, wound field synchronous machine, electrically excited synchronous machine, sensorless control, high frequency injection, traction motor I. INTRODUCTION Wound rotor synchronous machines (WRSM) are synchronous machines (SM), in which the rotor flux is generated by an electrical winding. Besides WRSM, other notations are used in the literature as well. Some of the most common ones are: • Wound rotor [1-6] or wound field SM [7-9] • Electrically excited [10-12] or energized SM [13] • Externally excited SM [14] • DC-excited SM [15] In the following the term WRSM will be used. WRSMs feature certain characteristics that suite the needs of automotive traction applications very well [1], [14-15]. If field oriented current control is applied to a WRSM, information about the rotor position is required. This information is usually obtained by a motion sensor (incremental encoder, resolver, etc.). Leaving out this sensor reduces cost and may increase the reliability of the whole drive system. Therefore sensorless control is highly desirable in automotive traction [15]. At high speed the rotor position can be obtained by evaluating the motional electromotive force (EMF) [4], [15]. These methods 978-1-4799-4749-2/14/$31.00 ©2014 IEEE 1152 cross saturation. For this purpose the prerequisites for the different approaches are analyzed and suitable intensity terms are introduced. With the help of identified parameters the most promising approach for the investigated machine is found. The validity of the comparison is confirmed by experimental results. MACHINE MODELING , , , , , With , (2) (3) denotes the self-inductance of the i-axis, the mutual inductance between the i-axis and the j-axis. Apart from the actual magnetic coupling , cross saturation effects are and [2-3], [10considered by the mutual inductances 11], [13]. The machine model is depicted in Fig 1. If HFvoltage injection is used, the current response is of interest and consequently the admittance matrix, which is the inverse of the impedance matrix, is required: , , , , , , III. Stator Transmitter => Stator Receiver Rotor Transmitter => Stator Receiver Stator Transmitter => Rotor Receiver • Alternating carrier • Evaluation in dq • PMSM [22-23] • EESM [7], [10] • Fig. 2 • Alternating carrier • Evaluation in dq • [2], [6], [13] • Fig. 3 • Alternating carrier • Evaluation in dq • [10], [21] • Fig. 4 • Rotating carrier • Evaluation in αβ • PMSM [24] • EESM [16] • Alternating carrier • Evaluation in αβ • [2], [5], [8-9], [12], [17-20] • Rotating carrier • Evaluation in dq • Section III.D the impedances in (1) are given by: , APPROACHES FOR HF-VI BASED SENSORLESS CONROL TABLE I. , , , , (1) Indirect , , Fig. 1. Machine model: the d-axis and the field winding are magnetically coupled by . The coupling between the d-axis and the q-axis and between the q-axis and the field winding is caused by saturation effects. Direct II. The rotor fixed fundamental wave model derived in [11] will be used throughout the paper. Moreover it is assumed that the HF-analysis and the fundamental wave analysis can be carried out separately from each other. Using complex phasor notation for ac steady state signals, the voltage equations for the HF-analysis at standstill are given by: Fig. 2 – Fig. 4 depict the basic structure of the possible indirect methods if HF-voltage injection is applied. The injection is marked in red, the evaluation in blue. CC stands for current control, EST for rotor position estimator. A. Stator Transmitter – Stator Receiver (Method 1, see Fig. 2) This method is well known from PMSMs [22-23] and has been applied to WRSMs as well [7], [10]. The most common approach uses an alternating carrier signal and is depicted in Fig. 2. To derive the underlying prerequisite, it is assumed that a HF-voltage is injected in the estimated -reference frame: (4) , HF-VOLTAGE INJECTION BASED SENSORLESS CONTROL HF-voltage injection (HF-VI) is the most common approach for carrier signal based sensorless control. If secondary saliencies are neglected, WRSMs enable three transmission directions. Furthermore it is possible to distinguish between direct and indirect methods. Direct methods directly compute the rotor position, while indirect methods rely on the minimization of an error