Magnet Temperature Estimation in Surface PM Machines During Six-Step Operation

�David Reigosa, Fernando Briz, �Michael W. Degner, Pablo García, Juan Manuel Guerrero�

University of Oviedo. Dept. of Elect., Computer & System Engineering Gijón, 33204 Spain.

reigosa@isa.uniovi.es, fernando@isa.uniovi.es, pgarcia@isa.uniovi.es, guerrero@isa.uniovi.es

�Ford Motor Company Dearbon, MI 48121-2053, USA

mdegner@ford.com�

�Abstract: This paper presents a method for estimating the

magnet temperature in surface permanent magnet synchronous machines (SPMSM's) during six-step operation. Six-step operation allows the maximum available DC bus voltage to be applied to a machine, which maximizes its torque and speed range. Six-step operation produces currents harmonics that induces additional losses in the permanent magnets and can therefore increase their temperature. Increase of magnet temperature can result in a reduced torque capability and eventually in a risk of demagnetization if excessive values are reached, with real-time rotor magnet temperature monitoring being, therefore, advisable. Six-step operation provides opportunities for rotor temperature monitoring from the electrical terminal variables (voltages and currents) of the motor. To achieve this goal, the rotor high frequency resistance is measured using the harmonic voltages and currents due to six-step operation, from which the magnet temperature can be estimated.1

Index Terms— Permanent magnet synchronous machines, six-step, magnet temperature estimation.

I. Introduction In the last two decades, the design and control of

permanent magnet synchronous machines (PMSM's) has been the focus of significant research effort due to their ability to provide higher performance and higher efficiency when compared to other machine types [1-8]. Reducing the machine losses has consequently become a major focus from a design perspective [4, 9, 12]. The machine losses can be divided into stator and rotor losses. The stator losses can be further divided into copper losses, iron hysteresis losses and iron eddy current losses, while the rotor losses can be split into eddy current losses and hysteresis losses in both the iron and the permanent magnets [4, 9-14]. The stator losses are a result of the fundamental excitation, harmonics of the fundamental excitation, and the inverter switching ripple, while the rotor losses are a result of only the switching ripple and fundamental excitation harmonics that do not rotate

��������������������������������������������������������1 �

This work was supported in part by the Research, Technological Development and Innovation Programs of the Spanish Ministry of Science and Innovation-ERDF under grant MICINN-10-ENE2010-14941 and the Ministry of Science and Innovation under grant MICINN-10-CSD2009-00046.

synchronously with the rotor [4, 9-14]. Saying this in another way, the stator losses are the results of all components of the excitation [10, 12, 14], while rotor losses are only caused flux harmonics that do not rotate synchronously with the rotor or change in amplitude [3, 4, 10, 11, 13, 14].

The temperature increase caused by these losses in both the stator and rotor [4, 9, 10] can have several adverse effects. An excessive increase of the stator winding temperature can degrade the winding insulation. Increases of the magnet temperature can result in a reduction of magnet strength, either transiently or permanently, which translates into a reduced torque production capability of the machine [14-16, 32]. Therefore, having accurate measurement or estimates of the magnet temperature is highly desirable in many applications. Although direct measurement of magnet temperature is possible, it is not practical in most applications for the following reasons. Contact type temperature sensors, e.g., thermistors, transmit the measurement signal electrically, which makes them difficult to use on the rotor without some sort of slip ring or telemetry device to transmit the measurement from the rotor to the stationary frame [10]. Non-contact sensors, e.g., infrared, can be used directly to measure the rotor temperature at a distance but are more expensive, less accurate and difficult to package, especially in production applications. In addition, measurement of the magnet temperature requires that the magnets be visible, which is impractical in many applications.

An alternative to the measurement of the magnet temperature is to estimate it from other quantities that are normally available in electric machine drives like the stator currents, stator voltages and rotor speed. The methods to estimate the magnet temperature can be divided into thermal models [17-19] and methods based on the injection of a high frequency signal [10]. Methods of the first type, model the heat transfer characteristic of the machine. Since this depends on the geometry and cooling system, these methods normally require the development of a thermal model for each machine design and application. The second type of method estimate the magnet temperature from the variation of the equivalent high frequency rotor resistance, which can be obtained from the estimated high frequency impedance of

978-1-4577-0541-0/11/$26.00 ©2011 IEEE 2429

the machine [10]. These methods require the prior knowledge of the high frequency impedance of the machine at the room temperature. However, they do not require the knowledge of the machine design or cooling system.

