A Highly-efficiency Position Sensorless Electric Vehicle Synchronous Reluctance Motor Drive

Ganisetti Vijay Kumar , Min-Ze Lu , Chang-Ming Liaw ^*

Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan

* Correspondence: Chang-Ming Liaw

Academic Editors: Marco Bortolini and Francesco Gabriele Galizia

Special Issue: Energy Efficiency in Flexible and Reconfigurable Manufacturing: Emerging Trends, Models and Applications in the Industry 4.0 Era

Received: May 02, 2021 | Accepted: July 27, 2021 | Published: August 11, 2021

Journal of Energy and Power Technology 2021, Volume 3, Issue 3, doi:10.21926/jept.2103037

Recommended citation: Kumar GV, Lu MZ, Liaw CM. A Highly-efficiency Position Sensorless Electric Vehicle Synchronous Reluctance Motor Drive. Journal of Energy and Power Technology 2021; 3(3): 037; doi:10.21926/jept.2103037.

© 2021 by the authors. This is an open access article distributed under the conditions of the Creative Commons by Attribution License, which permits unrestricted use, distribution, and reproduction in any medium or format, provided the original work is correctly cited.

1. Introduction

Electric motors [1] are the most popularly employed actuators in the industry. Improvements in their reliability and efficiencies are very important in the internet-of-things (IOT)- based automatic industry 4.0 era. Each type of motor possesses its own critical issues that need to be properly treated for achieving these goals. The synchronous reluctance motor (SynRM) [1,2,3] is a new type of motor compared to the commonly used induction motor and has high application potential, including EV driving. SynRM possesses two major features: (i) It has a simple and rigid rotor structure without permanent magnets and conductors and thus is suitable for high-speed driving applications; (ii) It has a highly developed torque similar to a series DC motor. However, an adequate commutation instant setting and tuning are recognized as the most challenging issues in obtaining a high-efficiency SynRM drive [4,5]. In particular, the inherent slotting effect [5,6,7,8,9] must also be considered, especially for a sensorless SynRM drive. A few advanced current control approaches [5,10,11] have been developed for achieving better performance considering the nonlinear behavior of SynRM.

For a standard SynRM drive, the absolute position of the rotor is required for implementing the vector control. Nevertheless, in harsh environments, a position sensorless controlled motor drive is preferable. Furthermore, the maloperation due to the failure of the position sensor can be avoided. The approaches developed for the permanent magnet synchronous motors (PMSMs) are also applicable to SynRM with suitable modifications. To date, a large number of position sensorless approaches have been developed, and their surveys can be found in the literature [12,13,14]. The key bottlenecks in the existing approaches and the future development trends have been commented on in detail [13]. The stable operation of a motor under heavier load and high speed is a key issue that needs to be solved, and accordingly, its successful application to electric vehicle (EV) driving is the major goal that is being pursued. The sensorless control approaches can be generally categorized into (i) observer-based methods, such as adaptive observers [15,16] and Kalman filter observers [17], (ii) extended back-electromotive force (back-EMF) methods [18,19,20], and (iii) methods based on rotor saliency [21,22,23,24,25,26,27], such as the high-frequency injection (HFI) approach, which is a typical method of this type.

The observed back-EMF-based approaches can only possess satisfactory running characteristics above a certain speed. In contrast, the HFI approach can be operated effectively in a standstill and low-speed mode, and thus this approach is applicable to EVs requiring frequent starting with a highly developed torque. However, the current ripples caused by its inherent slotting effect must be considered when making the current control and the HFI rotor position estimation.

In the HFI sensorless mechanism with sinusoidal signal injection, low-pass filters (LPFs) are used for extracting the current signal containing the estimated position error. The inherent time delay of LPFs limits the dynamic performances of the current and speed loops. To overcome these difficulties, the square-wave HFI sensorless schemes have been proposed [28,29,30,31,32,33]. By increasing the injection frequency, the effect of slot harmonics can be reduced, and fixed-frequency injection can be adopted. The number of LPFs used in the estimation scheme is reduced, and thus the bandwidths of the current, speed, and position estimation schemes are improved. In recent studies [32,33], the problem of instability under heavy loads has been pointed out, and to address it, improved square-wave HFI schemes have been proposed in order to enhance the performance of the motor under heavy load. However, only the ones at low speed are treated. At present, methods for achieving satisfactory driving characteristics under wide speed and load ranges for EV application are being pursued. As the speed and load are increased, the difference between d- and q-axis inductances (\({L_d} - {L_q}\)) will be decreased to reduce the sensitivity of the rotor position estimation. The effects of the load- and speed-dependent slot harmonics and their multiples cannot be ignored, especially for a high-power motor drive with low switching frequency. The sinusoidal HFI schemes can be divided into the following: (i) Rotating voltage signal type- In this type, the balanced two-phase voltages are injected into the d- as well as the q-axis. The sensed current along the two axes are processed through a band-pass filter, reverse rotating-frame transformation, low-pass filter, and the phase-locked loop (PLL) to yield the observed rotor angle. The inherent detected angle errors for the interior PMSM (IPMSM) and SynRM will exist while performing the rotating-frame transformation for the unbalanced d- and q-axis currents due to the \({\rm{\;}}{L_d} \ne {L_q}{\rm{\;}}\) condition. (ii) Pulsating voltage signal type- In this type, only the d-axis (or q-axis) voltage is injected. The detected q-axis (or d-axis) current is used to yield the rotor angle via band-pass filtering, modulation, and servo regulation mechanism.

As far as the single-axis HFI scheme is concerned, for the surface PMSM (SPMSM), \({\rm{\;}}{L_d} = {L_q}\). Thus, one can adopt the d- or q-axis injection scheme to yield identical results. In the case of IPMSM, the rotor permanent magnet (PM) flux linkage \({\rm{\;}}\lambda _m^{{'^r}} \ne 0{\rm{\;}}\)and\({\rm{\;}}{L_d} \ne {L_q}\). Thus, choosing either the d-axis or the q-axis would depend on the saliency extent and the amplitude of back-EMF harmonics. Finally, for a SynRM, \({\rm{\;}}\lambda _m^{{'^r}} = \;0{\rm{\;}}\)and\({\rm{\;}}{L_d} > {L_q}\). Thus, considering the slot harmonic effect, the q-axis injection scheme is suggested to yield a stable and better performance under wider speed and load ranges. Analytic and experimental explorations presented in the latter part of the main text will show that the conventionally adopted d-axis injection scheme can not be stably operated above a certain load, even if changed injection frequencies are applied. In this paper, the theoretical and experimental explorations done for making an adequate choice of the injection mechanism have been presented . Further, the q-axis injection HFI sensorless EV SynRM drive has been described and evaluated experimentally.

2. System Configuration

2.1 The Developed EV SynRM Drive

The developed EV SynRM drive is shown in Figure 1. The direct current (DC)-link is powered from the battery via a bidirectional interface converter with boosted voltage to achieve better driving performance over a wide speed range. A dynamic brake leg has been incorporated to avoid the over-voltage caused by the failure of regenerative braking.

Figure 1 System configuration of the developed EV SynRM drive.

2.1.1 Governing Equations of SynRM

The voltage and developed torque of a SynRM in the d-q domain of the rotor frame can be expressed as [1,2]

\[ \left[\begin{array}{c}v_{d s}^{r} \\ v_{q s}^{r}\end{array}\right]=\left[\begin{array}{cc}R_{s}+L_{d} \frac{d}{d t} & -\omega_{r} L_{q} \\ \omega_{r} L_{d} & L_{q} \frac{d}{d t}\end{array}\right]\left[\begin{array}{c}i_{d s}^{r} \\ i_{q s}^{r}\end{array}\right] \tag{1} \]

\[ T_{e}=\frac{3 P}{4}\left[\left(L_{d}-L_{q}\right) i_{q s}^{r} s_{d s}^{r}\right]=\frac{3 P}{4}\left(\frac{L_{q}-L_{d}}{2}\right) \hat{I}_{a s}^{2} \sin 2 \beta=T_{L}+B \omega_{r}+J \frac{d \omega_{r}}{d t} \tag{2} \]

where \({\rm{\;}}{\hat I_{as}}{\rm{\;}}\) is the peak of the a-phase current and \({\rm{\;}}\beta {\rm{\;}}\) is the shift angle between the a-phase current peak and the d-axis. The q-and d-axis inductances are defined as

\[ L_{q}=L_{l s}+\frac{3}{2}\left(L_{A}-L_{B}\right), L_{d}=L_{l s}+\frac{3}{2}\left(L_{A}+L_{B}\right) \tag{3} \]

2.1.2 Observations

(a) From Equation (2), it can be seen that the commutation angle for a SynRM drive must be set to \({\rm{\;}}\beta = 45^\circ {\rm{\;}}\) theoretically. In reality, by considering the motor core losses and the saturated d-axis and q-axis inductances, the actual shift angle \({\rm{\;}}\beta > 45^\circ {\rm{\;}}\) must be properly tuned depending on the system operating conditions [5].

