PMSM Magnetization State Estimation Based on Stator ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 51, NO. 5, SEPTEMBER/OCTOBER 2015

PMSM Magnetization State Estimation Based on Stator-Reflected PM Resistance Using High-Frequency Signal Injection David Díaz Reigosa, Member, IEEE, Daniel Fernandez, Zi-Qiang Zhu, Fellow, IEEE, and Fernando Briz, Senior Member, IEEE

Abstract—Permanent-magnet (PM) magnetization state estimation in PM synchronous machines (PMSMs) is of great importance for torque control and monitoring purposes. The magnetization state of a PMSM can change due to several reasons, injection of stator current (d-axis or q-axis) and variation of magnet temperature being the primary reasons. PM magnetization state estimation is not easy once the machine is assembled. Methods based on the back electromotive force can be used, but they require that the machine is rotating. This paper analyzes the use of high-frequency signal injection for PM magnetization state estimation in PMSMs. The magnetization state of the PMs in PMSMs affects the stator-reflected PM high-frequency resistance. The stator-reflected PM high-frequency resistance can be estimated by injecting a high-frequency voltage/current using the inverter. The high-frequency signal is superposed on the fundamental excitation used to produce torque, meaning that the method can operate at any speed, including zero speed, and without interfering with the normal operation of the machine. Index Terms—High-frequency signal injection, permanentmagnet (PM) magnetization state estimation, permanent-magnet synchronous machines (PMSM).

I. I NTRODUCTION

P

ERMANENT-MAGNET synchronous motors (PMSMs) have received increasing attention for the last three decades due to their high power density, high efficiency, and excellent dynamics. Due to the increased machine performance requirements in several applications (e.g., electric and hybrid electric vehicles, wind turbine generators, railway applications,

Manuscript received September 26, 2014; revised December 15, 2014, February 10, 2015, and April 14, 2015; accepted May 20, 2015. Date of publication June 1, 2015; date of current version September 16, 2015. Paper 2014-EMC-0663.R3, presented at the 2014 IEEE Energy Conversion Congress and Exposition, Pittsburgh, PA, USA, September 20–24, and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLICATIONS by the Electric Machines Committee of the IEEE Industry Applications Society. This work was supported in part by the Regional Ministry of Education Culture and Sport of the Principality of Asturias through the “Severo Ochoa Program” under Grant BP-13067. D. Díaz Reigosa, D. Fernandez, and F. Briz are with the Department of Electrical, Electronic, Computers and Systems Engineering, University of Oviedo, 33204 Gijón, Spain (e-mail: [email protected]; fernandezalodaniel@ uniovi.es; [email protected]). Z.-Q. Zhu is with the Department of Electronic and Electrical Engineering, The University of Sheffield, Sheffield, S1 3JD, U.K. (e-mail: z.q.zhu@sheffield. ac.uk). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2015.2437975

and more electric aircraft), design of PMSMs with higher efficiency and torque/power density has become a major research topic [1]–[9]. The performance of PMSMs is directly related to the magnetization state of the machine, i.e., PM strength. PMs using rare earths, e.g., neodymium–iron–boron (NdFeB), have been extensively studied during the last 30 years, [1]–[3], [5], [12]–[15]. Knowledge of the PM state in electric drives using different types of PMSMs is needed for torque control and monitoring purposes. While in many cases, a rough estimation of the magnetization state is enough (e.g., applications using conventional surface PMSMs (SPMSMs) and interior PMSMs (IPMSMs) and with moderate requirements in the estimated torque accuracy), there are applications where a precise estimation of the magnetization state is needed [16], [26]–[28]. Particularly critical are PMSMs where the PMs can be magnetized/ demagnetized during normal operation, e.g., variable flux machines (VFMs) [8], [9]. The magnetization state of a PMSM can change due to several reasons, with the injection of d-axis or q-axis current and changes in the magnet temperature being the most likely. The PM magnetization state variation by the injection of a d-axis current is frequently used to reduce the magnet flux and allow constant power operation above base speed [10], [11] in conventional IPMSMs and SPMSMs, to achieve maximum torque per ampere or other optimization strategies with IPMSM, as well as to magnetize/demagnetize the PMs in VFM [8], [9], [32]–[34]. Q-axis current can also make the magnetization state to change due to the cross-coupling that typically exists between d-axis and q-axis [6], [12]. On the other hand, it is well known that the PM remanent flux decreases as the temperature increases [13], [14]. This typically occurs in practice due the heat produced by the stator and rotor losses [13]–[15], with potential PM irreversible demagnetization if the temperature becomes too high [13], [14]. Knowledge of the PM magnetization state in classical PMSMs is therefore important for torque control and for monitoring purposes [13], [14], [25]. Magnet flux distribution measurement in PM machines is not trivial once the machine is assembled. Magnet remanent flux can be measured by inserting a magnetometer in the air gap. However, the end frame needs to be removed and can only be used with SPMSMs as the magnetometer has to be placed on the magnet surface. On the contrary, for the case of IPMSMs, the flux measured on the rotor surface does not account for