Measurement of the high frequency impedance is most easily achieved through the injection of some form of high frequency excitation (either current or voltage), with the resulting voltage or current then being used to estimate the impedance. Further more, for the method to work on-line, this signal needs to be superimposed on the fundamental excitation. The injection of a high frequency, small magnitude, carrier signal voltage, which was superimposed on the fundamental voltage, for temperature estimation purposes was proposed in [10, 34]. The injection of a high frequency signal requires a slight modification of the modulation pattern and sufficient voltage margin between the fundamental component of the applied voltage and the voltage limit of the inverter feeding the machine in order for the carrier signal to be generated. This margin may not be available under certain working conditions. For example, when the machine operates at high speeds at or near the overmodulation region the available voltage margin will be significantly reduced. However, overmodulation, and more specifically six-step operation, produces fundamental excitation harmonics [28-31], which can be used for temperature estimation purposes.

Magnet temperature estimation in SPMSM's working in six-step operation is in the focus of this paper. Six-step operation, as well as the analytical formulation of temperature estimation using a high frequency signal, is presented first, with implementation issues being discussed later. Experimental results are provided to demonstrate the viability of the proposed method.

II. Rotor temperature estimation using the high frequency resistance

This section briefly discusses the principles of rotor temperature estimation from the high frequency impedance. More detailed discussion can be found in [10].

The electromagnetic behavior of a PMSM depends on its temperature. Changes of the rotor temperature will cause the flux density of the permanent magnets to vary (1) [10, 27]. Similarly, changes in both the stator and rotor temperature will cause their resistances to change according to (2) [10, 27].

(1)

(2)

When there is voltage excitation, (3), present in a machine at frequencies sufficiently higher than the fundamental excitation, the resulting currents, (4), can be calculated using the machine's high frequency impedance.

(3)

vdqscs = Zdqscidqsc

s (4)

where is the magnitude of the high frequency voltage vector, is its frequency and Zdqsc is the high frequency impedance of the machine [10].

Substituting the temperature dependent terms in (1)-(2) into (3)-(4), the resulting high frequency current can be obtained (5)-(6), with the temperature dependence explicitly shown.

idqscs Ts ,Tr( ) = Vc

R2 Ts ,Tr( ) + (ω c )2 L2 Tr( )

*ej (ωct−ϕ

Zdqsc(Ts ,Tr ))

(5)

ϕZdqsc

Ts ,Tr( ) = a tan(ω c )

2 L2 Tr( )R2 Ts ,Tr( )

⎛

⎝⎜⎞

⎠⎟ (6)

where is the high frequency resistance, is the high frequency inductance and and are the stator and rotor temperatures, respectively.

The high frequency impedance (7) can be obtained from (4) and (5), with its resistive component being (8). The magnet temperature, which can be obtained from (8) using (2), is given by (9)

Zdqsc (Ts ,Tr ) = R(Ts ,Tr ) + jω cL(Tr ) =vdqscs

idqscs (7)

R(Ts ,Tr ) = Z(Ts ,Tr ) cos ϕZdqsc(Ts ,Tr )( ) =

= Rs (T0 ) 1+ α cu (T0 − Ts )[ ] + Rr (T0 ) 1+ αmag (T0 − Tr )⎡⎣ ⎤⎦ (8)

(9)

where is the copper thermal resistivity coefficient, is the permanent magnet thermal resistivity coefficient and Rs and Rr are the stator and rotor high frequency resistances [10, 27], respectively.

III. High frequency impedance measurement in six-step operation

The highest possible fundamental voltage from a three-phase inverter, (see Fig. 1), is obtained during six-step operation, with the modulation index being defined as m=1 for this case (see Fig. 2) [30]. Fig. 3 shows the phase voltages (va, vb and vc) applied to the machine during six-step operation and the resulting voltage complex vector (vd and vq), with the transformation of a generic three-phase

2430

quantity (voltage or current) f to a dq quantity being defined as (10).

Fig. 1 Simplified representation of the controller for a PMSM.