angle. Whether a method is direct or indirect depends on the injection (either rotating or alternating carrier signal) and on the evaluation (either evaluation in stator fixed αβ-coordinates or in rotor fixed dq-coordinates). Table I summarizes all the possible approaches. In the following only the indirect methods are investigated in detail because they seem to be more popular. The direct methods are addressed briefly in Subsection D. For the indirect methods, it is assumed that the estimated dq-reference frame is misaligned. The difference between the estimated rotor position and the actual rotor position is denoted by ∆ . Furthermore the error angle is assumed to be small and therefore a linearization is carried out around small error angles in the following [2], [10]. , 0 , 0 (5) Transforming this excitation to actual -reference frame and inserting it into (4) the HF-current response can be calculated. This current response is then transformed back to the estimated reference frame. The required transformation matrices are given in [10]. Linearizing the result around small error angles, the current response in the estimated -axis is given by: , ∆ , (6) As can be seen in (6) the current response contains information about the rotor position if there is a saliency regarding the admittances in the d- and q-axis. Due to the inversion of the impedance matrix in (1) the admittances include resistive and inductive parts. However in general the inductive voltage drop is dominant for HF-excitation. To extract a meaningful prerequisite, the resistive voltage drops as well as cross saturation is neglected in the following. 1153 Fig. 2. : HF-VI: The Stator is the transmitter and the receiver (Method 1) Fig. 3. HF-VI: The rotor is the transmitter and the stator the receiver (Method 2) carrier signal [2], [9], [12]. A drawback of this injection technique is that the amplitude and the phase of the carrier signal vary depending on the duty cycle of the rotor chopper [2]. In the following it is assumed that a cosine-shaped HF-voltage is superimposed to the DC field voltage: In this case the current response in (6) can be written as: , , ∆ (7) denotes the effective HF-inductance of the d-axis for a short circuited field winding and is given by (8) [2], [10]. , It can be seen that apart from the actual HF-inductance of the d-axis, the coupling between the d-axis and the field winding is of importance. For the HF-analysis the field winding can be regarded as short-circuited and therefore acts like a damper winding. Consequently the HF-flux in the d-axis is weakened which leads to a drop in the effective HF-inductance of the daxis. As a result no actual magnetic saliency is necessary like for PMSMs. Instead a saliency regarding the effective HFinductance of the d- and q-axis is required: / 0 (11) , ∆ , (12) , From (12) it can be concluded that the HF-current response in the estimated q-axis contains information about the rotor position. If resistive voltage drops and cross saturation are neglected (12) can be simplified, which results in: , , ∆ (13) It can be deduced that the d-axis and the field winding have to the inductance ratio be coupled magnetically. Apart from in (14) is of major importance. (9) This effect is also used in [31-33] to increase the saliency of a PMSM by adding a short circuited winding to the rotor. Analyzing (6), it can be concluded that an estimation error is introduced by cross saturation. This estimation error is given by: ∆ 0 Calculating the HF-current response due to this excitation and transforming it to the estimated -reference frame, one yields: (8) 0 Fig. 4. HF-VI: The stator is the transmitter and the rotor the receiver (Method 3) / (14) Moreover (12) shows that an error is introduced due to cross saturation which is given by: (10) ∆ B. Rotor Transmitter – Stator Receiver (Method 2, see Fig. 3) This intuitive approach is based on the principle of a resolver and is depicted in Fig. 3. Concerning the injection, the power transmission to the rotating field winding is of major importance. The transmission is either done via slip rings [10], [13-15], or brushless using inductive coupling and a rotating diode rectifier [5-6], [8]. Moreover capacitive power transmission has been suggested recently [34]. The easiest way to perform the injection is to superimpose the HF-voltage to the fundamental wave DC-voltage using the rotor converter [13]. This approach might not be feasibly for every machine, since the voltage reserve for the field current controller is reduced significantly. In certain cases the available DC-link voltage might even be insufficient to create detectable stator currents [2]. If a rotating diode rectifier is used, it is possible to overcome this problem by using the pulsation of the rectifier as a carrier signal [5-6], [8]. If a rotor chopper is used to create the field voltage, the switching of this chopper can be utilized as a / (15) C. Stator Transmitter – Rotor Receiver (Method 3, see Fig. 4) This approach is successfully applied to a WRSM in [10] and is depicted in Fig. 4. An advantage of this approach is that the measurement range of the field current is small compared to the one of the stator currents. Therefore even small signal amplitudes are detectable. The HF-injection for this approach is done in the q-axis of the estimated -reference frame: , 0 , 0 (16) Transforming this excitation to the actual -reference frame and calculating the resulting HF-current response in the field winding, one yields: , ∆ , (17) Comparing (17) to (12), it becomes apparent that both current responses differ only by the scalar 3/2 and by the excitation. 1154 The superscript * denotes set point values. (22) is now transformed to the actual dq-reference frame. Cross saturation is neglected in the following. If the HF-current control injects the set point in (22) with zero steady state error, the output of the HF-current controller in the estimated -axis is given by (23) and contains information about the rotor position. Consequently the prerequisite for this approach is the same like in Subsection B and the estimation error due to cross saturation is given by (18). ∆ ∆ (18) D. Direct methods If the stator is used as the transmitter and as the receiver of the carrier signal, the absolute rotor position can be estimated by injecting a rotating HF-voltage and evaluating the resulting HF-current response in the stator in stator fixed αβ-coordinates. Possible implementations for this approach can be found in [16] and [24]. If the rotor is used as the transmitter of the carrier signal, an estimate of the absolute rotor position can be obtained by evaluating the resulting HF-current response in the stator in stator fixed αβ-coordinates. Possible implementations can be found in [2], [5], [8-9], [12], [17-20]. If the rotor is used as the receiver of the carrier signal, an estimate of the absolute rotor position can be obtained by injection of a rotating carrier signal. Since this approach is not properly addressed yet in the literature, the basic idea is briefly discussed. The rotating carrier signal in stator fixed coordinates is given by: , , 0 , , 3 1 2 sin , IV. , / , , ∆ (24) B. Rotor Transmitter or Receiver If an alternating HF-current is injected into the field winding the output of the HF-current controller of the estimated -axis contains information about the rotor position. If an alternating HF-current is injected into the estimated -axis, the output of the HF-current controller of the field winding contains information about the rotor position. Compared to HF-voltage injection the prerequisites do not change: The d-axis and the field winding have to be coupled magnetically. Therefore these approaches are not addressed in detail. (20) The absolute rotor position can now be calculated by separating the real and the imaginary part in (20): arctan (23) It can be seen that either a resistive saliency or an inductive saliency can be evaluated. The inductive saliency however appears to be more frequently used. Furthermore it can be deduced that, since the HF-current in the field winding is controlled to zero, the damping effect described in Section III.A does not appear anymore. Consequently an actual magnetic saliency regarding the inductances in the d- and qaxis is required for this approach. (19) , ∆ In contrast to (6) a saliency regarding the impedances in the dand q-axis is a prerequisite for this approach. Inserting (2) in (23), one yields: Resistances and cross saturation are neglected in the