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DÍAZ REIGOSA et al.: PMSM MAGNETIZATION STATE ESTIMATION BASED ON STATOR-REFLECTED PM RESISTANCE

the actual PM flux due to the leakage flux. In either case, this method cannot be applied during the normal operation of the machine. To overcome the aforementioned limitations, estimation methods using measureable stator electrical variables have been proposed [8], [16], [29], [30]. Back electromotive force (back EMF) methods are particularly easy to implement, being therefore very popular [8], [16], [29],[30]. Obtaining the PM flux linkage from the stator terminals when Id = Iq = 0 is relatively simple. However, obtaining the PM flux linkage when Id = 0 and Iq = 0 or Id = 0 and Iq = 0 is not possible without previous knowledge of some machine parameters (e.g., d-axis and q-axis inductance maps, resistance, etc.). Injecting an additional signal [16], [30], measuring or estimating the machine parameters [28], or setting the machine parameters to their nominal values [31] has been proposed to overcome this problem. Using nominal values has low accuracy due to their variation with load and temperature. Measuring/ estimating machine parameters is therefore preferred. It is finally noted that back EMF methods require the machine to be rotating. Magnet flux variation can also be estimated from the variation of the electrical properties of the PM with its magnetization state. An example of this is the magnetoresistance, which is the change of a material electrical resistance when an external field is applied [17]–[20]. Although the magnetoresistance effect on NdFeB magnet materials has already been studied for other applications [19], [20], to the best of authors’ knowledge, its use for magnetization state estimation in PMSMs has not been proposed yet. In this paper, the use of the stator-reflected PM highfrequency resistance variation to estimate the magnetization state of the rotor PMs is analyzed. The proposed method measures the stator-reflected PM high-frequency resistance, from which a lumped magnetization state estimation is obtained. A small-magnitude high-frequency voltage superimposed on the fundamental excitation is applied for this purpose. The resulting stator high frequency current will be shown to be dependent on the magnet high-frequency resistance, the PM magnetization state being estimated from the measured PM high-frequency resistance variation. Implementation of this method will require compensating the contribution of the stator resistance to the overall high-frequency impedance of the machine. The stator resistance can be measured or estimated using the measured stator windings temperature. Previous knowledge of other machine parameters (e.g., d-axis and q-axis inductance maps) is therefore not needed, which is advantageous compared with the back-EMF-based methods, which require such parameters. In addition, the proposed method can be used in the whole speed range of the machine, even at standstill. This paper is organized as follows. Physical principles of the high-frequency PM resistivity variation are presented in Section II. Estimation of the high-frequency PM resistance is presented in Section III. The experimental platform developed for the analysis and measurement of the magntoresistive effect is presented in Section IV. Finally, simulation and experimental results on both SPMSM and IPMSM are presented in Section V.

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II. M AGNETORESISTIVE E FFECT IN PM S It is well known that the resistivity of conducting materials changes with the temperature [13]–[15], [25], with modern rare-earth PMs such as NdFeB not being an exception [13], [14], [25]. The use of the connection between the magnet resistance and magnet temperature for magnet temperature estimation purposes in PMSMs has been previously reported in [13], [14], [25]. In these papers, a high-frequency signal superimposed on the fundamental excitation was used for this purpose. The magnet resistance variation with the temperature can be described by (1), where R(T ) is the resistance at a temperature T , R(T0 ) is the resistance at the room temperature T0 , and αmag is the PM thermal resistive coefficient, i.e., R(T ) = R(T0 ) (1 + αmag (T − T0 )) .

(1)

PM’s resistivity also changes with the magnetization state, e.g., when an external field is applied due to the injection of fundamental current in the stator windings. This effect is commonly known as magnetoresistance [19], [20]. Equation (1) can be modified to include the effect of the resistivity change due to the magnetization state variation, i.e., R(T,B) = R(T0 ,Br_ini ) (1 + αmag ΔT + βΔB) = R(T0 ,Br_ini ) (1 + αmag (T − T0 ) + β(B − Br_ini )) (2) where R(T0 ,Br_ini ) is the resistance at the room temperature T0 , Br_ini is the initial remanent PM flux, and β is the coefficient that links the PM flux variation and the resistance variation. The magnetic field created by the PMs is a function of the temperature, as shown in the following: (3) B(T ) = Br(T0 ) 1 + αB(T ) (T − T0 ) where B(T ) is the magnet flux at a temperature T , Br(T0 ) is the remanent PM flux at the room temperature, and αB is the magnet flux thermal coefficient. Typically, β and αB in (2) and (3) are negative. It is noted in this regard that the reduction of the magnetization state due to a temperature increase can be transitory or permanent [13]–[15]. When a high-frequency signal voltage is injected in the stator windings, the PM resistivity variation due to the magnetization state variation (either due to the injection of fundamental current or temperature variations) will affect to the eddy current induced in the magnets, eventually producing effects that are measurable from the stator windings. Finite-element analysis (FEA) will be used to evaluate the eddy-current distribution when the magnetization state of the machine changes. Fig. 1 shows the SPMSM design, and the parameters of the machine are shown in Table I. Fig. 2(a) shows a pole pitch in more detail, whereas Fig. 2(b) shows the XY Z coordinate system to be used to represent the eddy current in the PM. Fig. 3 shows the eddy-current density distribution within a PM obtained using FEA when a pulsating high-frequency voltage is injected, and Iq and Id are equal to zero. The relative position of the rotor with respect to the stator is shown in Fig. 2(a), with the location of the stator slots being indicated in Fig. 3. The eddy-current direction and density are indicated