(b) Regenerative braking of a SynRM drive must be achieved by reversing the developed torque. For reversing the torque, two approaches are suggested. In the first approach, the q-axis current command is set to be negative when the motor speed starts decelerating and again set to be positive when the speed command reaches zero. In the second approach, the reversing of torque can be achieved by reversing the \({\rm{\;}}\beta \)-angle with respective to the d-axis. In this study, the alternative approach of reversing the q-axis current, \({\rm{\;}}i_{qs}^r\), has been adopted in the developed EV SynRM drive. The first approach has been implemented for regenerative braking, as described in the later section.

The EV SynRM drive system components are as follows :

(1) SynRM drive

• SynRM: 3P, 4-pole, 3.7 kW, 11.5 A, 2000 rpm.

• Load PMSG: 3P Y-connected, 8-pole, 5 kW, 2000 rpm.

• Inverter: It was constructed using three insulated-gate bipolar transistor (IGBT) modules, CM100DY-12H. Sinusoidal pulse-width modulator (PWM) switching frequency \({\rm{\;}}{f_s} = \;10\;{\rm{kHz}}\).

(2) Battery interface converter

• Battery voltage: \({\rm{\;}}{V_b} = \;160\;{\rm{V}}\), 18 Ah, (LiFePo₄).

• DC-link voltage: \({\rm{\;}}{V_{dc}} = \;550\;{\rm{V}}\).

• Power rating: \({\rm{\;}}{P_{dc}} = \;3.75\;{\rm{kW}}\),\({\rm{\;}}{I_b} = {I_L} = \;23.44\;{\rm{A}}\)

• Switching frequency: \({\rm{\;}}{f_s} = \;30{\rm{\;kHz}}\).

(3) Dynamic brake: Braking resistance \({\rm{\;}}{R_B} = 30\;{\rm{\Omega }}/100\;{\rm{W\;}}\) was used. The voltage command was set to 570 V, and the bang-bang control was applied with a hysteresis band of h = 3 V.

2.2 Control Schemes

The control schemes of the battery interface converter, the dynamic brake, and the EV SynRM drive are shown in Figures 2(a) to 2(c), respectively. Details of the design procedures and all the designed constituted controllers can be found in a previous study [5], which were simplified as follows:

Figure 2 Control schemes of the developed sensorless EV SynRM drive. (a) battery interface converter, (b) dynamic brake, and (c) the motor drive.

2.2.1 Battery Interface Converter

Current controller. Using a large-signal stability criterion for a ramp-comparison current control pulse-width modulator (RC-CCPWM), i.e.,\({\rm{\;}}\left( {d{v_c}/dt} \right) < \left( {d{v_{tri}}/dt} \right)\), the upper limit of the proportional gain under the transient period after the occurrence of disturbance was obtained as\({\rm{\;}}{K_{pi}} < 11.54\). Choosing\({\rm{\;}}{K_{pi}} = 3\), the integral gain of\({\rm{\;}}{K_{Ii}} = 10{\rm{\;}}\)was then obtained by computer-aided design with a cross-over frequency of\({\rm{\;}}{f_c} = 2.62\;{\rm{kHz}}\). Finally,

\[ G_{c i}(s)=K_{p i}+\frac{K_{I i}}{s}=3+\frac{10}{s} \tag{4} \]

Voltage controller. The controller \({\rm{\;}}{G_{cv}}\left( s \right){\rm{\;}}\)was designed to have the desired voltage response due to a step load power change of\({\rm{\;}}\Delta {P_{dc}} = \;201.67\;{\rm{W}}\). First, the voltage dynamic model was derived using arbitrarily set controller parameters, and then the designed controller was obtained by specifying the maximum voltage dip and rise time as follows:

\[ G_{c v}(s)=K_{p v}+\frac{K_{I v}}{s}=1.0558+\frac{15.6903}{s} \tag{5} \]

Voltage robust controller.

\[ W_{v}(s)=\frac{W_{v}}{1+\tau_{v} s}=\frac{0.5}{1+3.18 \times 10^{-3} s} \tag{6} \]

Robustness analysis. From the derivation corresponding to the voltage loop shown in Figure 2(a), it can be observed that the voltage tracking error, \({\varepsilon _v}\), by the proportional-integral (PI) feedback controller,\({\rm{\;}}{G_{cv}}\left( s \right){\rm{\;}}\), could only be reduced to\({\rm{\;}}\left( {1 - {W_v}\left( s \right)} \right){\varepsilon _v} \approx \left( {1 - {W_v}} \right){\varepsilon _v}\). However, the control effort\({\rm{\;}}i_L^*{\rm{\;}}\)was magnified by a factor of\({\rm{\;}}1/\left( {1 - {W_v}} \right)\). Thus, as the weighting factor,\({\rm{\;}}{W_v}\), was chosen closer to 1.0, the feedback voltage would closely follow its command under different operating conditions. However, the magnified control effort and system noise would affect the system stability. Hence, a compromised consideration for determining the value of the robust control weighting factor\({\rm{\;}}{W_v}{\rm{\;}}\)must be made.

2.2.2 SynRM Drive

For the SynRM drive, the critical controllers include the following: (i) An adaptive commutation scheme (ACS), which was used for determining the commutation angle\({\rm{\;}}\beta = {\beta _o}\;({\beta _o} > 45^\circ ){\rm{\;}}\)using the fitted motor parameters (\({\hat L_d},\;{\hat L_q},{\hat R_c}\)) for minimizing the total copper and core losses in the motor. (ii) The d-axis and q-axis current control schemes, each consisting of a PI controller, a robust controller, and an observed back-EMF feedforward controller. The PI current controller was designed considering the inherent slot harmonic effects. (iii) Speed control scheme that was used for yielding quick speed tracking response under different operating conditions and a quantitatively designed PI feedback controller was augmented with a speed robust error cancellation controller (SRECC). The listed controller parameters are given as follows:

Current controller. Similar to the current control of a battery interface, the corresponding controller of the SynRM drive is expressed as:

\[ G_{c i q}(s)=5+\frac{50}{s}, G_{c i d}(s)=10+\frac{100}{s} \tag{7} \]

Speed controller. The dynamic model of the SynRM was estimated under a small step command change. By defining the speed command tracking response, the designed speed controller was derived as

\[ G_{c \omega}(s)=2.57334+\frac{1.1353576}{s} \tag{8} \]

Robust controllers.

\[ W_{i}(s)=\frac{W_{i}}{1+\tau_{i} s}=\frac{0.8}{1+3.18 \times 10^{-3} s} \tag{9} \]

\[ W_{\omega}(s)=\frac{W_{\omega}}{1+\tau_{\omega} s}=\frac{0.4}{1+1.2538 \times 10^{-3} s} \tag{10} \]

Similar to the robustness analysis made above, if the weighting factor,\({\rm{\;}}{W_\omega }\), was chosen closer to 1.0; the motor speed would closely follow the speed command. Further, the speed regulation response due to load torque change could also be greatly improved. For a sensorless SynRM drive using the observed rotor speed, a low value of\({\rm{\;}}{W_\omega } = \;0.4{\rm{\;}}\)was chosen for reducing the effect of noise and the sluggish response of the observed speed.

The detailed analysis and design description of the proposed HFI sensorless control scheme will be presented in the following sections.