following. The HF-current response in the field winding resulting from the excitation in (19) can then be written as: , , (21) V. PARAMETER IDENTIFICATION The differential HF-inductances are identified using the HFcurrent injection based technique suggested in [29-30]. The investigated drive system is summarized in Table II. The identification is carried out while the machine is rotating at 2.5 rpm and the results are averaged over one electrical period. The alternating carrier signal used for the identification has got a frequency of 1 kHz. To reduce the number of dependencies a new fictive magnetization in the d-axis is defined: HF-CURRENT INJECTION BASED SENSORLESS CONTROL Recently, HF-current injection (HF-CI) has been applied instead of HF-voltage injection (HF-VI) [26-30]. In order to inject the HF-currents with zero steady state control error advanced control techniques have to be applied. [26] for instance uses resonant controllers in combination with a flatness based feed forward control. Fig. 5 depicts the basic structure for an indirect carrier signal based approach, if the stator is used as the transmitter and as the receiver. In this scheme CC stands for a current controller, which is suitable for fundamental wave current control as well as for HF-current control. It can be seen that the output of the current controllers is used to estimate the rotor position. (25) A. Stator Transmitter – Stator Receiver (Fig. 5) Like suggested in [26-28] an alternating HF-current is injected into the estimated d-axis. The HF-currents in the estimated q-axis and in the field winding are controlled to zero. The HF-excitation in estimated rotor fixed coordinates is consequently given by (22). , , 0 0 Fig. 5. HF-CI: The Stator is the transmitter and the receiver of an alternating carrier signal. The evaluation is done in the dq-reference frame (22) 1155 Fig. 6. Self-inductances of the d- and of the qaxis Fig. 7. Self-inductance of the field winding Fig. 8. Mutual inductance between the d-axis and the field winding Fig. 9. Effective HF-self-inductance of the d-axis and self-inductance of the q-axis Fig. 10. Mutual inductance between the d-axis and the q-axis due to cross saturation Fig. 11. Mutual inductance between the q-axis and the field winding due to cross saturation is a transmission ratio, which makes the currents magnetically comparable, such that: , 0 0, and TABLE II. SUMMARY OF THE INVESTIGATED DRIVE SYSTEM Wound Rotor Synchronous Machine (26) denotes the stator flux linkage of the d-axis. Fig. 6 depicts the self-inductance of the d- and q-axis. It can be seen that for an unmagnetized d-axis a large saliency is present due to the salient rotor. This saliency however vanishes for large magnetization currents in the d-axis. The reason is that the air-gap, which has got linear magnetic characteristics, is relatively large in the q-axis and therefore the self-inductance of the q-axis is comparatively constant. The d-axis on the other hand saturates quickly due to the small air gap of the d-axis. Consequently the HF-CI based approach in Section IV.A is not applicable for large magnetization currents and is therefore not further analyzed. The effective HF-inductance of the d-axis for HF-VI is given by (8) and is identified by turning off the HF-current controller of the field winding during the identification process. The identification results are depicted in Fig. 9. Since the field winding damps the HF-flux in the d-axis, the inductance is smaller than the self-inductance of the q-axis. It can be seen that the investigated machine features a large saliency regarding the effective HF-inductances of the stator if HF-VI is applied. This saliency is present for all operating points. Fig. 7 depicts the self-inductance of the field winding, Fig. 8 the mutual inductance between the field winding and the d-axis. It can be seen that saturation effects manifest themselves in a similar manner for both inductances. Therefore, the inductance ratio in (14) does not change significantly for different operating point. Fig. 10 and Fig. 11 depict the two mutual cross saturation inductances. It can be seen that cross saturation only appears for a q-current unequal to zero [29-30]. Stator 3-phase distributed winding Rotor Salient