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to the injection of the high-frequency voltage decrease as Id becomes more negative (higher flux weakening). A decrease in the eddy currents with the injected stator high-frequency voltage kept constant implies an increase in the high-frequency resistance seen from the stator, which can be used to estimate the magnetization state of the PM. The PM stator-reflected high-frequency resistance responds to the model shown in (2), which can therefore be used for PM magnetization state estimation. III. PM H IGH -F REQUENCY-R ESISTANCE E STIMATION

Fig. 1. SPMSM FE model. TABLE I M ACHINE PARAMETERS

The injection of a high-frequency signal in the stator terminals of a PMSM has been shown to be a viable option to estimate the magnet high-frequency impedance [13], [14]. The following high-frequency rotating voltage vector (4) or a sinusoidal pulsating (5) can be used for this purpose [13], [25]: Vhf cos(ωhf t) s (4) = Vhf ej(ωhf t) vdqhf = Vhf sin(ωhf t) V cos(ωhf t) r vdqhf = hf (5) 0

where ωhf is the frequency of the high-frequency signal, Vhf s is the magnitude of the high-frequency signal, vdqhf is the stator high-frequency-voltage complex vector in the stationary r is the stator highreference frame (see Fig. 5), and vdqhf frequency-voltage complex vector in the synchronous rotor reference frame (see Fig. 5). Other forms of high-frequency Fig. 2. Rotor position relative to the stator for all the (a) simulations and excitation such as a square wave [15] are also viable. (b) XY Z coordinated system. While all these forms of high-frequency excitation respond to the same physical principles and can potentially provide the same performance, some differences exist in their practical implementation. In SPMSM, the rotor magnets shield the rotor lamination [13]–[15], [25]. The injected high-frequency voltage will induce eddy current mainly in the PMs. Consequently, the variations in the measured stator high-frequency resistance will be dominated by the resistivity variation of the PMs, independently of the type of high-frequency signal injection. Rotating (4) and pulsating (5) high-frequency injection could therefore be used for this machine design [25]. On the contrary, for IPMSMs, both the rotor lamination and the PMs are affected by the high-frequency flux due to the high-frequency signal injection. The assumption that the estimated high-frequency resistance only depends on the PM high-frequency resistance does not hold in this case. The use of pulsating injection in Fig. 3. Eddy-current distribution in a PM. Pulsating high-frequency signal injection, Vhf = 0.05 p.u., 250 Hz. Iq = 0, Id = 0, ωr = 50 Hz. the d-axis is preferred in this case as it will be more sensitive to effects occurring in the PM. On the contrary, injection of a by the arrows and the color bar, respectively. The coordinate rotating signal will have the undesirable effect of increasing the reference system shown in Fig. 3 is as for Fig. 2(b). It is sensitivity to effects occurring in the rotor lamination [25]. Pulobserved in Fig. 3 that the highest value of the eddy-current sating high-frequency signal injection (5) is therefore preferred density due to the injected high-frequency signal is seen to and will be discussed following. occur in the region of the PM facing the stator slots (stator The model of a PM machine in the dq synchronous rotor slotting effect). reference frame (dq r , see Fig. 5) is given as follows: r r Fig. 4(a)–(d) shows the eddy-current density distribution, r vd id id 0 0 Rd Ld when Id varies from −15 A (−1 pu) to 0 A in steps of 5 A. = + p vqr 0 Rq irq 0 Lq irq The flux due to a negative Id current partially counteracts 0 −ωr Lq ird 0 the magnet flux (e.g., flux weakening). It is observed in + + (6) irq ωr L d 0 λpm ωr Fig. 4(a)–(d) that the eddy currents induced in the PM due


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Fig. 4. (a)–(d) Eddy-current density distribution in the PM when Id current changes from −15 to 0 A. Pulsating high-frequency signal injection, Vhf = 0.05 p.u., 250 Hz. Iq = 0, ωr = 50 Hz.