3. Determination of the Key Attributes for the HFI Scheme

For a pulsating HFI scheme [21,22,23], the high-frequency (HF) voltage can be injected into the q-axis (or d-axis), and the detected d-axis (or q-axis) current is processed to yield the observed rotor angle. In determining the adequate injected axis, the current levels in both axes must be observed. Hence, the back-EMF coupling effects were considered in the derivations.

For the injected high-frequency signal voltages,\({\rm{\;}}v_{dsh}^r{\rm{\;}}\)and\({\rm{\;}}v_{qsh}^r\), at\({\rm{\;}}\omega = {\omega _h}\), the voltage equations can be written from Equation (1) as

\[ \left[\begin{array}{c}v_{d s h}^{r} \\ v_{q s h}^{r}\end{array}\right]=\left[\begin{array}{cc}z_{d h}^{r} & -\omega_{r} L_{q h}^{r} \\ \omega_{r} L_{d h}^{r} & z_{q h}^{r}\end{array}\right]\left[\begin{array}{l}i_{d s h}^{r} \\ i_{q s h}^{r}\end{array}\right] \tag{11} \]

where\({\rm{\;}}z_{dh}^r = r_{dh}^r + j{\omega _h}L_{dh}^r{\rm{\;}}\)and\({\rm{\;}}z_{qh}^r = r_{qh}^r + j{\omega _h}L_{qh}^r{\rm{\;}}\)are the impedances at \({\omega _h}\).

The relationship between the estimated rotor reference frame with the estimated rotor angle,\({\rm{\;}}{\hat \theta _r}\), and the actual rotor reference frame is shown in Figure 3, where the rotor position estimation error is defined as

\[ \tilde{\theta}_{r} \triangleq \theta_{r}-\hat{\theta}_{r} \tag{12} \]

Figure 3 Schematic showing the relationship between the estimated and the actual rotor reference frames.

Using \({\tilde \theta _r}\), one can obtain the following high-frequency voltage equations:

\[\left[\begin{array}{l} v_{d s h}^{\hat{r}} \\ v_{q s h}^{\hat{r}} \end{array}\right]=\left[\begin{array}{cc} z_{d h}^{\hat{r}}-\omega_{r} L_{d i f f} \sin 2 \tilde{\theta}_{r} & z_{c h}^{\hat{r}}-\omega_{r} L_{a v g}+\omega_{r} L_{d i f f} \cos 2 \tilde{\theta}_{r} \\ z_{c h}^{\hat{r}}+\omega_{r} L_{a v g}+\omega_{r} L_{d i f f} \cos 2 \tilde{\theta}_{r} & z_{q h}^{\hat{r}}+\omega_{r} L_{d i f f} \sin 2 \tilde{\theta}_{r} \end{array}\right]\left[\begin{array} \\i_{d s h}^{\hat{r}} \\ i_{q s h}^{\hat{r}} \end{array}\right]\tag{13}\]

where

\[ z_{a v g} \triangleq \frac{z_{d h}^{r}+z_{q h}^{r}}{2}, z_{d i f f} \triangleq \frac{z_{d h}^{r}-z_{q h}^{r}}{2}, L_{a v g} \triangleq \frac{L_{d h}^{r}+L_{q h}^{r}}{2}, L_{d i f f} \triangleq \frac{L_{d h}^{r}-L_{q h}^{r}}{2} \tag{14} \]

\[ z_{d h}^{\hat{r}}=z_{a v g}+z_{d i f f} \cos 2 \tilde{\theta}_{r}, z_{c h}^{\hat{r}}=z_{d i f f} \sin 2 \tilde{\theta}_{r}, z_{q h}^{\hat{r}}=z_{a v g}-z_{d i f f} \cos 2 \tilde{\theta}_{r} \tag{15} \]

3.1 D-axis Injection

The normally employed d-axis injected mechanism is analyzed first. By applying the input voltage vector

\[ \left[\begin{array}{c}v_{d s h}^{\hat{r}} \\ v_{q s h}^{\hat{r}}\end{array}\right]=\left[\begin{array}{c}V_{i n j} \cos \omega_{h} t \\ 0\end{array}\right] \tag{16} \]

into Equation (13) and rearranging, the resultant q-axis current can be expressed as

\[ i_{q s h}^{\hat{r}}=\frac{z_{d i f f} \sin 2 \tilde{\theta}_{r}+\omega_{r} L_{a v g}+\omega_{r} L_{d i f f} \cos 2 \tilde{\theta}_{r}}{z_{d i f f}^{2}-z_{a v g}^{2}+\omega_{r}^{2} L_{d i f f}^{2}-\omega_{r}^{2} L_{a v g}^{2}} V_{i n j} \cos \omega_{h} t \tag{17} \]

3.1.1 Observations

The current expressed in Equation (17) contains the speed-dependent bias as well as the small-signal terms with the information \({\tilde \theta _r}\). Although the former will be removed in the HFI modulation process, it exists in actual armature current, which affects the stable operation of an HFI sensorless SynRM drive.

Speed-dependent biased current. Generally, \({\rm{\;}}{\tilde \theta _r}\) is very small under sensorless operation. By neglecting the terms included with \({\tilde \theta _r}\) in Equation (17), the component for estimating the current magnitude can be obtained as follows:

\[ \underline{i}_{q s h}^{\hat{r}}=\left(\frac{\left(-\omega_{r} L_{a v g}-\omega_{r} L_{d i f f}\right) V_{i n j}}{z_{a v g}^{2}-z_{d i f f}^{2}+\omega_{r}^{2} L_{a v g}^{2}-\omega_{r}^{2} L_{d i f f}^{2}}\right) \cos \omega_{h} t\]

\[ =\left(\frac{\omega_{r} L_{d h}^{r} V_{i n j}}{\omega_{h}^{2} L_{d h}^{r} L_{q h}^{r}-\omega_{r}^{2} L_{d h}^{r} L_{q h}^{r}}\right) \cos \omega_{h} t \tag{18} \]

Small-signal current $(\tilde{\theta}_{r})$. By neglecting the \({\omega _r}\) terms and rearranging Equation (17), the current with \({\tilde \theta _r}\) is given by

\[ \tilde{i}_{q s h}^{\hat{r}}=\frac{z_{c h}^{\hat{r}} V_{i n j}}{z_{c h}^{\hat{r}}-z_{d h}^{\hat{r}} z_{q h}^{\hat{r}}} \cos \omega_{h} t=\frac{z_{d i f f} \sin 2 \tilde{\theta}_{r} V_{i n j}}{2 z_{d h} Z_{q h}} \cos \omega_{h} t \tag{19} \]

3.2 Q-axis Injection

The following q-axis injected vector was adopted:

\[ \left[\begin{array}{c}v_{d s h}^{\hat{r}} \\ v_{q s h}^{\hat{r}}\end{array}\right]=\left[\begin{array}{c}0 \\ V_{i n j} \cos \omega_{h} t\end{array}\right] \tag{20} \]

Similarly, substituting Equation (20) into Equation (13), we get,

\[ i_{d s h}^{\hat{r}}=\frac{z_{d i f f} \sin 2 \tilde{\theta}_{r}-\omega_{r} L_{a v g}+\omega_{r} L_{d i f f} \cos 2 \tilde{\theta}_{r}}{z_{d i f f}^{2}-z_{a v g}^{2}+\omega_{r}^{2} L_{d i f f}^{2}-\omega_{r}^{2} L_{a v g}^{2}} V_{i n j} \cos \omega_{h} t \tag{21} \]

Following the same procedure as above, the following current components can be obtained from Equation (21):

(i) Speed-dependent biased current

\[ \underline{i}_{d s h}^{\hat{r}}=\left(\frac{\left(\omega_{r} L_{a v g}-\omega_{r} L_{d i f f}\right) V_{i n j}}{z_{a v g}^{2}-\omega_{r}^{2} L_{d i f f}^{2}-z_{d i f f}^{2}+\omega_{r}^{2} L_{a v g}^{2}}\right) \cos \omega_{h} t= \]

\[ \left(\frac{-\omega_{r} L_{q h}^{r} V_{i n j}}{\omega_{h}^{2} L_{d h}^{r} L_{q h}^{r}-\omega_{r}^{2} L_{d h}^{r} L_{q h}^{r}}\right) \cos \omega_{h} t \tag{22} \]