�Fig. 2 Voltage space vectors and limits of linear modulation, non-linear modulation, and six-step operation

The injected voltage complex vector shown in Fig. 3 can be expressed using a Fourier series as (11).

(10)

(11)

where when n<0, when n>0, is the fundamental excitation frequency and is defined by (12).

(12)

where is the maximum value of the phase voltage (See Fig. 3). The resulting frequency spectrum of the voltage complex vector in six-step operation is shown in Fig. 4.

Six-step operation creates harmonics having the following orders: −5, 7, −11, 13, …, (11), with the harmonic magnitudes being inversely proportional to the harmonic order, (12), Fig. 4. These voltage harmonics can be modeled as shown in (13), where n is the harmonic order, is the harmonic voltage space vector, and is the amplitude of the “nth” harmonic. Each harmonic present in the voltage will produce a corresponding harmonic in the current, . The magnitude of these current harmonics due to six-step

can be calculated using a simplified high frequency model (14) of the electric machine, where Zdqsn is the high frequency impedance of the machine at the frequency of

.

Fig. 3 Voltage waveforms during six-step operation.

�Fig. 4 Voltage complex vector spectrum under six-step operation.

Fig. 5 a) magnitude, and b) phase of the high frequency impedance as a function of frequency.

(13)

vdqsns = Zdqsnidqsn

s (14)

Although it could be concluded from (7)-(9) and (13)-(14) that any harmonic present in the applied voltage due to six-step operation could be used for measurement of the high frequency resistance, this is not true in practice due to implementation issues. As the harmonic order increases, the magnitude of the corresponding voltage harmonic being decreases, which combined with the high frequency impedance increase due to its inductive nature, result in a significant reduction of the resulting harmonic current, and consequently in a reduction the signal–to-noise ratio. Furthermore, the relative ratio of the resistive term to the

a)

b)

2431

inductive terms in the high frequency impedance decreases as the frequency increases, Fig. 5, further complicating the measurement of the high frequency resistance. It can be concluded from this, that using lower order harmonics would be preferred. It should be noted however that lower-order harmonics are closer to the fundamental component and may not have sufficient spectral separation, increasing the risk of spectral interference and making the signal processing more difficult. The selection of the harmonic used for resistance estimation is discussed further in the next section.

IV. Implementation This section discusses the implementation of the

proposed temperature estimation method for a surface PMSM. The test machine's parameters are shown in Table I. The test machine has a magnet pole arc of 150 electrical degrees, Fig. 6.

�

Fig. 6 Photographs of the test machine.

The schematic representation of the signal processing used for magnet temperature estimation is shown in Fig. 7. The high frequency impedance, (7), is estimated from the selected harmonic voltage, (13), and the measured resulting harmonic current, (14), which are obtained from the measured current complex vector ( ) and from the commanded voltage complex vector ( vdqs

s* ) by a filtering process. The magnet temperature is estimated continuously whenever the machine is operated in six-step from the estimated high frequency impedance using (8) and (9). It should be noted that the stator temperature and the stator high frequency resistance at the room temperature are needed to decouple the stator resistance contribution to the overall high frequency impedance, (9). The stator resistance at the room temperature can be easily measured and stored for use during operation of the algorithm using a wide variety of temperature devices. For this paper a PTC thermistor was used. To evaluate the performance of the proposed method, the magnet temperature was also measured during machine operation using an infrared, non-contract-type thermometer. A window was drilled in the cover of the machine, Fig. 8a, to place the thermometer, Fig. 8b. The infrared thermometer covers a temperature range from 40-1030ºC, with a resolution of 0.1ºC, an accuracy of ±1.5ºC, an optical resolution of 15:1, a spectral range of 8 to

14 μm, and a minimum spot of 8 mm @ 10 mm. It should be noted that the magnet width is10 mm.

Table I PRated [kW] VRated [V] IRated [A] ωr [rpm] Poles 8.6 300 18.5 1000 8

V. Experimental results Experimental results showing the viability of the

proposed method are presented in this section. Although six-step operation is normally used at high-speeds to maximize output voltage capabilities of a voltage source inverter (VSI) with a fixed DC-bus voltage [28-31], there could be applications where the DC-bus voltage is not fixed and the six-step operation is not restricted to high-speed operation. An example of such applications are electric vehicles (EV’s) where the DC-bus voltage of the inverter is either directly equal to the battery voltage, which varies with current and state-of-charge, or set by a boost converter from the battery voltage, with the boost converter output voltage varying depending on the operating point of the system [33]. In cases like these, the machine can work in six-step at rotor speeds significantly below rated speed. To show the feasibility of the proposed method for such applications, experimental results at various speeds and DC-bus voltages are included in this section.