pole with slip rings 3 Number of pole pairs 12 Rated power/Rated Speed / 3325 250 / Rated/Maximum stator current (rms) 320 18.3 Rated phase voltage (rms) 16 Rated/Maximum field current Power Electronics (3-phase VSI Stator, 2-phase VSI Rotor) 45 DC-link voltage Switching frequency stator/rotor VI. , 16 / , 8 COMPARISON The Comparison is carried out for the indirect HF-VI approaches described in Section III. HF-CI is not addressed since the investigated WRSM does not feature the necessary saliency if the stator is used as the transmitter and as the receiver. If the rotor is used either as the transmitter or as the receiver, the magnetic coupling between the d-axis and the field winding is utilized for both HF-VI and HF-CI. The three HF-VI based approaches are compared in terms of signal-tonoise ratio and estimation errors due to cross saturation. In the following it will be assumed that only the imaginary part of the current responses in (6), (12) and (17) is evaluated which means that the imaginary part of the admittances (susceptance) in (4) is of importance. Consequently mainly, but not solely, inductive effects are evaluated. 1156 The susceptances are identified by injecting a cosine-shaped HF-voltage with the amplitude , into the i-axis of the stator and evaluating the resulting current response in each axis. With , , one yields: , (27) , , (28) , , (29) , The identification is carried out for a carrier signal frequency of 1 kHz and for the carrier signal amplitudes in (30). , , , , , 1 Fig. 12. Comparison of intensitiy terms for ( ), Rotor Stator ( ), Stator Rotor ( 2.2 % 20.7 46 % B. Missalignment due to cross saturation If the stator is used as the transmitter and as the receiver of the carrier signal, the estimation error due to cross saturation is given by (10). If the rotor is utilized either as the transmitter or as the receiver this estimation error is given by (15). Fig. 13 compares the absolute values of the estimation errors for the three different HF-VI based approaches if only the susceptances (imaginary part of the admittance) are evaluated. It can be seen that above a magnetization current in the d-axis of 80 A, the estimation error is always smaller if the rotor is either used as the transmitter or as the receiver of the carrier signal. (31) (32) If the stator is used as the transmitter and the rotor as the receiver, the intensity term is given by (33). , Stator Fig. 13. Estimation error due to cross saturation: Stator transmitter and receiver (red), rotor transmitter or receiver (black) If the rotor is used as the transmitter and the stator as the receiver, the intensity term is given by (32). , : Stator (30) A. Signal-to-Noise Ratio (SNR) In order to make the three indirect HF-VI approaches comparable in terms of SNR new intensity terms are introduced. These intensity terms indicate what HF-current amplitude is evaluated for each approach if the error angle equals 1 rad. These HF-current amplitudes are then normalized with the maximum current of the respective axis and expressed in percent. In other words the intensity terms describe, how many percent of the maximum current of the respective axis is evaluated for a misalignment of 1 rad. A similar approach is suggested in [35] to describe the effectiveness of carrier signal based sensorless control of PMSMs. If the stator is used as the transmitter and as the receiver the intensity term is given by (31). , 1 ) (33) VII. EXPERIMENTAL VALIDATION Fig. 12 depicts a comparison of the intensity terms in (31-33) for the investigated machine. The utilized carrier signal amplitudes are given in (30). It can be seen that for almost every operating point the best SNR is provided if the stator is used as the transmitter and the rotor as the receiver. For a strong magnetization of the d-axis the saliency regarding the effective HF-inductances of the stator becomes larger and therefore the SNR increases significantly if the stator is used as the transmitter and as the receiver. For values of above 320 A the worst SNR is always provided if the rotor is used as the transmitter and the stator as the receiver. Additionally this approach implicates a large carrier signal amplitude (see (30)) due to the relatively large field winding inductance (see Fig. 