(ii) Small-signal current $(\tilde{\theta}_{r})$

\[ \tilde{i}_{d s h}^{\hat{r}}=\frac{z_{c h}^{\hat{r}} V_{i n j}}{z_{c h}^{\hat{r}}-z_{d h}^{\hat{r}} z_{q h}^{\hat{r}}} \cos \omega_{h} t=\frac{z_{d i f f} \sin 2 \tilde{\theta}_{r} V_{i n j}}{2 z_{d h} Z_{q h}} \cos \omega_{h} t \tag{23} \]

3.2.1 Comments

(1) From Equations (18), (19), (22), and (23), it is observed the small-signal currents, \(\tilde {l}_{qsh}^{\hat r}{\rm{\;}}\)and \({\rm{\;}}\tilde {l}_{dsh}^{\hat r}\), for the two injection approaches are identical. However, \({\rm{\;}}\tilde {l}_{qsh}^{\hat r}\) of d-axis injection is much larger than \({\rm{\;}}\tilde {l}_{dsh}^{\hat r}\) of q-axis injection since the q-axis inductance is much lower than the d-axis inductance for its air-slot rotor structure shown in Figure 1. From Equations (18) and (22), the defined current ratio is found to be

\[ C R_{i} \triangleq \frac{\left|\underline{i}_{q s h}^{\hat{r}}\right|}{\left|\underline{i}_{d s h}^{\hat{r}}\right|}=\frac{L_{d h}^{r}}{L_{q h}^{r}>1} \]

(2) Hence, the q-axis injection scheme is suitable for a SynRM drive over a wide speed and load range, especially for EV drives. The numerical analysis of the experimental results will be presented in the subsection below, following the discussion on the experimental verification. The developed q-axis injected HFI EV SynRM drive will be presented in Section 4.

3.3 Experimental Verification

Let the established SynRM drive shown in Figure 1 be operated under the standard mode at \(\omega _r^* = \;2000\;{\rm{rpm}},\;{R_L} = \;16.67\;{\rm{\Omega }},{\rm{\;and}}\;\beta = {\beta _{o1}} = \;45^\circ \). The high-frequency signal is injected into the d- as well as the q-axis, respectively. In the HFI scheme shown in Figure 2(c), the amplitude and frequency of the injected voltage were set as\({\rm{\;}}{V_{inj}} = \;25\;{\rm{V\;}}\)and\({\rm{\;}}{f_h} = \;600{\rm{\;Hz}}\), and the band-pass filter (BPF) was chosen from experience as:

\[ H_{B P F}(s)=\frac{5.685 \times 10^{5} s^{2}}{s^{4}+1508 s^{3}+2.899 \times 10^{7} s^{2}+2.143 \times 10^{10} s+2.02 \times 10^{14}} \]

with the center frequency being 600 Hz.

3.3.1 D-axis Injection

First, the HF voltage was injected into the d-axis. The measured steady-state $\omega_{r}^{\prime},\left(i_{a s}^{\prime}, i_{d s}^{\prime}, i_{q s}^{\prime}\right)$, and the spectrum of $i_{a s}^{\prime}$ are shown in Figures 4(a) and 4(b). The corresponding q -axis current, $i_{q s}^{\prime}$ was sensed to yield the band-pass filtered $i_{q s h}^{\hat{r}}$, plotted in Figure 5(a), and its spectrum is shown in Figure 5(b).

Figure 4 Measured steady-state characteristics of the developed standard EV SynRM drive at \(\omega _r^* = \;2000\;{\rm{rpm}},\;{R_L} = \;16.67\;{\rm{\Omega }},{\rm{and}}\;\beta = {\beta _{o1}} = \;45^\circ \) with the high-frequency voltage injected in the d-axis. (a) $\omega_{r}^{\prime}, i_{a s}^{\prime}, i_{d s}^{\prime} and i_{q s}^{\prime}$, and $(\mathrm{b}) $the spectrum of $i_{a s}^{\prime}$.

Figure 5 Measured steady-state characteristics of the developed standard EV SynRM drive at $\omega_{r}^{*}=2000 \mathrm {rpm}, R_{L}=16.67 \Omega, $and $\beta=\beta_{o 1}=45^{\circ}$ with the high-frequency voltage injected in the d-axis. (a) $\omega_{r}^{\prime}$ and $i_{q s h}^{\hat{r}}$, and (b) the spectrum of $i_{q s h}^{\hat{r}} $.

3.3.2 Q-axis Injection

Next, the injection was applied to the q-axis. The measured steady-state characteristics are plotted in Figure 6 and Figure 7.

Figure 6 Measured steady-state characteristics of the developed standard EV SynRM drive at \(\omega _r^* = \;2000\;{\rm{rpm}},\;{R_L} = \;16.67\;{\rm{\Omega }}\;{\rm{and}}\;\beta = {\beta _{o1}} = \;45^\circ \) with the high-frequency voltage injected in the q-axis. (a) $\omega_{r}^{\prime}, i_{a s}^{\prime}, i_{d s}^{\prime} and i_{q s}^{\prime}$, and $(\mathrm{b})$ the spectrum of $i_{a s}^{\prime}$.

Figure 7 Measured steady-state characteristics of the deve loped standard EV SynRM drive at \(\omega _r^* = \;2000{\rm{\;rpm}},\;{R_L} = \;16.67\;{\rm{\Omega }},{\rm{and}}\;\beta = {\beta _{o1}} = \;45^\circ \) with the high-frequency voltage injected in the q-axis. (a) $\omega_{r}^{\prime} $and $i_{d s h}^{\hat{r}}$, and (b) the spectrum of\({\rm{\;}}i_{dsh}^{\hat r}\).

3.3.3 Comments

(i) From the measured results shown in Figures 5 and 7, it can be seen that the ratio of the magnitude of the q-axis current\({\rm{\;}}\left( {i_{qsh}^{\hat r}} \right){\rm{\;}}\)to the magnitude of the d-axis current\({\rm{\;}}\left( {i_{dsh}^{\hat r}} \right){\rm{\;}}\)is\({\rm{\;}}C{R_i} = 0.66/0.165 = \;4.0\).

(ii) For theoretical proof, the motor is running at $\omega_{r}^{\prime} = 2000 rpm$,\(\;{R_L} = \;16.67\;{\rm{\Omega \;}}\)and\({\rm{\;}}{\beta _o} = \;45^\circ \) and an injected frequency of\({\rm{\;}}{f_h} = \;600\;{\rm{Hz}}\). The steady-state current\({\rm{\;}}{i_{ds}} = {i_{qs}} = {\hat I_s}cos\;\beta \; = \;\)11 A is obtained from the results. The inductances at 11 A are\({\rm{\;}}{L_d} = \;44.6\;{\rm{mH}}\) and\({\rm{\;}}{L_q} = \;11.3\;{\rm{mH\;}}\)from the fitted curves in [5]. The magnitude of the q- and d-axis currents from Equations (18) and (22) are found to be

\[\underline{i}_{q s h}^{\hat{r}}=\left(13.08 \times 10^{-4}\right) V_{i n j} \cos \omega_{h} t \tag{24} \]

\[\underline{i}_{d s h}^{\hat{r}}=\left(3.314 \times 10^{-4}\right) V_{i n j} \cos \omega_{h} t \tag{25} \]

Hence, analytically, from Equations (24) and (25), \(C{R_i} = \;13.08/3.3314\; = \;44.6/11.3\; = \;3.947\). The signal ratio is also\({\rm{\;}}\left( {S{R_{iq}}} \right)/\left( {S{R_{id}}} \right) = C{R_i} = \;3.947\). Hence, the measured results are close to the analytic values, and the explored facts are thus confirmed.