Fig. 5. abc and dq reference systems. dq s = stationary reference frame, dq r = synchronous rotor reference frame.

r where vdq is the stator voltage complex vector in the synchronous rotor reference frame, and irdq is the stator current complex vector in the synchronous rotor reference frame. If the stator of the machine is fed with a high-frequency voltage signal and assuming that the frequency of the highfrequency signal is significantly higher than the rotor speed (i.e., ωhf ωr ), the terms depending on the rotor speed in (6) can be safely neglected, with the following model being obtained: r r r vdhf idhf idhf 0 0 Rdhf Ldhf = +p (7) r vqhf 0 Rqhf irqhf 0 Lqhf irqhf r where vdqhf is the stator high-frequency-voltage complex vector in the synchronous rotor reference frame; irdqhf is the stator high-frequency-current complex vector in the synchronous rotor reference frame; Rdhf and Rqhf are the d-axis and q-axis high-frequency resistances, respectively; and Ldhf and Lqhf are the d-axis and q-axis high-frequency inductances, respectively. Due to the constant high-frequency excitation, the derivative operator p in (7) can be substituted by jωhf , with the following being obtained: r r vdhf idhf 0 Rdhf + jωhf Ldhf = . r vqhf 0 Rqhf + jωhf Lqhf irqhf (8)

The resulting stator high-frequency current in the synchronous rotor reference frame when the pulsating highfrequency voltage defined by (5) is applied to the stator terminals is given by r irdqhf =

vdhf Rdhf +jωhf Ldhf

0

.

(9)

Both (5) and (9) can be expressed as the sum of two complex vectors rotating in opposite directions, (10) and (11), respectively, whose amplitude is half of that of the original signal. The d-axis impedance (12)–(15) can be obtained from (10) and (11) using either the positive or the negative sequence components. The d-axis high-frequency resistance resulting from the combined effect of stator and rotor high-frequency resistances is obtained from (14). The rotor contribution to the stator d-axis high-frequency resistance is estimated using (15), where αcu is the copper thermal resistive coefficient, Rdrhf is the stator-reflected rotor d-axis high-frequency resistance, and Rdshf is the stator d-axis high-frequency resistance. It is seen from the following that knowledge of the stator high-frequency resistance at room temperature is required: Vhf j(ωhf t) Vhf j(−ωhf t) e e + 2 2 r r idqhf idqhf ej(ωhf t−ϕZd ) + ej(−ωhf t+ϕZd ) = 2 2

r = vdqhf

(10)

irdqhf

(11)

Vhf /2∗ ej(ωhf t) Zd = Rdhf + jωhf Ldhf = irdqhf /2∗ ej(ωhf t−ϕZd )

ϕZd

Vhf /2ej(−ωhf t) = irdqhf /2∗ ej(−ωhf t+ϕZd )

ωhf Ldhf = tan−1 Rdhf

Rdhf = Zd cos(ϕZd )

(12)

(13) (14)

Rdrhf = Rdhf −Rdshf = Rdhf −Rdshf(T0 ) (1+ αcu (Ts −T0 )) . (15) It is noted that, although the stator high-frequency resistance mainly depends on the stator winding resistance, it could be also influenced by eddy current and proximity effects occurring in the slot windings. However, the stator winding resistance at the room temperature can be easily estimated and stored in a previous commissioning process, and later accessed during machine operation, with its effects being therefore compensated. It is finally noted that the stator-reflected PM high-frequency resistance obtained from (15) is a lumped parameter, i.e., it does not contain information on the spatial distribution of the magnetization state. Fig. 6 shows the signal processing used to obtain the statorreflected rotor d-axis high-frequency resistance. Two bandpass

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Fig. 6. Signal processing for rotor high-frequency-resistance estimation using pulsating voltage injection.

filters (BPF1 and BPF2) are used to isolate the positive sequence component of the high-frequency voltage and current. The inputs to the estimation block are the commanded highr∗ , the measured high-frequency current frequency voltage vdqhf irdqhf , the stator temperature Ts , and the stator resistance at the room temperature Rhfs(T0 ) . The stator temperature can be measured using contact-type sensors [13], [14], [25]: thermocouples (e.g., PT-100) being commonly used for this purpose. PT-100 temperature sensors will be used for the experimental results presented in this paper. The proposed method has practically no effect on the motor performance. The high-frequency signal is injected on top of the fundamental excitation, with the torque production capability of the machine not being affected. A relatively simple filtering process effectively separates the high frequency and the fundamental signals, avoiding any interference with the current control or any other outer control loop [1], [3], [12]–[14], [25], [36], [37]. IV. E XPERIMENTAL V ERIFICATION OF M AGNETORESISTIVE E FFECT Experimental verification in PMSMs of the magnetoresistive effect described earlier is not trivial, due to the large number of design parameters and geometries that can affect to the results (stator teeth shape, number of stator slots, number of poles, rotor geometry, number of PMs layers, PMs shape and size, flux barriers, etc.) and that would therefore need to be considered. Building and testing of multiple motor designs were therefore disregarded due to cost and time issues. It is also noted that the magnetoresistive effect itself is a property of the magnet and does not depend therefore on the machine design. A. Experimental Setup In order to evaluate the magnetoresistance in the magnets that are used in commercial PMSMs, two experimental platforms with a simple geometry have been built; they are shown in Fig. 7. Both platforms consist of a magnetic core made of solid iron [see Fig. 7(a)] and iron powder [see Fig. 7(b)], respectively, and a coil. The iron powder core was constructed using Fe–Si alloy iron powder blocks (BK8320-26 and CK2020-26, μr = 26) [21]. The coil can be used to inject short high current pulses to magnetize/demagnetize the PMs and to inject the high-frequency voltage needed to measure the magnetoresistive effect.

