SPMSMs HFI Based Self-Sensing Using Intentional Magnetic Saturation

High-frequency injection (HFI) is widely used for zero-to-low speed self-sensing in machines with saliency. HFI algorithms use inductive saliency in the d- and q-axes to estimate the rotor position in permanent magnet synchronous machines (PMSMs). Generally speaking, surface PMSMs (SPMSMs), which are designed without inductive saliency, are not suitable for HFI inductive based self-sensing. In this article, a method to enhance HFI algorithms at zero-to-low speed for classically designed SPMSMs with low inductive saliency is presented. The proposed method is based on using intentional magnetic saturation under flux-intensifying (FI) operation, which will temporarily enable robust self-sensing operation in the zero-to-low speed region in machines that are not suitable for traditional HFI self-sensing.

The associate editor coordinating the review of this manuscript and approving it for publication was Jinquan Xu .
i , αHF i βHF Alpha-and beta-axes high-frequency currents. I , i0 I i1 Average and differential carrier currents. I ch Characteristic current. L dd,qq D-and q-axes inductances. L dq,qd D-and q-axes cross-coupling inductances. L p ,L uv Phase and phase-to-phase inductances.

L, L
Differential and average inductances. θ HFI High-frequency injection angles. f HFI High-frequnecy injection freuqnecy in Hz. R p Phase resistance. ε Injection angle error.

V HFI
High-frequency injection voltage. FI Permanent magnet flux-intensifying operation. FW Permanent magnet flux-weakening operation.

I. INTRODUCTION
High-frequency injection (HFI) is a self-sensing technique widely used in machines with inductive saliency in the zero-to-low speed operational region [1]. Since surface permanent magnet synchronous machine (SPMSM) rotor geometry is symmetrical, no inductive saliency exists based on VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ the machine's rotor geometry. SPMSM is therefore not considered a suitable machine for HFI based self-sensing.
To improve the use of HFI techniques in SPMSMs, research efforts have been focused on increasing the signal-to-noise ratio (SNR) [2]- [4], and increasing inductive saliency by modifying the design of SPMSMs [5]- [8]. Saturation and cross-saturation effects and self-sensing control strategies have been investigated in depth for interior permanent magnet synchronous machines (IPMSMs). In [9]- [12] inductance ellipse variation under load condition is analyzed for IPMSMs. Orientation and eccentricity of the inductance ellipse have been shown to vary depending on the dq-axes current level; the orientation of the ellipse has been shown to depend on the cross saturation, while the eccentricity of the ellipse has been shown to depend on the inductive saliency between d-and q-axes. In [10], self-sensing performance is improved by decoupling the cross-saturation effect under loaded conditions. In [11], [12], HF is injected in tilted phase angle to improve the self-sensing performance of an IPMSM while operating the machine near the maximum torque per ampere (MTPA) trajectory. In [9]- [12], additional efforts based on offline characterization of saturation and cross-saturation have been made to enhance the self-sensing performance of PMSMs.
For the case of SPMSMs, large HF injection voltages have been proposed to be used, which results in changes in d-axis impedance based on magnetic saturation effect [13]. SPMSMs operation in MTPA trajectory did not affect the self-sensing ability [14], [15]. In [15], control algorithm to enable non-salient SPMSM using d-axis current planning is investigated with stationary reference frame HF injection. However, the optimal HF injection phase angle for SPMSMs has not been investigated. In [16], the variation of inductive saliency of a SPMSM under loaded conditions is experimentally investigated. Nevertheless, generalization of the use of intentional magnetic saturation induced inductive saliency has not been made.
This article proposes a novel technique based on intentional magnetic saturation with PM flux-intensifying (FI) current, i.e., positive fundamental d-axis current, + i d , injection, on SPMSMs. The physics-based model with variable inductance is developed from the machine design perspective of view considering characteristic current, I ch , offset biasing on d-axis flux path. The generalized SPMSM magnetic saturation characteristic model and analysis are supported by Finite Element Analysis (FEA) and machine characterization experimental results. The proposed technique utilizes positive fundamental d-axis current injection to intentionally increase the inductive saliency; making reliable use of classical HFI self-sensing techniques in machines with very low saliency, e.g., SPMSMs. FI operation with positive d-axis current in the estimated rotor reference frame will results in a decrease of d-axis incremental inductance which results in an increased inductive saliency; therefore, saliency-based self-sensing ability will be enhanced [17]. No pre-characterization of SPMSM nor complex saturation, cross-saturation compensation techniques are required considering the main flux path saturation effect on d-axis which is the dominant factor of SPMSM self-sensing. The increasing self-sensing sensitivity is verified experimentally, using decoupled differential current, I i1 [18].
The article is organized as follows: Section II presents basics of HFI based self-sensing control, Section III presents the concept of FI operation using intentional magnetic saturation; Section IV presents simulation results of the proposed self-sensing technique using intentional magnetic saturation; Section V discusses implementation issues of the proposed technique; Section VI shows experimental results to demonstrate the viability of the proposed technique; Finally, the conclusions of the article are presented in Section VII.