3.4 Slotting Effect of the HFI Operation

3.4.1 Current Harmonics by Slotting Effect

The inverter-powered stationary armature winding facing the rotating slotted rotor can yield ripple currents. The dominant low-order current harmonics of the employed SynRM are\({\rm{\;}}h = \;\)17 and 19. Accordingly, the transformed d-axis and q-axis currents possess the ripples (\(h = {\rm{\;}}\)(17+19)/2 = 18) to affect the current control and the HFI operation. Hence, the key HFI parameters must be set appropriately, as will be described in Section 4.2.

3.4.2 Spectral Characteristics

During real operation, the injected frequency is fixed, whereas the d-q domain slot harmonic frequency\({\rm{\;}}{f_{sl}} = \;18{f_1}{\rm{\;}}\)is varied with the fundamental frequency, and its magnitude is increased with the load. As the slot harmonic frequency gradually approaches the injected frequency, the estimated rotor angle will exhibit oscillations, leading to unstable operation. Hence, the changed injection frequencies must be adopted to avoid the oscillating behavior of the rotor as\({\rm{\;}}{f_{sl}}{\rm{\;}}\)is close to the injected frequency\({\rm{\;}}{f_h}\).

3.5 Injected Axis Choice for Pulsating Voltage Injection

From the previous exploration, the following distinct facts for an HFI SynRM drive can be noted: (i) The d-q slot harmonic currents increase with the load at the frequency\({\rm{\;}}{f_{sl}} = \;18{f_1}\). (ii) The resultant currents increase with the speed,\({\rm{\;}}{\omega _r}\), with\({\rm{\;}}C{R_i} = L_{dh}^r/L_{qh}^r\; > 1\) and the current of d-axis injection is much larger. Hence, (iii) as the load and/or speed are increased, the d-axis injection scheme is prone to become unstable. Thus, for yielding a stable operation of the sensorless EV SynRM drive over a wide speed and load range, q-axis injection has been adopted in this work.

4. The Developed HFI Position Sensorless EV SynRM Drive

4.1 System Configuration and Operation Principle

The control scheme of the developed q-axis injected HFI sensorless SynRM drive is shown in Figure 2(c), and the proposed changed-frequency injection mechanism and the frequency distributions are shown in Figures 8(a) and 8(b). The HF voltage,\({\rm{\;}}v_{qsh}^* = {V_{inj}}t\;\left( V \right)\), with changed frequencies is injected into the q-axis, and the d-axis current is detected to yield the estimated rotor position and speed via proper signal processing. The small-signal current with \({\tilde \theta _r}{\rm{\;}}\)can be directly obtained from Equation (21) by neglecting the\({\rm{\;}}{\omega _r}{\rm{\;}}\)terms.

Figure 8 Frequency distribution in the proposed changed frequencies injection mechanism for (a)\({\rm{\;}}{f_1} < 41.67\;{\rm{Hz}}\) and (b)\({\rm{\;}}41.67{\rm{Hz}} \le {f_1} < 66.67\;{\rm{Hz}}\).

The small-signal current, as a function of\({\rm{\;}}{\tilde \theta _r}\), of the proposed q-axis injected HFI sensorless SynRM can be re-expressed from Equation (22) as follows [23]:

\[ \tilde{i}_{d s h}^{\hat{r}}=\left(\frac{z_{d i f f} \sin 2 \tilde{\theta}_{r}}{2 z_{d h} Z_{q h}} V_{i n j}\right) \cos \omega_{h} t \tag{26} \]

Generally,\({\rm{\;}}{\tilde \theta _r}{\rm{\;}}\)is very small under sensorless operation and\({\rm{\;}}{\omega _h}{L_{diff}} > > {r_{diff}}\). Thus, Equation (26) can be simplified to

\[ i_{d s h}^{\hat{r}}=\frac{V_{i n j}}{2}\left[\frac{-\omega_{h} L_{d i f f} \sin \omega_{h} t}{\omega_{h}^{2} L_{d h}^{r} L_{q h}^{r}}\right] \sin 2 \tilde{\theta}_{r} \tag{27} \]

Based on Equation (27), the rotor position and speed estimation scheme are shown in Figure 9(a). In order to yield the rotor position estimation error from Equation (27), a BPF was adopted to extract the high-frequency current,\({\rm{\;}}i_{dsh}^{\hat r}\), from the sensed current,\({\rm{\;}}{i'_{ds}}\). Then,\({\rm{\;}}i_{dsh}^{\hat r}{\rm{\;}}\)was multiplied by (\( - t\;\)) to yield

\[ i_{d s h}^{\hat{r}} \times\left(-\sin \omega_{h} t\right)=\frac{V_{i n j}}{2}\left[\frac{\omega_{h} L_{d i f f} \sin 2 \tilde{\theta}_{r}}{\omega_{h}^{2} L_{d h}^{r} L_{q h}^{r}}\right]\left[\frac{1-2 \cos \omega_{h} t}{2}\right] \tag{28} \]

The signal in Equation (28) is composed of a DC and a 2nd order harmonic component. Using an LPF, the DC component, $i_{\widetilde{\theta}_{r}}$, can be extracted as follows:

\[ i_{\widetilde{\theta}_{r}}=L P F\left[i_{q s h}^{\hat{r}} \times\left(-\sin \omega_{h} t\right)\right] \cong \frac{V_{i n j} L_{d i f f}}{4 \omega_{h}^{2} L_{d h}^{r} L_{q h}^{r}} \sin 2 \widetilde{\theta}_{r} \tag{29} \]

Further, applying linearization to Equation (29), we get,

\[ i_{\widetilde{\theta}_{r}} \approx \frac{V_{i n j} L_{d i f f}}{2 \omega_{h} L_{d h}^{r} L_{q h}^{r}} \tilde{\theta}_{r} \triangleq K_{e r r} \tilde{\theta}_{r}, K_{e r r} \triangleq \frac{V_{i n j} L_{d i f f}}{2 \omega_{h} L_{d h}^{r} L_{q h}^{r}} \tag{30} \]

Equation (30) indicates that $i_{\widetilde{\theta}_{r}}$ is proportional to the rotor position error, $\tilde{\theta}_{r}$, by a sensitivity factor, $K_{e r r}$. In the rotor position and speed estimation scheme shown in Figure 9(a), the disturbance signal is eliminated by a PI controller,

\[ G_{c \theta}(s)=K_{P \widehat{\omega}}+\frac{K_{I \widehat{\omega}}}{s} \tag{31} \]

to yield the estimated rotor speed. Then, the estimated rotor position is obtained by the integration process.

Figure 9 Rotor position and speed estimation scheme based on the q-axis injection scheme. (a) the estimation mechanism, (b) equivalent estimated rotor position tracking control block, and (c) equivalent block of (b) after adding PRECC.

To enhance the rotor position estimation performance, an estimated position robust error cancellation controller (PRECC) with the following weighting function was added:

\[ W_{\theta}(s)= \frac{W_{\theta}}{1+\tau_{\theta} s} \approx W_{\theta}, 0 \leq W_{\theta} < 1.0 \tag{32} \]

Similarly, the LPF time-constant,\({\rm{\;}}{\tau _\theta }\), and the weighting factor,\({\rm{\;}}{W_\theta }\), must be properly chosen to yield the compromised performance, considering the effects of system noise and the sluggish response of the observed rotor position.

The equivalent tracking control block representing the HFI sensorless control scheme can be presented by the block diagram shown in Figure 9(b), and its equivalent block obtained through derivation after applying the robust control is presented in Figure 9(c). The closed-loop tracking transfer function is found to be

\[ H_{d \theta}(s)=\frac{\hat{\theta}_{r}}{\theta_{r}}=\frac{K_{P \widehat{\omega}} K_{e r r}^{\prime} S+K_{I \widehat{\omega}} K_{e r r}^{\prime}}{s^{2}+K_{P \widehat{\omega}} K_{e r r}^{\prime} S+K_{I \widehat{\omega}} K_{e r r}^{\prime}} \tag{33} \]

with

\[ K_ {err}^{\prime} \equiv \frac{1}{1-W_{\theta}} K_{e r r} \tag{34} \]

From Equations (33) and (34), the following facts can be noted: (i) Since\({\rm{\;}}{H_{d\theta }}\left( 0 \right) = \;1\), there is no steady-state rotor position estimation error. (ii) By adding the robust control, the sensitivity factor\({\rm{\;}}{K_{err}}{\rm{\;}}\)becomes\({\rm{\;}}{K'_{err}} \equiv {K_{err}}/\left( {1 - {W_\theta }} \right)\), or equivalently, the estimated position error can be reduced by a factor of (\(1 - {W_\theta }\)). However, the effect of the system noise and the estimated response delay must be considered.