Fig. 7. Experimental setup (a) with a solid iron core used for PMs magnetization and demagnetization and (b) using an iron powder core used to measure the PMs properties.

TABLE II C OMPARISON B ETWEEN S OLID I RON AND I RON P OWDER C ORES

The solid iron core is adequate for magnetization/ demagnetization of the PMs, due to its high relative permeability (typically in the range of several thousands, versus a few tens for the iron powder). In addition, the iron saturation magnetic flux density (≈1.6 T) is typically higher than that of the iron powder (1.1–1.6 T). However, the solid iron core is inadequate for high-frequency signal injection due to the large induced eddy currents, which produce excessive heating, placing practical problems to realize the experiments. In addition, the solid core shows a significant magnetoresistive effect, which interferes with the magnetoresistive effect due to the magnet. On the contrary, the iron powder core is inferior compared with the solid iron core for magnetization/demagnetization of the PMs, due to its lower relative permeability and its lower saturation magnetic flux density, but is superior for the evaluation of the PM magnetoresistance effect, due to its reduced eddy currents and magnetoresistive effect. Consequently, the solid iron core was used to magnetize/demagnetize the PMs, whereas the iron powder core was used to verify the magnetoresistive effect in the PMs. Details for both cores are summarized in Table II. To magnetize/demagnetize PMs, a short current pulse is applied to the excitation solid iron core coil shown in Fig. 7(a), which operates therefore as a pulse magnetizer [22], [23]. Fig. 8 shows the schematic representation of the circuit, where “L” is the excitation coil [see Fig. 7(a)]. The capacitor “C” is charged using an external voltage source, the voltage at which it is charged depending on the desired PM magnetization level.


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Fig. 8. Schematic representation of the circuit used for PM magnetization and demagnetization. TABLE III C OIL PARAMETERS

TABLE IV M AGNETIZATION C IRCUIT PARAMETERS

TABLE V S INGLE P HASE I NVERTER R ATED PARAMETERS

Fig. 9. (a) Capacitor voltage, (b) coil voltage, (c) coil current, and (d) diode current, during a magnetization process.

Once the capacitor is charged, switch “S” is opened, and the insulated-gate bipolar transistor (IGBT) is closed, the capacitor is discharged throughout the excitation coil “L”, inducing a short current pulse in the coil. The coil and magnetization circuit parameters are shown in Tables III and IV, respectively, while the single phase inverter rated parameters are shown in Table V. Fig. 9 shows the capacitor voltage, coil voltage, coil current and freewheeling diode (“D”, see Fig. 8) current during a magnetization process. The capacitor was initially charged to 500 V. The IGBT is closed at t = 0.05 s, with the capacitor being then discharged throughout the coil and the current peak induced in the coil being ≈510 A. The PMs used for that tests are Nd38 disks of dimensions height = 5 mm, and diameter = 10 mm (see Fig. 10(a), [24]). The magnet has the same diameter and perfectly coincides with the central column of the solid iron and iron powder cores [see Fig. 10(b)]. B. Equivalence With a PMSM The high-frequency model of the experimental setup after inserting the magnet [see Fig. 10(b)] is shown in Fig. 10(c). It corresponds to a transformer model, in which the primary corresponds to the coil and the secondary to the magnet [see Fig. 7(a) and (b)]. This equivalent circuit was proposed in [35] to model the high-frequency behavior of a PMSM, when a pulsating d-axis high-frequency current is being injected [35]. The signal injection and signal processing shown in Section III and the experimental results that will be shown in Section V (SPMSM and IPMSM) are for the case of pulsating d-axis

Coil

Core

(a)

Magnet

(b) p

ihfp p

vhfp

Primary

s

Mps

ihfs

rhfp j

Secondary

rhfs hf Lhfp

j

hf Lhfs

(c) Fig. 10. (a) Neodymium disk (Nd38). (b) Magnet position. (c) Equivalent high-frequency model of the experimental setup.

high-frequency signal injection. Therefore, the experimental verification of the magnetoresistive effect in PMs presented here can be directly applied to PMSMs (see Section V). p and iphfp are the primary high-frequency In Fig. 10(c), vhfp voltage and current, respectively; ωhf is the frequency of the high-frequency signal; Lhfp and Rhfp are the primary highfrequency self-inductance and resistance, respectively; ishfs is the secondary high-frequency current; Mps is the mutual coupling between the primary and the secondary; and Lhfs and Rhfs are the secondary high-frequency self-inductance and

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TABLE VI E QUIVALENCES B ETWEEN E XPERIMENTAL S ETUP AND A PMSM

Fig. 12. H-bridge.

Fig. 13. Estimated magnet high-frequency resistance using the iron powder core as a function of the magnetization level. Vhf = 0.1 p.u., ωhf = 250 Hz.