7). Consequently the voltage reserve for the fundamental wave field current controller is reduced significantly. The experiments are carried out in current control mode for the three indirect HF-VI based approaches with a carrier signal frequency of 1 kHz and the carrier signal amplitudes in (30). The implementation is done like suggested in [2] and [10] using a tracking observer. The compensation for cross saturation is left out on purpose in order to quantify the resulting estimation error. The demodulation is done using the goertzel algorithm. The tracking observer together with the demodulation is shown in Fig. 14. The dynamic characteristics of this observer are set using pole placement. The first test is an unloaded start-up from standstill to 50 rpm (Experiment 1). The observer poles are placed according to Table III with the same dynamics for all approaches. Fig. 15 depicts the experimental results and shows a comparison between the measured 1157 OBSERVER POLES FOR EXPERIMENTAL VALIDATION TABLE III. and the estimated rotor position . Moreover the estimation errors (Δ ) are compared for all three approaches. The comparison of the estimation errors for Experiment 1 proves that for unloaded operation the best SNR is provided if the stator is used as the transmitter and the rotor as the receiver of the carrier signal (Method 3). This result confirms the conclusion drawn from the comparison in Fig. 12. The second experiment starts with a step change in the stator current from 0 to 320 during standstill. The field current is maximal during the whole experiment. After the step change a startup and a speed reversal with maximal field current and with maximal stator current in the negative q-axis is performed. The observer poles are chosen such that a stable operation is possible for this experiment. The dynamics of Method 1 and Method 2 have to be reduced. The reduction is necessary due to the lower SNR (compared to Method 3) and due to the step change in the stator currents. The chosen observer poles for this experiment are given in Table III. Fig. 16 depicts the results for Experiment 2. It can be seen that the steady state estimation error due to cross saturation is largest for this operating point if Method 1 is applied. The steady state estimation errors for Method 2 and Method 3 are almost identical. Stator Rotor Stator This work provides a detailed review of carrier signal based approaches for sensorless control of WRSMs. If HF-current injection is applied and the stator is used as the transmitter and as the receiver, a magnetic saliency is evaluated. If HF-voltage injection is employed, a different saliency is evaluated. Furthermore methods are considered in which the rotor winding is either used as the transmitter or as the receiver of the carrier signal. The different approaches are made comparable in terms of signal-to-noise ratio (SNR) and estimation errors due to cross saturation. Regarding these criterions the best suited strategy for the investigated machine is to use the stator as the transmitter and the rotor as the receiver. The approach in which the rotor is used as the transmitter on the other hand shows the worst SNR above a certain magnetization in the d-axis. The conclusions drawn from the comparison are confirmed by experimental results. Finally the author would like to point out that the comparison carried out in this work is only valid for the investigated machine and for the specified conditions. Stator -> Stator (Method 1) [rad] [rad] γ γest 5 γ γest 0 Rotor -> Stator (Method 2) γ γest [rad] [rad] Rotor -> Stator (Method 2) 5 γ γest 0 0 Stator -> Rotor (Method 3) Stator -> Rotor (Method 3) γ γest [rad] [rad] -50 rad/s -25 rad/s -150 rad/s VIII. CONCLUSION 0 5 -150 rad/s -150 rad/s -150 rad/s Stator Stator Rotor Stator -> Stator (Method 1) 5 Experiment 2: speed reversal with full load These results confirm the conclusions drawn from the comparison in Fig. 13. Moreover the reduced dynamics of Method 2 compared to Method 3 can be observed in the estimation error depicted in Fig. 16 during the time when the rotor speed changes the sign. Fig. 14. Utilized tracking observer for the experimental validation of HF-VI 5 Experiment 1: unloaded start-up 0 5 γ γest 0 Estimation error Estimation