II. HFI BASED SELF-SENSING CONTROL CONSIDERING MAGNETIC SATURATION EFFECT
This section shows the PM machine model used for HFI based self-sensing. The flux-linkage model of a PMSM in a reference frame synchronous with the rotor is shown in (1), where L, L are the differential and average inductances, (2) and (3), respectively, L dd and L qq are the d-and q-axes incremental inductances which are function of dq-current [10], [13], [14], [19]. λ θ r dsHF , λ θ r qsHF , i θ r dsHF , and i θ r qsHF are the d-and q-axes stator flux-linkages and stator currents in a reference frame synchronous with the rotor.
Using the inverse of the Park transform (4), the dq-axes flux-linkage model can be transformed into the stator reference frame, i.e., stationary reference frame (5), where λ αHF , λ βHF , i αHF , and i βHF are the alpha-and beta-axes stator flux-linkages and currents. Pulsating HF voltage command is shown in the estimated rotor reference frame and in the stationary reference frame in (6) and (7) respectively, where θ HFI is the high-frequency injection angle (9), ω HFI is the angular frequency of the high-frequency signal, V HFI is the magnitude of the highfrequency signal,θ r is the estimated rotor position and is the rotor position. When (7) is injected into the PMSM terminals, the resulting pulsating HF flux is (8), where 1/p represents an integrator. Substituting (8) into (10), the resulting HF currents in the stationary reference frame are represented by (11).
The position estimation will be achieved by controlling the q-axis current in (13), iθ r qsHF (14), to zero; I i1 in (14) being the magnitude of the differential HF current (15). Note that (15) is a function of dq-current; it can be, therefore, concluded that the sensitivity of I i1 with respect to estimated position error, (θ r −θ r ) , depends on the operating condition. It can be concluded from (13)-(15) that without having L, i.e., inductive saliency, HFI based self-sensing speed/position control cannot be performed. It will be shown in the next section that injecting positive d-axis current, flux intensifying (FI) current, will increase the inductive saliency ( L), making HFI based self-sensing techniques more reliable in machines with low inductive saliency.
iθ r qsHF = sin(θ HFI )I i1 sin(2(θ r −θ r )) (14) It is important to note that the nature of the inductive saliency-based self-sensing control does not require to know precise inductance values, unlike other model-based control algorithms, e.g., observer-based field-oriented control (FOC) [20] or deadbeat direct torque and flux control (DB-DTFC) [21]. As it can be observed from (15), the inductive saliency-based self-sensing control requires a certain degree of saliency (i.e., differential inductance); the following section will present the proposed control technique to temporarily increase the machine saliency using intentional magnetic saturation.

III. SPMSM SALIENCY CHARACTERISTIC AND MAGNETIC SATURATION EFFECT AND PM FLUX
This section shows how to induce an intentional magnetic saturation to enhance HFI based self-sensing capability in low saliency machines.   Fig. 1 being biased with the PM flux-linkage, λ PM ; I ch , see (16), representing the characteristic current where L d is the absolute d-axis inductance [22]. The incremental d/q-axes inductance, L dd , L qq , L qd , and L dq , respectively, are defined as the slope of the dq-axes flux-linkage at each operating point (i.e., at each d/q-axes current) (17), (18), (19), and (20) respectively. It can be observed from Fig. 1 that L dd decreases if positive d-axis current is injected, i.e., flux intensifying (FI) current, while it decreases if negative d-axis current is applied, i.e., flux weakening FW current. On the other hand, L qq is seen to decrease if positive/negative q-axis current is applied, symmetrical behavior being observed.
It can be concluded from Fig. 1 that although a machine is symmetrically designed, i.e., no inductive saliency exists from the rotor geometry, e.g., SPMSM, magnetic saturation results in no-load inductive saliency; unfortunately, this saliency is typically very small [23], placing reliability concerns for HFI based self-sensing control. However, it can also be concluded from Fig. 1 that injecting d-axis FI current will increase the machine saliency; the proposed technique in this article will take advantage of this behavior to enhance HFI based self-sensing capability in low saliency machines.