Fig. 11. Final PM remanent flux (BR ) depending on the capacitor voltage.

resistance, respectively. When applied to the high-frequency model of a PMSM, the correspondence between variables is shown in Table VI. C. Results and Discussion The coil peak current and, consequently, the final PM remanent flux (BR ) depends on the initial capacitor voltage. Fig. 11(a) shows the PM remanent flux (BR ) versus the required capacitor voltage, whereas Fig. 11(b) shows the PM remanent flux (BR ) versus the magnetic field produced by the coil. It is observed from Fig. 11 that, if the PM is initially fully magnetized, a capacitor voltage of 300 V is enough to change the PM magnetization level from 1.0 T (1 p.u.) to ≈ −0.7 T (≈ −0.7 p.u.). Once the PM is magnetized/demagnetized using the solid iron core [see Fig. 7(a)], the iron powder core [see Fig. 7(b)] is used to measure its magnetoresistive properties. The coil is fed from an H-bridge, shown in Fig. 12; Table IV shows its main characteristics. To measure the high-frequency resistance, a high-frequency voltage signal of Vhf = 0.1 p.u. and ωhf = 250 Hz is applied to the coil. Fig. 13 shows the estimated highfrequency resistance using the iron powder, as a function of the magnetization level of the PM. The PM magnetization level is changed using the solid iron core. The high-frequency resistance is obtained as the real component of the commanded highfrequency voltage divided by the measured high-frequency

Fig. 14. Estimated magnet high-frequency resistance using the iron powder core as a function of the magnetic flux density. The PM is a demagnetized magnet, with the magnetic flux density being created by a dc. Vhf = 0.1 p.u., ωhf = 250 Hz.

current. It is observed that the higher the magnetization level of the PM is (higher BR ), the lower is the reflected high-frequency resistance (i.e., the maximum high-frequency resistance occurs for BR = 0 t). It is observed that the change of the highfrequency resistance with the flux decreases as the magnetic flux density increases, i.e., as the magnet and core becomes more saturated. The results in Fig. 13 demonstrate the link between the PM remanent flux and the high-frequency resistance. In the results in Fig. 13, no dc magnetic field was produced by the coil. It is also possible, using the experimental setup shown in Figs. 7 and 12, to inject a dc in the coil to produce a constant magnetic field superposed to the PM field. This is important to understand the impact that the injection of d-axis or q-axis current in PMSMs will have on the magnetoresistive effect and on the PM highfrequency resistance reflected in the stator of the machine. The iron powder core was used for these experiments, as its advantageous due to its reduced eddy-current losses. A dc is injected to produce a dc magnetic field, which can either increase (i.e., similar to a flux intensifying current) or decrease (i.e., similar to a flux weakening current) the magnet field due to the PM. A high-frequency signal voltage, which is superposed to the voltage producing the dc, is injected for PM highfrequency-resistance estimation purposes. Same magnitude and frequency as detailed in Fig. 13 are used for the high-frequency voltage. Fig. 14 shows the estimated high-frequency resistance


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TABLE VII IPMSM M ACHINE PARAMETERS

Fig. 15. Estimated core high-frequency resistance when the magnet is removed. (a) Iron powder core. (b) Solid iron core. Vhf = 0.1 p.u., ωhf = 250 Hz.

Fig. 17. SPMSM and IPMSM test machines.

Fig. 18. Experimental test bench (IPMSM).

Fig. 16. Estimated magnet high-frequency resistance as a function of the magnetic flux density, after decoupling the effect of the iron powder core magnetoresistance. (a) For PM with different magnetization levels. (b) Demagnetized magnet, with the magnetic flux density being set by a dc. Vhf = 0.1 p.u., ωhf = 250 Hz.

for the case of a demagnetized magnet, the iron powder core magnetic flux density varies from −1.6 to 1.6 T by means of the injected dc. The same behavior in Fig. 13 is observed in Fig. 14. It is noted regarding the results shown in Figs. 13 and 14 that the magnetoresistive effect can exist both in the PM and core. To separate the contribution of the magnet from that of the core, the PM was removed. A dc was then injected into the coil to vary the core magnetic flux density from −1.1 t → 1.1 t → −1.1 t for the case of the solid iron core and −1.6 t → 1.6 t → −1.6 t for the case of the iron powder core. Fig. 15(a) and (b) show the estimated high-frequency resistance when the magnet is removed for the case of the iron powder core and solid iron core, respectively. It is observed that the magnetoresistive effect for the case of the iron powder core [see Fig. 15(a)] is very small compared with the PM plus iron powder core shown in Figs. 13 and 14. This means that the magnetoresistive effects observed in Figs. 13, 14 are dominated by the PM. This is due to the fact that the induced eddy currents in the iron power core by the high-frequency signal injection are very small. On the contrary, the high-frequency resistance

Fig. 19. Estimated d-axis stator-reflected magnet high-frequency resistance obtained both by FEA and experiment. Pulsating d axis high-frequency voltage injection, ωhf = 250 Hz, Vhf = 0.05 p.u.. Iq = 0 p.u. and ωr = 0 p.u.

for the case of the solid iron core [see Fig. 15(b)] experiences large variations with the magnetic field, i.e., it is strongly affected by the magnetoresistive effect [17], what makes this core inadequate to measure the magnet properties. Finally, Fig. 16 shows the same results as Figs. 13 and 14 but after decoupling the iron powder core magnetoresistive effect. The same conclusion of Figs. 13 and 14 applies to Fig. 16. V. S IMULATION AND E XPERIMENTAL R ESULTS Simulation results using FEA and experimental results using a SPMSM and an IPMSM are presented in this section. The machines’ parameters are shown in Tables I and VII, respectively. Fig. 17 shows the test machines, whereas Fig. 18 shows the experimental setup. An induction machine (IM) was used to load the test machines.