error 20 Method 1 Method 2 Method 3 10 Δγ [°] Δγ [°] 5 0 -10 -5 0 0 Method 1 0.2 0.4 0.6 Time [s] 0.8 1 -20 0 1.2 Fig. 15. Experiment 1: Start-up perfomance from standstill to 50 rpm with no current flowing in the rotor and the stator 0.5 1 Method 2 1.5 Time [s] Method 3 2 2.5 3 Fig. 16. Experiment 2: Start-up and speed reversal from 50 rpm to -50 rpm with maxiumum field current and maximum stator current in the negative q-axis 1158 [18] C. E. Anghel, R. Divito and N. A. Morcov, “Position sensing method and apparatus for synchronous motor generator system”, U.S. Patent 7,045,986 B2, May 16, 2006 [19] C. E. Anghel, R. Divito and N. A. Morcov, “Adaptive position sensing method and apparatus for synchronous motor generator systems, US. Patent 7,184,927 B2, Feb. 27, 2007 [20] C. E. Anghel, and M. A. Eldery, “Energy based position and speed selfsensing method and apparatus for synchronous machine”, U.S. Patent 7,571,072 B2, Aug. 04, 2009 [21] Satake Akira and Wada Noriyuki, “Magnetic pole position detecting device for winding field-type synchronous machine”, Japan Patent, Pub. No. 2006136123 A, 25.05.2006 [22] A. Markunas, and C. Romenesko, “Brushless wound field synchronous machine rotor position tracking with exciter stator current harmonic tracking”, U.S. Patent 7,132,816 B1, Nov. 07, 2006 [23] M. Linke, R. Kennel, and J. Holtz, “Sensorless speed and position control of synchronous machines using alternating carrier injection,” in IEEE International Electric Machines and Drives Conference, 2003. IEMDC'03., 2003, pp. 1211–1217 vol.2. [24] J. Reill, B. Piepenbreier, and I. Hahn, "Utilisation of magnetic saliency for sensorless-control of permanent-magnet synchronous motors," 2010 International Symposium on Power Electronics Electrical Drives Automation and Motion (SPEEDAM), pp.1484-1489, 14-16 June 2010 [25] H. Kim, and R.D. Lorenz, "Carrier signal injection based sensorless control methods for IPM synchronous machine drives," Industry Applications Conference, 2004. Conference Record of the 2004 IEEE 39th IAS Annual Meeting. , vol.2, pp.977-984, 3-7 Oct. 2004 [26] S. Ebersberger, M. Seilmeier, and Bernhard Piepenbreier, “Flatness Based Sensorless Control of PMSM Using Test Current Signal Injection and Compensation for Differential Cross-Coupling Inductances at Standstill and Low Speed Range,” 4th Symposium on Sensorless Control for Electrical Drives 2013 (SLED 2013), 2013 [27] M. Seilmeier, and B. Piepenbreier “Sensorless Control of PMSM for the whole speed range using Two-Degree-of-Freedom current control and HF test current injection for low speed range,” International Power Electronics Conference (IPEC) 2014, in press. [28] M. Seilmeier, S. Ebersberger, and B. Piepenbreier, “HF Test Current Injection Based Self-Sensing Control of PMSM for Low and Zero Speed Range using Two-Degree-of-Freedom Current Control,” 5th Symposium on Sensorless Control for Electrical Drives 2014, 2014, in press. [29] M. Seilmeier, A. Boehm, I. Hahn, and B. Piepenbreier, “Identification of time-variant high frequency parameters for sensorless control of PMSM using an internal model principle based high frequency current control,” 2012 XXth International Conference on Electrical Machines (ICEM), pp.987-993, 2-5 Sept. 2012 [30] M. Seilmeier, S. Ebersberger, and B. Piepenbreier, "Identification of high frequency resistances and inductances for sensorless control of PMSM," 2013 IEEE International Symposium on Sensorless Control for Electrical Drives (SLED), pp.1-8, 17-19 Oct. 2013 [31] T. A. Nondahl, C. Ray, P. B. Schmidt, and M. L. Gasperi "A permanentmagnet rotor containing an electrical winding to improve detection of rotor angular position", IEEE Trans. Ind. Appl., vol. 35, no. 4, 1999, pp.819 -824. [32] N. Bianchi, S. Bolognani, and A. Faggion, "A ringed-pole SPM motor for sensorless drives - electromagnetic analysis, prototyping and tests," 2010 IEEE International Symposium on Industrial Electronics (ISIE), pp.1193-1198, 4-7 July 2010 [33] J. Graus, A. Rambetius, and I. Hahn, “Comparison of the Resistance-and Inductance-Based Saliency of a PMSM due to a Short-Circuited Rotor Winding,” IPEC 2014, 2014, in press. [34] D.C. Ludois, J.K. Reed, and K. Hanson, "Capacitive Power Transfer for Rotor Field Current in Synchronous