The machine's operating points for the experimental results are shown in Table II. It can be seen that they cover a wide range of rotor speeds and DC-bus voltages. In all the cases the machine was operated in six-step. The results presented in this section used both the −5th and the 7th harmonic for the magnet temperature estimation as a comparison. The corresponding frequencies and magnitudes of these harmonics for each operating condition are shown in Table II.

Table II

-5th harmonic 7th harmonic Exp. Vbus (V)

Wr (rpm) Mag. f(Hz) Mag. f(Hz)

#1 50 150 12.73 -50 9.08 70

#2 103 307 26.22 -103 18.70 143

#3 143 430 36.48 -143 26.03 200

#4 200 600 50.92 -200 36.34 280

#5 300 900 76.38 -300 54.51 420

Figs. 9a and 10a show the phase-to-neutral voltages and the measured phase currents under six-step operation while Figs. 9b and 10b show the frequency spectrum of both signals versus harmonic order for Exp.#1 in Table II.

Figs. 11-15 shows the experimental results of the temperature estimation method, the measured rotor

2432

temperature and the temperature error versus the stator temperature, using the −5th and 7th harmonics.

�Fig. 7 Block diagram for the magnet temperature estimation under six-step operation.

It can be noted from Fig. 11 (low-speed) and Figs. 12-14 (medium-speed) that the accuracy of the temperature estimation with the −5th harmonic is slightly better compared with the 7th harmonic. As already mentioned, this can be explained by the fact that the magnitude of the injected harmonic voltage decreases inversely proportional to the harmonic order, Fig. 9 and (12), and the resulting harmonic current magnitude decreases even faster, Fig. 10. This translates into a reduced signal to noise ratio when the 7th harmonic is used, which is further compounded by the reduced sensitivity to the resistance as the frequency increases, as can be observed form Fig. 5, i.e., the impedance becomes more inductive in nature.

� Fig. 8 a) Detail of the drill in the cover of the machine, and b) infraredthermometer.

For high-speed operation, Fig. 15, the estimation with the -5th harmonic is significantly better compared to the 7th harmonic. This can be explained by the increased significance of the factors mentioned above for the low speed and medium speed cases.

It can also be observed from Figs. 12 and 13 that the results for Exp.#3, using the -5th harmonic, and the experimental results for Exp.#2, using the 7th harmonic, are almost identical. Under these conditions the frequency of the two harmonics is the same (see Table II), which confirms that the primary difference between the use of the two harmonics is primarily due to the reduced sensitivity to resistance and decreased signal-to-noise ratio as frequency increases. The same behavior can be observed comparing Exp.#3, using the 7th harmonic, and Exp.#4, using -5th

harmonic, Figs. 13 and 14, although the accuracy of the estimation using the -5th harmonic is always slightly better.

�Fig. 9 a) measured phase-to-neutral voltages under six-step operation, and b) spectrum. DC bus voltage=55V, ωr=150rpm.

�

�Fig. 10 a) measured phase currents under six-step operation and b) spectrum. DC bus voltage=55V, ωr=150rpm.

Although not presented in this paper, the use of the -11th harmonic was found to be unviable for temperature estimation purpose at any speed due to its reduced magnitude.

Table III shows the average magnet temperature error when using the -5th and 7th harmonics, form 50 to 85ºC. It can be observed from Table III and also from Figs. 11-15 that the accuracy of the estimated temperature, decreases as the speed increases. This can be seen from the slight increase of the temperature error from Exp.#1 to #4 (See Table III and Figs. 11 to 14) that becomes more obvious when the speed increases as shown in Exp.#5 (Table III and Fig. 15), which might by caused by the frequency increase of the additional harmonics and the reduction of the relative value of the high frequency resistance effect over the high frequency impedance as the speed does.

a)

b)

a)

b)

a) b)

2433

�

�Fig. 11. Exp#1. a) Measured magnet temperature (o), estimated magnet temperature using -5th harmonic (◻) and estimated magnet temperature using 7th harmonic (▷). b) Magnet temperature estimate error using the -5th harmonic (◻) and using the 7th harmonic (▷) to estimate the magnet temperature.