4.2 HFI Scheme System Parameters

(1) Injected voltage:\({\rm{\;}}{v_{qsh}} = {V_{inj}}{\rm{sin}}{\omega _h}t\;\left( {\rm{V}} \right),{\rm{\;}}{V_{inj}} = \;60\;{\rm{V}}\), and

\[ 0 \leq \omega_{r} \leq 1250 \mathrm{~rpm} \Rightarrow f_{h}=f_{h 1}=800 \mathrm{~Hz}\]

\[ 1250 \mathrm {~rpm} < \omega_{r} \leq 2000 \mathrm {~rpm} \Rightarrow f_{h}=f_{h 2}=600 \mathrm{~Hz} \]

(2) Rotor position estimation regulator:\(\;{G_{c\theta }}\left( s \right) = \;4 + \frac{{60}}{s}\)

Robust rotor position error cancellation controller:

\[ W_{\theta}(s)=\frac{W_{\theta}}{1+\tau_{\theta} s}=\frac{0.3}{1+0.00318 s} \]

(3) Signal processing filters:

\[LPF of i_{d s}^{\prime} and i_{q s}^{\prime}: H_{L F}(s)=1 /(1+0.00159 s)\].

LPF of \({\rm{\;}}{i_{{{\tilde \theta }_r}}}\):\(\;{H_{LF}}\left( s \right) = \;1/\left( {1 + 0.0053s} \right)\).

LPF of \({\rm{\;}}{\hat \omega _r}\):\({\rm{\;}}{H_{LF}}\left( s \right) = \;1/\left( {1 + 0.0159s} \right)\).

BPFs of\({\rm{\;}}i_{dsh}^{\hat r}\): The used ones under \({f_h} = {\rm{\;}}\)800 Hz and 600 Hz were:

\[ H_{B P F}(800 \mathrm{~Hz})=\frac{1.011 \times 10^{6} s^{2}}{s^{4}+2011 s^{3}+5.145 \times 10^{7} s^{2}+5.08 \times 10^{10} s+6.384 \times 10^{14}} \]

\[ H_{B P F}(600 \mathrm{~Hz})=\frac{5.685 \times 10^{5} s^{2}}{s^{4}+1508 s^{3}+2.899 \times 10^{7} s^{2}+2.143 \times 10^{10} s+2.02 \times 10^{14}} \]

4.3 Comparative Evaluation of the d- axis and q- axis Injected SynRM Drives

4.3.1 d-axis Injection Scheme

As explored above, for d-axis injection, the resultant current level of\({\rm{\;}}i_{qsh}^{\hat r}\;\)is much larger than that of q-axis injection. Hence, for stable operation, the key parameters of the HFI scheme were carefully set to the following values:

(1) Injected voltage:\({\rm{\;}}{v_{dsh}} = {V_{inj}}{\rm{sin}}{\omega _h}t\;\left( {\rm{V}} \right)\),\({\rm{\;}}{V_{inj}} = \;40\;{\rm{V\;}}\)and

\[ 850 \mathrm{~rpm} \leq \omega_{r} \leq 1250 \mathrm{~rpm} \Rightarrow f_{h}=f_{h 1}=450 \mathrm{~Hz} \]

\[ \omega_{r}<850 \mathrm{~rpm}, \omega_{r}>1250 \mathrm{~rpm} \Rightarrow f_{h}=f_{h 2}=600 \mathrm{~Hz} \]

(2) Rotor position estimation regulator:\({\rm{\;}}{G_{c\theta }}\left( s \right) = 4 + \frac{{40}}{s}\)

(3) BPFs of\({\rm{\;}}i_{qsh}^{\hat r}\): The BPFs adopted under\({\rm{\;}}{f_h} = {\rm{\;}}\)450 Hz and 600 Hz were:

\[ {H_{BPF}}\left( {450\;{\rm{Hz}}} \right) = \frac{{566}}{{{s^2} + 566s + 7.99\; \times \;{{10}^6}}} \]

\[ {H_{BPF}}\left( {600\;{\rm{Hz}}} \right) = \frac{{754}}{{{s^2} + 754s + 1.42\; \times \;{{10}^7}}} \]

4.3.2 Comparative Evaluation

At \({V_{dc}} = 550\;{\rm{V}},{\rm{\;and}}\;{R_L} = \;33.33\;{\rm{\Omega }}\), Figures 10(a) to 10(c) show the measured values of \(\omega _r^*\;and\;{\hat \omega _r}\) as a function of time and the estimated rotor position error\({\rm{\;}}{\theta _{err}}\left( { \buildrel \Delta \over = - {{\tilde \theta }_r} = {{\hat \theta }_r} - {\theta _r}} \right){\rm{\;}}\)of the developed q-axis injected HFI sensorless SynRM drive resulting from the preset speed pattern\(\;{\rm{of}}\;\omega _r^* = \;0 \to 2000 \to 0\;{\rm{rpm\;}}\)and acceleration/deceleration rates of 100 rpm/s with\({\rm{\;}}\left( {{W_\theta } = \;0,\;{W_\omega } = \;0} \right),{\rm{\;}}\left( {{W_\theta } = \;0.3,{\rm{\;}}{W_\omega } = \;0.0} \right),{\rm{\;}}\)and\({\rm{\;}}\left( {{W_\theta } = \;0.3,{\rm{\;}}{W_\omega } = \;0.4} \right).{\rm{\;}}\)From the figures, the gradual decrease in\({\rm{\;}}{\theta _{err}}{\rm{\;}}\)and\({\rm{\;}}{\varepsilon _\omega }\left( {\omega _r^* - {{\hat \omega }_r}} \right){\rm{\;}}\)after adding\({\rm{\;}}{W_\theta }{\rm{\;}}\)and\({\rm{\;}}{W_\omega }{\rm{\;}}\)can be observed.

Figure 10 Measured time variation of\({\rm{\;}}\omega _r^*,{\hat \omega _r},\;and\;{\theta _{err}}\) of the established q-axis injected HFI sensorless EV SynRM drive as the speed command changes in the order\({\rm{\;}}\omega _r^* = \;0 \to 2000 \to 0\;{\rm{rpm}}\), with the acceleration/deceleration rates being 100 rpm/s at \({V_{dc}} = \;550\;{\rm{V}},\;{R_L} = \;33.33\;{\rm{\Omega }},{\rm{\;}}\)and\({\rm{\;}}\beta = {\beta _o}\). (a) results for\({\rm{\;}}{W_\theta } = \;0,{W_\omega } = \;0\), (b) results for\({\rm{\;}}{W_\theta } = \;0.3,{\rm{\;}}{W_\omega } = \;0{\rm{\;}}\), and (c) results for\({\rm{\;}}{W_\theta } = \;0.3,{\rm{\;}}{W_\omega } = \;0.4\).

Figures 11(a) and 11(b) show the measured values of \(\omega _r^*,{\hat \omega _r}\) and\({\rm{\;}}{\theta _{err}}{\rm{\;}}\)of the d-axis and q-axis injected SynRM drives at \({V_{dc}} = \;550{\rm{\;V}}\;{\rm{and}}\;{R_L} = \;33.33\;{\rm{\Omega }}\). All normal operations can be seen, and the case of q-axis injected SynRM drives yields smaller\({\rm{\;}}{\theta _{err}}\).

Figure 11 Measured time variation of \(\omega _r^*,{\hat \omega _r},\;and\;{\theta _{err}}\) of the established HFI sensorless EV SynRM drive as the speed command changes in the order\({\rm{\;}}\omega _r^* = \;0 \to 2000 \to 0\;{\rm{rpm}}\), with the acceleration/deceleration rates being 100 rpm/s at \({V_{dc}} = \;550{\rm{\;V}},\;{R_L} = \;33.33\;{\rm{\Omega }},{\rm{\;and}}\;\beta = {\beta _o}\). (a) results for d-axis injection, and (b) results for q-axis injection.