IV. SPMSM INDUCTANCE CHARACTERIZATION UNDER FI AND FW OPERATION USING FEA
This section presents the inductance characterization, FEA based, of the two SPMSMs that will be used for the experimental verification of the method: a Distributed Windings (DW) SPMSM and a Factional Slot Concentrated Windings (FSCW) SPMSM; parameters of both machines are shown in TABLE 1.  Figures 2 and 3 show the incremental inductances maps, L dd and L qq , including FI and FW operation regions, of the DW and FSCW SPMSMs, respectively; L dd and L qq being obtained as the slope of the respective flux-linkages at each operating point. As expected, L dd in both SPMSMs, decreases as FI current is injected (i.e., positive d-axis current), resulting therefore in a saliency increase; the differential inductances maps being shown in Fig. 4. It can be  concluded from Figs. 2-4 that FSCW SPMSM shows higher L dd variation with FI current, meaning that FSCW SPMSM has a higher ability for FI operation utilizing intentional magnetic saturation. This is expected since FSCW machines have larger inductance than DW machines [24].
It is interesting to note that SPMSMs has low cross-coupled inductances, L dq and L qd , which are the results of crosssaturation. This is because of the absence of flux barriers, which are typically included in IPMSMs to increase reluctance torque production, and can be highly cross-saturated under loaded operation [25]. In addition, the equivalent airgap in SPMSMs is larger than in IPMSM due to the surfacemounted PMs, which makes the rotor iron saturation level to be lesser affected by the stator currents than in IPMSMs. For these reasons, the HFI model of SPMSMs can be simplified to (1), where the cross-coupled inductances are merged to main-inductance. Even more, all these issues pointed out that the optimal HF injection angle in SPMSMs is 0 deg., i.e., d-axis pulsating HF signal injection.

V. IMPLEMENTATION OF FI HFI SELF-SENSING
In this section, the control block diagram of HFI based self-sensing using FI current injection is presented. The proposed implementation includes also PM polarity estimation and the tradeoff of the proposed self-sensing technique in the additional power.  Figure 5 shows the control block diagram of classical HFI based self-sensing based filed-oriented control (FOC) in the estimated rotor reference frame. The HF pulsating voltage in (6) can result in HF current in the orthogonal axis as in (13) when reference frame error exists. Positive d-axis current is commanded for FI operation in zero-to-low speed self-sensing using intentional magnetic saturation, creating required inductive saliency on SPMSMs with small saliency.

A. CONTROL BLOCK DIAGRAM OF HFI BASED SELF-SENSING AND FI CURRENT
PM polarity is detected using secondary saliency induced on the d-axis by the magnetic saturation effect [26], [27]. The initial inductive saliency, although small typically <5∼10%, can be used to find the d-axis by using the HFI self-sensing technique shown in Section II [1]; the magnet polarity can be detected using the secondary harmonic HF current component induced by saturation effect [26], [27]. The left and the right figure in Fig. 6 show the d-axis flux-linkage map and d-axis incremental inductance near zero d-axis current, respectively. The resulting d-axis incremental inductance, L dd , decreases when the pulsating current is in the FI region; L dd increases in FW region. It can be observed from (21) that the d-axis HF current will change inversely proportional to L dd . Figure 7 shows the d-axis current response with saturation induced secondary harmonic component, i d2 , the first order harmonic current, i d1 , and the total current response, i d , which is the sum of i d1 and i d2 . When the north (N) pole is aligned with d-axis, the saturation induces positive secondary harmonic; the negative secondary harmonic will be induced when the south (S) pole is aligned with d-axis. By extracting the secondary harmonic component, as shown in Fig 8, PM polarity can be detected. The detection process is only required once at the starting of the SPMSMs.