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Fig. 20. Estimated d-axis stator-reflected magnet resistance versus magnetization state & speed, for the case of a) SPMSM and b) IPMSM; magnetization state estimation error versus magnetization state & speed for the case of c) SPMSM and d) IPMSM. Pulsating current injection ωhf = 250 Hz, Vhf = 0.05 p.u.

Injection of Id current is the most commonly used method to change the PM magnetization state [8]–[11]. However, PM magnetization state also can be influenced by the injection of Iq current due to the cross-coupling that typically exists between d-axis and q-axis. However, cross-coupling between d-axis and q-axis in the test machines is almost negligible; hence, magnetization state is only proportional to the Id current magnitude. Fig. 19 shows the estimated d-axis stator-reflected magnet high-frequency resistance as a function of the magnetization state due to Id current injection, obtained both by FEA and experiment. Machines designs and injected high-frequency signals are the same in both cases. Both simulation and experimental results are obtained using the same variables (stator voltages and currents) and signal processing (see Section III and Fig. 6). The minimum magnetization state that can be achieved by Id current injection is ≈0.957 T for the SPMSM and ≈0.804 T for the IPMSM; the magnetization state is changed in steps of ≈0.072 T for the SPMSM and ≈0.129 T for the IPMSM. The variation of the estimated d-axis stator-reflected high-frequency resistance with the magnetization state is readily observed in both machines. This confirms the connection between the PM magnetization state and the d-axis stator-reflected magnet highfrequency resistance and therefore supports the use of the high-frequency resistance for PM magnetization state estimation. It is observed that the higher the magnetization state of the machine is, the lower the rotor magnet resistance due to the magnetoresistive effect. In obtaining the results shown in Fig. 19, the rotor is locked. A good agreement between simu-

lation and experimental results is observed. This confirms that the variation of the d-axis stator-reflected PM high-frequency resistance can be used for magnetization state estimation. It is also noted that the tendencies observed in the measurement system described in Section IV (see Figs. 13, 14, and 16), are confirmed by the simulation and experimental results with an SPMSM and an IPMSM in Fig. 19. It is observed that the rate of variation of the estimated high-frequency resistance with the PM magnetization state decreases as the magnet and core become more saturated (higher magnetization state), which is consistent with the results shown in Figs. 13, 14, and 16. Consequently, a careful design of the signal acquisition and signal processing will then be required in this case due to the reduction in the sensitivity. Fig. 20 shows experimental results of estimated d-axis statorreflected magnet high-frequency resistance and magnetization state estimation error versus the magnetization state and speed for two test machines (SPMSM and IPMSM). Magnetization state was varied from the minimum value that can be achieved for each machine (i.e., ≈0. 957 and ≈0.804 T for the SPMSM and IPMSM, respectively). The speed varies in steps of 0.1 p.u. from zero to the maximum speed that can be achieved for each magnetization state condition. It is observed that the estimated d-axis stator-reflected magnet high-frequency resistance decreases as the magnetization state increases, which is consistent with results shown in Figs. 13, 14, 16, and 19. It is also observed that the speed has a negligible impact on the estimated d-axis stator-reflected magnet high-frequency resistance [see Fig. 20(a) and (b)] and consequently on the magnetization state


estimation error [see Fig. 20(c) and (d)]. This confirms that the proposed method can be used in the whole speed range of the machine, including standstill. It is also observed that the magnetization state estimation error slightly increases as the magnetization state does due to the reduction of the sensitivity of the estimated high-frequency resistance variation with the PM magnetization at high magnetization states. This is also consistent with the results shown in Figs. 13, 14, 16, and 19. It is noted that, even in the high magnetization state region, the accuracy of the method is acceptable, with the maximum magnetization state estimation error being ≈0.031 T for the SPMSM and ≈0.052 T for the IPMSM. The larger error in the magnetization state estimation for the IPMSM compared to the SPMSM is explained by the reduced sensitivity of the IPMSM at high magnetization states observed in Fig. 19.