Machines," IEEE Transactions on Power Electronics, , vol.27, no.11, pp.4638,4645, Nov. 2012 [35] Z.Q. Zhu, and L.M. Gong, "Investigation of Effectiveness of Sensorless Operation in Carrier-Signal-Injection-Based Sensorless-Control Methods," IEEE Transactions on Industrial Electronics, , vol.58, no.8, pp.3431-3439, Aug. 2011 REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] C. Rossi, D. Casadei, A. Pilati, and M. Marano, “Wound Rotor Salient Pole Synchronous Machine Drive for Electric Traction,” in Industry Applications Conference, 2006, Conference Record of the 2006 IEEE 41st IAS Annual Meeting, 2006, pp. 1235–1241. A. Rambetius, and B. Piepenbreier, “Sensorless control of wound rotor synchronous machines using the switching of the rotor chopper as a carrier signal”, 4th Symposium on Sensorless Control for Electrical Drives 2013 (SLED 2013), 2013 A. Rambetius, and B. Piepenbreier, “Modeling of Wound Rotor Synchronous Machines considering Harmonics, Geometric Saliencies and Saturation induced Saliencies,” International Power Electronics Conference (IPEC) 2014, in press. A. Rambetius, S. Luthardt and B. Piepenbreier, “Speed Estimation and Compensation for Harmonics in Sensorless Wound Rotor Synchronous Machines,” 5th Symposium on Sensorless Control for Electrical Drives 2014 (SLED 2014), 2014, in press. D. Uzel, V. Łmdl and Z. Peroutka, ”Resolver Motivated Sensorless Rotor Position Estimation of Wound Rotor Synchronous Motors with Kalman Filter”, in Conf. ICMTMA.vol.3, no., pp.195-198, Jan.2011. D. Uzel, and Z. Peroutka, "Resolver motivated sensorless rotor position estimation of wound rotor synchronous motors," 2013 IEEE International Symposium on Industrial Electronics (ISIE), pp.1–6, 2013 A. Griffo, D. Drury, T. Sawata, and P. H. Mellor, “Sensorless starting of a wound-field synchronous starter/generator for aerospace applications,” IEEE Transactions on Industrial Electronics, vol. 59, no. 9, pp. 3579– 3587, 2012. Y. Kato and S. Nishikata, “Studies on a sensorless starting method for self-controlled synchronous motors without,” in International Conference on Electrical Machines and Systems, 2009. ICEMS 2009., 2009, pp. 1–5. C. Hasegawa and S. Nishikata, “A sensorless rotor position detecting method for self-controlled synchronous motors,” in International Conference on Electrical Machines and Systems, 2008. ICEMS 2008., 2008, pp. 1017–1021. A. Rambetius, S. Ebersberger, M. Seilmeier, and B. Piepenbreier, "Carrier signal based sensorless control of electrically excited synchronous machines at standstill and low speed using the rotor winding as a receiver," 15th European Conference on Power Electronics and Applications (EPE), 2013, pp.1–10, 2-6 Sept. 2013 M. Seilmeier, “Modelling of electrically excited synchronous machine (EESM) considering nonlinear material characteristics and multiple saliencies,” in Proceedings of the 2011-14th European Conference on Power Electronics and Applications (EPE 2011), , 2011, pp. 1–10. Xianming Deng, Lei Wang, Jiamin Zhang, and Zhixun Ma, “Rotor Position Detection of Synchronous Motor Based on High-frequency Signal Injection into the Rotor,” in Third International Conference on Measuring Technology and Mechatronics Automation (ICMTMA), 2011, pp. 195–198. J. Choi, I. Jeong, S. Jung, and K. Nam, “Sensorless Control for Electrically Energized Synchronous Motor Based on Signal Injection to Field Winding,” 39th Annual Conference of the IEEE Industrial Electronics Society 2013 (IECON 2013), 2013. M. Ma rgner, and W. Hackmann, "Control challenges of an externally excited synchronous machine in an automotive traction drive application," Emobility - Electrical Power Train, 2010 , pp.1-6, 8-9 Nov. 2010 I. Boldea, G. D. Andreescu, C. Rossi, A. Pilati, and D. Casadei, “Active flux based motion-sensorless vector control of DC-excited synchronous machines,” in Energy Conversion Congress and Exposition, 2009. ECCE 2009. IEEE, 2009, pp. 2496–2503. J.F. Defenbaugh, M. Harke, A. Markunas, C. Romenesko and D. Saban, “North-south pole determination for carrier injection sensorless position sensing systems”, U.S. Patent 6,967,461 B1, Nov. 22, 2005 C. E. Anghel, R. Divito and N. A. Morcov, “Postion sensor emulator for a synchronous motor/generator”, U.S. Patent 6,809,496 B2, Oct. 26, 2004 1159