�

�Fig. 12. Exp#2. a) Measured magnet temperature (o), estimated magnet temperature using -5th harmonic (◻) and estimated magnet temperature using 7th harmonic (▷). b) Magnet temperature estimate error using the -5th harmonic (◻) and using the 7th harmonic (▷) to estimate the magnet temperature.

�

�Fig. 13. Exp#3. a) Measured magnet temperature (o), estimated magnet temperature using -5th harmonic (◻) and estimated magnet temperature using 7th harmonic (▷). b) Magnet temperature estimate error using the -5th harmonic (◻) and using the 7th harmonic (▷) to estimate the magnet temperature.

�

�Fig. 14. Exp#4. a) Measured magnet temperature (o), estimated magnet temperature using -5th harmonic (◻) and estimated magnet temperature using 7th harmonic (▷). b) Magnet temperature estimate error using the -5th harmonic (◻) and using the 7th harmonic (▷) to estimate the magnet temperature.

a)

b)

a)

b)

a)

b)

a)

b)

2434

�

�Fig. 15. Exp#5. a) Measured magnet temperature (o), estimated magnet temperature using -5th harmonic (◻) and estimated magnet temperature using 7th harmonic (▷). b) Magnet temperature estimate error using the -5th harmonic (◻) and using the 7th harmonic (▷) to estimate the magnet temperature.

Table III

Exp. Harmonic #1 #2 #3 #4 #5

-5th 2.2ºC 3.28ºC 3.3ºC 3.86ºC 4.6ºC 7th 2.8ºC 3.36ºC 3.42ºC 4.36ºC 10.6ºC

Finally, Table IV shows the difference in temperature between the final measured temperature (See Fig. 11-15) and the room temperature, for the experiments shown in Table II. It can be observed that the differential temperature between the stator and rotor is higher as the speed increases. This can by explained by the fact that the core losses in the machine, increase as the speed increases. Additionally, the increase of the impedance value, Fig. 5, does not match the increase of the DC-bus voltage, Table II, as the speed increases and, as a consequence, the induced harmonic currents (-5th, 7th, -11th …) increase in value (12), which increases the induced losses and the final temperature.

It should be noted, from Table IV and Fig. 11, that the minimum temperature difference (low-speed condition) between the stator and rotor is ≈20 ºC, which is ≈5 ºC higher that the temperature difference obtained for the case of linear operation (sinusoidal excitation) in [10]. This can be explained by the fact that in six-step operation, there are additional harmonics that do not rotate synchronously with

the rotor, which producing additional losses in both the stator and rotor [14].

Table IV Exp. Temp.

#1 #2 #3 #4 #5 ºC 19.8 21.5 23.3 25.3 29.6

VI. Conclusions Magnet temperature estimation is a concern for the

control and protection of PMSM. A method to estimate the magnet temperature in SPMSM's operated in six-step operation from the measured currents has been presented. The method uses the harmonic voltages and currents inherent to this type of excitation to estimate the rotor high frequency resistance, from which the temperature is estimated. Experimental results have been provided to support the viability of the method. It has been shown that the temperature estimation using the -5th harmonic is slightly better at low/medium-speed conditions compared with the 7th harmonic and that the estimation at high-speed condition is better when the -5th harmonic is used.

VII. Acknowledgments The authors would like to acknowledge the motivation and

support provided by the University of Oviedo and Ford Motor Company.

VIII. References. [1] N. Limsuwan, Y. Shibukawa, D. Reigosa, M. Leetmaa and R.D.

Lorenz, “Novel Design of Flux-Intensifying Interior Permanent Magnet Synchronous Machine Suitable for Power Conversion and Self-Sensing Control at Very Low Speed”. IEEE-ECCE’10, pp.555 – 562, Sep. 2010.