The results of d-axis injection when the load is further increased to\({\rm{\;}}{R_L} = 32\;{\rm{\Omega \;}}\)is shown in Figure 12(a). From the figure, it can be seen that \({\theta _{err}}{\rm{\;}}\)becomes worse compared to that observed from Figure 11(a). Figures 11(a) and 12(a) also indicate that \({\theta _{err}}{\rm{\;}}\)increases with speed and load, as explored theoretically. As the load is slightly increased to\({\rm{\;}}{R_L} = \;31.247\;{\rm{\Omega }}\), the d-axis injected SynRM drive fails to operate, as can be observed from Figure 12(b). Hence, q-axis injection was adopted for further measured results.

Figure 12 Measured time variation of \(\omega _r^*,{\hat \omega _r},\;{\rm{and}}\;{\theta _{err}}\) of the established d-axis injected HFI sensorless EV SynRM drive as the speed command changes in the order\({\rm{\;}}\omega _r^* = \;0 \to 2000 \to 0\;{\rm{rpm}}\), with the acceleration/deceleration rates being 100 rpm/s at \({V_{dc}} = \;550{\rm{\;V}}\;{\rm{and}}\;\beta = {\beta _o}\). (a) results for\({\rm{\;}}{R_L} = \;32{\rm{\;\Omega }}\), and (b) results for\({\rm{\;}}{R_L} = \;31.247\;{\rm{\Omega }}\).

Figures 13(a) and 13(b) show the measured time variation of \(\omega _r^*,{\hat \omega _r}\), and\({\rm{\;}}{\theta _{err}}{\rm{\;}}\)of the developed q-axis injected SynRM drive with \({W_\theta } = \;0.3,{\rm{\;}}{W_\omega } = \;0.4\), and\({\rm{\;}}{V_{dc}} = \;550\;{\rm{V\;}}\)for two different loads, respectively. Smoother operation and satisfactory driving performance can be observed from the results.

Figure 13 Measured time variation of \(\omega _r^*,{\hat \omega _r},{\rm{and}}\;{\theta _{err}}\) of the established q-axis injected HFI sensorless EV SynRM drive as the speed command changes in the order\({\rm{\;}}\omega _r^* = \;0 \to 2000 \to 0{\rm{\;rpm}}\), with the acceleration/deceleration rates of 100 rpm/s at \({V_{dc}} = \;550\;{\rm{V}}\;{\rm{and}}\;\beta = {\beta _o}\). (a) results for\({\rm{\;}}{R_L} = \;25\;{\rm{\Omega }}\) and (b) results for\({\rm{\;}}{R_L} = \;16.67\;{\rm{\Omega }}\).

4.4 Operation Characteristics of the Developed q- axis Injected EV SynRM Drive

4.4.1 Starting Process

Figure 14 shows the measured time variation of\({\rm{\;}}{\theta _r},{\hat \theta _r}\), and\({\rm{\;}}{\theta _{err}}{\rm{\;}}\)of the developed q-axis injected HFI position sensorless EV SynRM drive during the starting process with the speed rising rate of 100 rpm/s, \({V_{dc}} = \;550\;{\rm{V}},\;{R_L} = \;16.67\;{\rm{\Omega }},{\rm{\;and}}\;\beta = {\beta _o}\). The results show the smooth starting process.

Figure 14 Measured time variation of \({\theta _r},{\hat \theta _r},{\rm{\;and}}\;{\theta _{err}}\) during starting process of the developed sensorless SynRM drive with the speed rising rate of 100 rpm/s, \({V_{dc}} = \;550\;{\rm{V}},\;{R_L} = \;16.67{\rm{\;\Omega }},{\rm{\;and}}\;\beta = {\beta _o}\).

4.4.2 Steady- state Characteristics

The measured time variation of (\({\theta _r},{\hat \theta _r},{\theta _{err}}\)), (\(\omega _r^*,{\hat \omega _r}\)), and $(i_{a s}^{*}, i_{a s}^{\prime})$ of the developed drive is presented in Figures 15(a) and 15(b) for the speed command of\({\rm{\;}}\omega _r^* = \;50\;{\rm{rpm\;}}\)at\({\rm{\;}}{V_{dc}} = \;550\;{\rm{V}},\;{R_L} = \;16.67\;{\rm{\Omega }},\;and\;\beta = {\beta _o}\). For the same set of parameters, the measured results for\({\rm{\;}}\omega _r^* = \;2000\;{\rm{rpm\;}}\)are plotted in Figure 16 and the results exhibit satisfactory sensorless controlled characteristics. In addition, accurately estimated\({\rm{\;}}{\hat \theta _r}\), close current, and speed command tracking behavior can be observed.

Figure 15 Measured steady-state characteristics of the developed sensorless EV SynRM drive for \({\hat \omega _r} = \;50\;{\rm{rpm}},{V_{dc}} = \;550\;{\rm{V}},{R_L} = \;16.67\;{\rm{\Omega }},{\rm{\;and}}\;\beta = {\beta _o}\). (a) measured time variation for\({\rm{\;}}{\theta _r},{\hat \theta _r},{\rm{and\;}}{\theta _{err}}\), and (b) the corresponding variation for (\(\omega _r^*,{\hat \omega _r}\)) and $(i_{a s}^{*}, i_{a s}^{\prime})$.

Figure 16 Measured steady-state characteristics of the developed sensorless EV SynRM drive for \({\hat \omega _r} = \;2000{\rm{\;rpm}},\;{V_{dc}} = \;550\;{\rm{V}},{R_L} = \;16.67\;{\rm{\Omega }},{\rm{\;and}}\;\beta = {\beta _o}\). (a) results for\({\rm{\;}}{\theta _r},{\hat \theta _r},and\;{\theta _{err}}\) and (b) results for (\(\omega _r^*,{\hat \omega _r}\)) and $(i_{a s}^{*}, i_{a s}^{\prime})$.

4.4.3 Dynamic Response

Figure 17(a) show the measured speed tracking response of the developed EV drive by PI control without and with SRECC for a speed command change of\({\rm{\;}}\Delta \omega _r^* = \;100\;{\rm{rpm\;}}\)at\({\rm{\;}}\omega _r^* = \;1900{\rm{\;rpm}},{V_{dc}} = \;550\;{\rm{V}},\;{R_L} = \;33.9\;{\rm{\Omega }},{\rm{and}}\;\beta = {\beta _o}\). Figure 17(b) shows the measured results corresponding to a step resistance change of\({\rm{\;}}{R_L} = \;51\;{\rm{\Omega }} \to 33.9\;{\rm{\Omega }}\) and\({\rm{\;}}\omega _r^* = \;2000\;{\rm{rpm}},\;{V_{dc}} = \;550\;{\rm{V}},{R_L} = \;51\;{\rm{\Omega }},{\rm{and}}\;\beta = {\beta _o}\). The results indicate good tracking and regulation dynamic response and the effectiveness of applying the robust control.

Figure 17 Measured values of\({\rm{\;}}\left( {\omega _r^*,{{\hat \omega }_r}} \right),\;{\theta _{err}},{\rm{\;and}}\;{\hat I_s}{\rm{\;}}\)of the established EV SynRM drive corresponding to (a) a step speed command change of 100 rpm and \(\omega _r^* = \;1900\;{\rm{rpm}},{V_{dc}} = \;550{\rm{\;V}},{R_L} = \;33.9\;{\rm{\Omega }},{\rm{and}}\;\beta = {\beta _o}\) and (b) a step load resistance change\({\rm{\;}}{R_L} = \;50.1\;{\rm{\Omega }} \to 33.9\;{\rm{\Omega \;}}\)at\({\rm{\;}}\omega _r^* = \;2000{\rm{\;rpm}},{V_{dc}} = \;550{\rm{\;V}},\;{R_L} = \;51{\rm{\;\Omega }},{\rm{and}}\;\beta = {\beta _o}\).