VI. C ONCLUSION This paper has presented a method to estimate the PM magnetization state in PMSMs, which is based on the dependence between the PM electrical high-frequency resistance and the PM magnetization state. The high-frequency resistance is estimated from the stator high-frequency current, which results from the injection of a high-frequency voltage. The proposed method is suitable for both SPMSMs and IPMSMs and can operate in real time and without interfering with the normal operation of the machine. The proposed method can be used in the whole speed range of the machine, even at standstill. Compensation of the contribution of the stator high-frequency resistance to the overall high-frequency impedance of the machine is required for the implementation of the method. Experimental setups using solid iron and magnetic powder cores have been built to evaluate the magnetoresistive properties of PMs used in commercial PMSMs. The physical results obtained using the setups confirm the theoretical predictions and the feasibility of the proposed method. Finally, the applicability of the method to PMSM has been confirmed by experimental verification. R EFERENCES [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 selfsensing control at very low speed,” IEEE Trans. Ind. Appl., vol. 47, no. 5, pp. 2004–2012, Sep./Oct. 2012. [2] K. Akatsu, M. Arimitsu, and S. Wakui, “Design and control of a field intensified interior permanent magnet synchronous machine,” IEEJ Trans. Ind. Appl., vol. 126, no. 7, pp. 827–834, Jul. 2006. [3] S. Wu et al., “IPM synchronous motor design for improving self-sensing performance at very low speed,” IEEE Trans. Ind. Appl., vol. 45, no. 6, pp. 1939–1946, Nov./Dec. 2009. [4] N. Bianchi and S. Bolognani, “Influence of rotor geometry of an interior PM motor on sensorless control feasibility,” IEEE Trans. Ind. Appl., vol. 43, no. 1, pp. 87–96, Jan./Feb. 2007. [5] J. F. Gieras and M. Wing, Permanent Magnet Motor Technology: Design and Application. 2nd ed. Boca Raton, FL, USA: CRC Press, 2002. [6] N. Limsuwan, T. Kato, K. Akatsu, and R. D. Lorenz, “Design and evaluation of a variable-flux flux-intensifying interior permanent magnet machine,” IEEE Trans. Ind. Appl., vol. 50, no. 2, pp. 1015–1024, Mar./Apr. 2014. [7] T. Fukushige, N. Limsuwan, T. Kato, and R. D. Lorenz, “Efficiency contours and loss minimization over a driving cycle of a variable-flux flux-

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David Díaz Reigosa (S’03–M’07) was born in Spain in 1979. He received the M.E. and Ph.D. degrees in electrical engineering from the University of Oviedo, Gijón, Spain, in 2003 and 2007, respectively. He was a Visiting Scholar with the Wisconsin Electric Machines and Power Electronics Consortium, University of Wisconsin, Madison, WI, USA, in 2007. His research interests include sensorless control of induction motors, permanent-magnet synchronous motors, and digital signal processing. He is currently an Associate Professor with the Department of Electrical, Electronic, Computers and Systems Engineering, University of Oviedo. Dr. Reigosa received a Fellowship from the Personnel Research Training Program for 2004–2008 funded by the Regional Ministry of Education and Science of the Principality of Asturias.

Daniel Fernandez was born in Spain in 1987. He received the B.S. degree in industrial electronic engineering and the M.S. degree in power electronic engineering from the University of Oviedo, Gijón, Spain, in 2011 and 2013, respectively, where he is currently working toward the Ph.D. degree in electrical engineering. From July 2013 to December 2013, he served an internship at the Nissan Advanced Technology Center. His research interests include electric motors and drives, magnets, and wireless measurement systems. Mr. Fernandez received a Fellowship from the Personnel Research Training Program funded by the Regional Ministry of Education and Science of the Principality of Asturias in 2013.

Zi-Qiang Zhu (M’90–SM’00–F’09) received the B.Eng. and M.Sc. degrees from Zhejiang University, Hangzhou, China, in 1982 and 1984, respectively, and the Ph.D. degree from The University of Sheffield, Sheffield, U.K., in 1991, all in electrical engineering. Since 1988, he has been with The University of Sheffield, where he currently holds the Royal Academy of Engineering/Siemens Research Chair and is the Head of the Electrical Machines and Drives Research Group, the Academic Director of the Sheffield Siemens Wind Power Research Centre, and the Director of the CSR Electric Drives Technology Research Centre. His research interests include the design and control of permanent-magnet brushless machines and drives for applications ranging from automotive to renewable energy.

Fernando Briz (A’96–M’99–SM’06) received the M.S. and Ph.D. degrees from the University of Oviedo, Gijón, Spain, in 1990 and 1996, respectively. From June 1996 to March 1997, he was a Visiting Researcher with the University of Wisconsin, Madison, WI, USA. He is currently a Full Professor with the Department of Electrical, Electronic, Computers and Systems Engineering, University of Oviedo. His research interests include control systems, power converters and ac drives, machine diagnostics, and digital signal processing. Prof. Briz received the 2005 IEEE T RANSACTIONS ON I NDUSTRY A P PLICATIONS Third Place Prize Paper Award and five IEEE Industry Applications Society (IAS) Conference and IEEE Energy Conversion Congress and Exposition Prize Paper Awards. He is currently the Program Chair of the Industrial Drives Committee of the IAS Industrial Power Conversion Systems Department.