[2] D. Reigosa, K. Akatsu, N. Limsuwan, Y. Shibukawa and R.D. Lorenz, “Self-sensing Comparinson of Fractional Slot Pitch Winding Versus Distributed Winding for FW- and FI-IPMSMs based on Carrier Signal Injection at Very Low Speed”. IEEE Trans. on Ind. Appl., 46(6):2467–2474, Nov.-Dec. 2010.

[3] H. Toda, Z. Xia, K. Atallah and D. Howe, “Rotor eddy-current loss in permanent magnet brushless machines”. IEEE Trans. on Mag., 40(4):2104–2106, Jul. 2004.

[4] K. Atallah, D. Howe and D. Stone, “Rotor loss in permanent-magnet brushless AC machines”. IEEE Trans. on Ind. Appl., 36(6):1612–1618, Nov.-Dec. 2000.

[5] K. Akatsu and S. Wakui, "Torque and Power Density Comparison between Fractional-slot Concentrated Winding SPMSMs", Intl. Conf. on Elect. Machines & Systems,, CD-ROM, Nov. 2006, Nagasaki.

[6] K. Akatsu, K. Narita, Y. Sakashita and T. Yamada, "Characteristics Comparison between SPMSM and IPMSM Based on both Analytical and Experimental Results", Intl. Conf. on Elect. Machines & Systems, CD-ROM, Oct. 2008, Wuhan, China.

[7] S. Wu, D. Reigosa, Y, Shibukawa, M.A. Leetmaa, R.D. Lorenz and Y. Li, "IPM Synchronous Motor Design for Improving Self-sensing Performance at Very Low Speed", IEEE Trans. on Ind. Appl., 45(6):1939–1946, Nov.-Dec. 2009.

[8] N. Bianchi and S. Bolognami, “Influence of Rotor Geometry of an Interior PM Motor on Sensorless Control Feasibility”, IEEE Trans. on Ind. Appl., 43(1):87–96, Jan.-Feb. 2007.

a)

b)

2435

[9] J. F. Gieras and M. Wing, “Permanent Magnet Motor Technology”. Second edition 2002.

[10] D. Reigosa, F. Briz, P. García, J. M. Guerrero and M. W. Degner, “Magnet Temperature Estimation in Surface PM Machines Using High frequency signal Injection”. IEEE Trans. on Ind. Appl., 46(4):1468–1475, July-Aug. 2010.

[11] Seok-Hee Han, T.M. Jahns and Z.Q. Zhu, “Analysis of rotor core Eddy-Current losses in interior permanent magnet synchronous machines”. IEEE IAS Ann. Meeting, CD–ROM, Oct. 2008.

[12] D. Ionel, M. Popescu, C Cossar, M.I. McGilp, A. Boglietti and A. Cavagnino, “A General Model of the Laminated Steel Losses in Electric Motors with PWM Voltage Supply”. IEEE Industry Applications Society Annual Meeting IAS’2008 , CD–ROM, Oct. 2008.

[13] M. R. Shah and S. B. Lee, “Rapid Analytical Optimization of Eddy-current Shield Thickness for Associated Loss Minimization in Electrical Machines”. IEEE Trans. on Ind. Appl., 42(3):642–649, May-June 2006.

[14] D. Reigosa, F. Briz, M. W. Degner, P. García and J. M. Guerrero, “Temperature Issues in Saliency-Tracking Based Sensorless Methods for PM Synchronous Machines”. IEEE-ECCE’10, pp.3123 – 3130, Sep. 2010.

[15] T. Sebastian, “Temperature Effects on Torque Production and Efficiency of PM Motors Using NdFeB Magnets” IEEE Trans. Ind. Appl., pp. 353–357, Apr 1995.

[16] Y. S. Kim, S. K. Sul, “Torque Control Strategy of an IPMSM Considering the Flux Variation of the Permanent Magnet” IEEE-IAS’07, pp.1301 – 1307, Sep. 2007.

[17] Z. J. Liu, K. J. Binns, T. S. Low, “Analysis of Eddy current and thermal problems in permanent magnet machines with radial-field topologies”. IEEE Trans. on Mag., 31(3):1912–1915, May. 1995.

[18] N. Bianchi and T. M. Jahns "Design, Analysis, and Control of Interior PM Synchronous Machines," Tutorial Course Notes, IEEE-IAS’04, Oct. 2004.