4.4.4 Acceleration/Deceleration and Reversible Operations

Initially, the motor is stably operated at\({\rm{\;}}\omega _r^* = \;2000{\rm{\;rpm}},\;{V_{dc}} = \;550\;{\rm{V}},{R_L} = \;25\;{\rm{\Omega }},{\rm{and}}\;\beta = {\beta _o}\). Now let the ramp speed command change be set to\({\rm{\;}}\omega _r^* = \;2000\;{\rm{rpm}} \to 0 \to - 2000{\rm{\;rpm\;}}\)with the falling rate of 100 rpm/s. The measured values of (\({\theta _r},{\hat \theta _r}\)) and (\(\omega _r^*,{\hat \omega _r},{\hat I_s}\)) for these settings are plotted in Figure 18.

Figure 18 Measured results of the established sensorless EV SynRM drive at \({V_{dc}} = \;550\;{\rm{V}},{R_L} = \;25\;{\rm{\Omega }},{\rm{and}}\;\beta = {\beta _o}\) for the ramp command change of\({\rm{\;}}\omega _r^* = \;2000\;{\rm{rpm}} \to 0 \to - 2000{\rm{\;rpm}}\). (a) measured values of (\({\theta _r}, {\hat \theta _r}\)) and \({\rm{\;}}{\theta _{err}}\), and (b) measured values of \(\omega _r^*,{\hat \omega _r},{\rm{\;and}}\;{\hat I_s}\).

Let the reversible speed command be set to\({\rm{\;}}\omega _r^* = \;0 \to 2000{\rm{\;rpm}} \to - 2000{\rm{\;rpm}} \to 0\;{\rm{rpm\;}}\)with a changing rate of 100 rpm/s. The measured values of\({\rm{\;}}\left( {\omega _r^*,{{\hat \omega }_r}} \right),\;{\hat I_s},{\rm{and\;}}{\theta _{err}}{\rm{\;}}\)at\({\rm{\;}}{V_{dc}} = \;550{\rm{\;V}},\;{R_L} = \;25\;{\rm{\Omega }},{\rm{\;and}}\;\beta = {\beta _o}{\rm{\;}}\)are presented in Figure 19. From the results, it can be seen that the characteristics of smooth speed reversible operation and good speed tracking are preserved by the developed SynRM drive.

Figure 19 Measured values of \(\left( {\omega _r^*,{{\hat \omega }_r}} \right),{\hat I_s},\;and\;{\theta _{err}}\) of the established sensorless EV SynRM drive at \({V_{dc}} = \;550{\rm{\;V}},{R_L} = \;25\;{\rm{\Omega }},{\rm{and}}\;\beta = {\beta _o}\) for the ramp command change in the order\({\rm{\;}}\omega _r^* = \;0 \to 2000{\rm{\;rpm}} \to - 2000{\rm{\;rpm}} \to 0\;{\rm{rpm}}\).

4.4.5 Regenerative Braking

Since the total moment of inertia of the established SynRM drive is not sufficiently large, the maximum speed is increased to 2500 rpm when applying regenerative braking. The SynRM drive is stably operated at\({\rm{\;}}{V_{dc}} = \;550\;{\rm{V}},\;{R_L} = \;150\;{\rm{\Omega }},\;\beta = {\beta _o},{\rm{and}}\;\;\omega _r^*\; = \;2500\;{\rm{rpm}}\) and Figures 20(a) and 20 (b) show the measured values of $(\left(\omega_{r}^{*}, \omega_{r}^{\prime}\right), \hat{I}_{s})$ and (\({v_b}\),\({v_{dc}}\),\({\rm{\;}}{i_b}\)) for a ramp speed command change with a deceleration rate of 500 rpm/s. The negative value of\({\rm{\;}}{i_b}{\rm{\;}}\)verifies the successful implementation of the regenerative braking operation.

Figure 20 Measured results of the sensorless EV SynRM drive for a ramp speed command change from 2500 rpm with the deceleration rate of 500 rpm/s at \({V_{dc}} = \;550\;{\rm{V}},{R_L} = \;150\;{\rm{\Omega }},{\rm{and}}\;\beta = {\beta _o}\). (a) measured values for\({\rm{\;}}\left( {\omega _r^*,{{\omega '}_r}} \right){\rm{\;}}\)and\({\rm{\;}}{\hat I_s}\), and (b) measured values for \({v_b}\),\({v_{dc}}\), and\({\rm{\;}}{i_b}\).

4.4.6 ECE15 Speed Pattern

The measured results of the developed sensorless EV SynRM drive under the programmed ECE15 speed pattern for\({\rm{\;}}\beta = {\beta _o}{\rm{\;}}\)(the results for\({\rm{\;}}\beta = \;{45^ \circ }\;\)have been neglected here) are shown in Figure 21(a) and the corresponding energy consumption of the battery in the two cases of \(\beta = {\beta _o}{\rm{\;}}\)and\({\rm{\;}}\beta = \;{45^ \circ }\) are compared in Figure 21(b). The results show that by applying\({\rm{\;}}\beta = {\beta _o}\), less energy is consumed.

Figure 21 Efficiency assessment for the developed q-axis infected HFI sensorless SynRM drive. (a) measured values of $\omega_{r}^{*}, \omega_{r}^{\prime}, v_{d c}, v_{b}, \mathrm{i}_{\mathrm{b}}$, and $P_{b}$ for a programmed ECE15 speed pattern with a changing rate of 100 rpm/s at \({R_L} = \;25\; {\rm{\Omega }}\) and \({\rm{\;}} \beta = {\beta _o}\). (b) \({\rm{\;}}{E_b} = \smallint {P_b}dt{\rm{\;}}\) corresponding to \({\rm{\;}} \beta = \;45^\circ {\rm{\;}}\)and\({\rm{\;}}\beta = {\beta _o}{\rm{\;}}\) corresponding to the same ECE15 speed pattern.

4.4.7 Efficiency Assessment

For the same condition, i.e., \({V_{dc}} = \;550\;{\rm{V}},{R_L} = \;16.67\;{\rm{\Omega }},{\rm{\;and}}\;\beta = {\beta _o}\), the measured steady-state characteristics of the established sensorless EV SynRM drive and the standard drive are compared in Table 1 for various speeds. The efficiencies are defined as:\({\rm{\;}}{\eta _{mg}} \equiv {P_g}/{P_m},{\eta _m} \equiv \sqrt {{\eta _{mg}}} \). As can be seen from the table, the efficiencies of the position sensorless SynRM drive are comparable to those of the standard SynRM drive.

Table 1 Measured powers and efficiencies of the HFI position sensorless SynRM drive and the standard drive at \({V_{dc}} = \;550\;{\rm{V}},{R_L} = \;16.67\;{\rm{\Omega }},{\rm{\;and\;}}\beta = {\beta _o}\) for various speeds.

5. Conclusions

This study presents a high-efficiency sensorless EV SynRM drive using a pulsating sinewave HF voltage injection. Through analytic and experimental explorations and by comparing the characteristics of the d-axis and q-axis injected HFI sensorless controlled SynRM drives, the q-axis injection was adopted. Experimental observations indicated that the d-axis injected mechanism could not be operated stably above a certain load level. Hence, only the q-axis injection mechanism was tested further. Because of the influence of speed-and load-dependent slot harmonic effects on the sensorless control behavior, the changed injection frequency with rotor speed was proposed. The slotting effects were also considered in the current controller design. It was shown that the EV SynRM drive can be operated under wider speed and heavier load ranges with the designed feedback and robust controllers. To achieve maximum efficiency, ACS was applied to conduct a proper commutation shift of SynRM. The measured results indicated that the developed sensorless EV drive exhibits stable operation over a wide speed and load range, and the EV drive exhibits good driving performance in terms of acceleration/deceleration, reversible, and regenerative braking operations. The experimental demonstration of the high energy conversion efficiencies being comparable to the standard drive was also presented in this study.

Author Contributions

G. Vijay Kumar: Main author involving the measurements and the paper writing; Min-Ze Lu: Assisting the author and doing the proofreading; Chang-Ming Liaw: Advisor, giving suggestion and revisions for research results and writing.

Funding

No organization or foundation that funded this research.

Competing Interests

The authors have declared that no competing interests exist.