C. POWER REQUIRED FOR FI HFI
The required power for FI HFI operation, P FI HFI , is represented by (22). P FIHFI = P HFI + P FI (22) As it can be observed, P FIHFI is composed of two terms: • P FI : required power to operate a machine in the FI region, i.e., additional power due to positive d-axis current injection (23); where R p is the rated phase resistance. Figure 9 shows measured and estimated (using (23)) P FI . As expected, P FI increases as the VOLUME 8, 2020   d-axis current does. It is noted that this additional power required for intentional magnetic saturation will be required only temporarily when zero-to-low speed self-sensing is required. At medium-to-high speed operation region, where trackable back-EMF exists, back-EMF based self-sensing method can be used, d-axis current can be therefore controlled to be zero.
• P HFI : required power to inject the HF signal (24) where L p is rated phase inductance, and V HFI and f HFI are the magnitude and frequency of the injected HF signal. Figure 10 shows the measured and estimated (using (24)) P HFI as a function of V HFI and ω HFI . It can be observed that the higher the frequency of the HF signal, the lower the losses, and, as expected, the lower the magnitude of the HF signal, the lower the losses.

VI. EXPERIMENTAL RESULTS
This section provides experimental to demonstrate the viability of the proposed technique. Figure 11 shows the experimental setup, which consists of an XCS2000 controller, DRV8301 inverters with 20kHz switching frequency, and back-to-back connected SPMSMs (load and test machines).

A. NO LOAD INDUCANCE ESTIMATION D
and q-axes incremental inductances, L dd and L qq , have been measured in both test machines (DW and FSCW SPMSMs); L dd and L qq being obtained form (25). The procedure to measure L dd and L qq is the following: 1. Phase-to-phase inductance, L uv (25), is measured using an RLC meter while the rotor of the machine is positioned at π/3 and 5π/6; two frequencies for the HF signal have been used 10 2 and 10 3 Hz.
2. L dd and L qq are obtained from the measurements provided by the RLC meter as (26) and (27).
L uv (θ e ) = L qq + L dd + (L qq − L dd ) cos 2θ e + π 3 (25) The results are summarized in TABLE 2. It can be observed from TABLE 2 that the no-load inductive saliency for both machines is ≈10%. It can also be observed that the inductances decrease as the frequency of the HF signal increases; this is because skin effect on a coil tends to make resistance higher, and the skin effect on the lamination makes inductance lower. The inductance drop with frequency can be therefore explained from the decreasing effective axial direction area of lamination [28]. Nevertheless, the inductance drop due to skin effect will not affect the inductive saliency ratio since the effect exists in both dq-axes.

B. INDUCTIVE SALIENCY VARIATION DUE TO FI CURRENT INJECTION
To measure the influence of soft-iron saturation effects on inductance, the dq-axes flux-linkage is estimated at the standstill position [29], [30]. At a locked rotor position, back-EMF does not exist; therefore, flux-linkage in dq-axes can be measured using (28)- (29). Dq-inductances can be estimated from (17)-(18) after applying a low-frequency square wave voltage to the machine. Figure 12 shows the inductance variation as a function of dq-current; it is observed a sharper d-axis inductance drop with positive I d current on the FSCW SPMSM than on the DW SPMSM. Figure 13 shows I i1 vs. fundamental d-axis current for FSCW and DW SPMSMs measured directly using high-frequency voltage injection in between dq-axes given the rotor position from the encoder [18]. Choosing (θ r −θ r ) = 45 [deg.] in (14), I i1 in (15) is estimated given the encoder position as the reference. As expected, the I i1 increases if the positive d-axis current is injected, FI current, and decreases if negative d-axis current is injected, FW current.   Figure 14 shows the command tracking ability of the conventional HFI based self-sensing position control, i.e., without FI current injection, while Fig. 15 shows the command tracking ability of the proposed HFI based self-sensing position control, i.e., with FI current injection. In both cases, see Fig. 14 (a) and 15 (a), a swept sine i ‡ qsi command from 0 to 20Hz was applied to the test machine. Figure 14 Table 1. measured and estimated position. It can be clearly observed that the proposed FI operation technique enhances the self-sensing ability.

VII. CONCLUSION
This article proposes injecting FI current to intentionally increase the inductive saliency of a PMSM, making reliable use of HFI self-sensing in machines with very low saliency, e.g., SPMSMs. It has been shown that low saliency machines became a better self-sensor under FI operation with positive d-axis current injection; injecting FI current will decrease d-axis inductance, which results in an increase of the inductive saliency required for HFI self-sensing. It has been demonstrated that by using the proposed method, neither machine design nor pre-characterization for current path planning is required for using HFI self-sensing techniques in low saliency machines. Experimental results have been provided to demonstrate the viability of the proposed technique.