[19] Z. J. Liu, D. Howe, P. H. Mellor and M. K. Jenkins "Thermal Analysis of Permanent Magnet Machines," IEEE-IEMDC, pp.359-364, Sep. 1993.

[20] J.-I. Ha, K. Ide, T. Sawa, and S.-K. Sul, “Sensorless rotor position estimation of an interior permanent-magnet motor from initial states,” IEEE Trans. Ind. Appl., vol. 39, pp. 761-767, May-June 2003.

[21] A. Consoli, G. Scarcella, and A. Testa, “Industry application of zero-speed sensorless control techniques for PM synchronous motors,” IEEE Trans. Ind. Appl., vol. 37, pp. 513 – 521, March-April 2001.

[22] P.L. Jansen and R.D. Lorenz, “Transducerless position and velocity estimation in induction and salient AC machines,” IEEE Trans. Ind. Appl., Mar./Apr. 1995, Vol. 31, pp. 240–247.

[23] Yu-seok Jeong, R.D. Lorenz, T.M. Jahns, and Seung-Ki Sul, “Initial rotor position estimation of an interior permanent-magnet synchronous machine using carrier-frequency injection methods” IEEE Trans. Ind. Appl., 41(1): 38–45 , Jan.-Feb. 2005.

[24] P. García, F. Briz, M.W. Degner†, D. Díaz-Reigosa, “Accuracy and Bandwidth Limits of Carrier Signal Injection-Based Sensorless Control Methods”, IEEE Trans. on Ind. Appl., 43(4):990–1000, July-Aug. 2007.

[25] D. Reigosa, P. García, D. Raca, F. Briz, and R.D. Lorenz, “Measurement and Adaptive Decoupling of Cross-Saturation Effects and Secondary Saliencies in Sensorless-Controlled IPM Synchronous Machines,” IEEE Trans. on Ind. Appl., 44(6):1758–1767, Nov.-Dec. 2008.

[26] D. Raca, P. García, D. Reigosa, F. Briz, and R.D. Lorenz, “Carrier Signal Selection for Sensorless Control of PM Synchronous Machines at Very Low and Zero Speeds,” IEEE Trans. on Ind. Appl., 46(1):167–178, Jan.-Feb. 2010.

[27] D. Reigosa, P. García, F. Briz, D. Raca and R.D. Lorenz, “Modeling and adaptive decoupling of high-frequency resistance and temperature effects in carrier-based sensorless control of PM synchronous machines”. IEEE Trans. on Ind. Appl., 46(1):139–149, Jan.-Feb. 2010.

[28] X. Xu and G. Hirzinger, “Design of Current Control of Fully Integrated Surface-mounted Permanent Magnet Synchronous Motor Drive Servo Actuator ”. IEEE EPE’05, CD-ROM, 2005.

[29] S. Morimoto, Y. Inoue, T.F. Weng and M. Sananda, “Position Sensorless PMSM Drive System Including Square-wave Operation at High-speed ”. IEEE IAS’07, pp. 676-682, 2007.

[30] T.S. Kwon, G.Y. Choi, M.S. Kwak and S.K.Sul, “Novel Flux-Weakening Control of an IPMSM for Quasi-Six-Step Operation” . IEEE Trans. on Ind. Appl., 44(6):1722–1731, Nov.-Dec. 2008.

[31] J.I. Itoh and T. Ogura, “Evaluation of Total Loss for an Inverter and Motor by Applying Modulation Strategies”, IEEE EPE’10, CD-ROM, 2010.

[32] S Ruoho, J. Kolehmainen, J. Ikaheimo and A. Arkkio, “Iterdependence of Demagnetization, Loading, and Temperature Rise in a Permanent-Magnet Synchronous Motor” . IEEE Trans. on Mag., 46(3):949–953, Mar. 2010.

[33] M Becherif and M. Y. Ayad, “Advantages of Variable Dc Bus Voltage for Hybrid Electrical Vehicle” . IEEE VPPC’10, CD-ROM, 2010.

[34] Fernando Briz, Michael W. Degner, Juan M. Guerrero, Alberto B. Diez, “Temperature Estimation in Inverter Fed Machines Using High Frequency Carrier Signal Injection”, IEEE Transactions on Industry Applications, vol.: 44, nº 3, pp. 799-808, May. 2008.

2436