Speed Range Extension of Dual-Stator PM Machine Using Multi-Mode Winding Switching Strategy

Abstract

In this paper, a novel winding switching (WS) strategy is proposed for the speed range extension of a dual-stator permanent magnet machine (DS-PMM), which can achieve simple and effective dynamic mode conversion over an entire operating region. Two types of WS circuits with an inverter and two switch groups were first designed to enable the winding reconfiguration of the machine, which could operate in three modes. The WS principle was then elucidated by introducing simplified equivalent circuits. Besides, the torque–speed curves of the machine under different operating modes were analyzed, based on the mathematical model. A speed-based WS controller was, subsequently, designed to generate the WS control signal and realize the multi-mode operation according to real-time operating conditions. The feasibility of the proposed WS strategy for extending the speed range of the DS-PMM was, finally, verified by experiments.

1. Introduction

Due to the advantages of high-power density and high efficiency, permanent magnet (PM) machines have been widely used in many industrial and traction applications [1,2]. However, the speed range of conventional PM machines is relatively limited, due to the non-adjustable magneto-motive force (MMF) of rare-earth PMs, having very high coercive forces [3]. As an example, the machine for electric vehicles commonly requires a constant power operating range of around 3–4 times the base speed [1]. The most frequently used method for solving this issue is applying a negative d-axis flux weakening (FW) current to reduce the back-electric motive force (back-EMF), which inevitably leads to extra copper loss and potential demagnetization risk of PMs. Other FW concepts have been introduced to extend the speed range of PM machines, such as hybrid excitation [4,5], memory machines [6,7], variable flux leakage [8], mechanical-variable-flux [9], and winding switching (WS) [10,11,12,13,14,15,16,17,18,19,20,21]. Amongst them, the WS strategy does not require a change in the machine structure, but only an external circuit to reconfigure the winding connection, which has, in theory, good compatibility to all PM machines.

The existing WS strategies for PM machines can be classified as series/parallel switching [10], wye/delta switching [11], and winding turns changing [12]. A WS strategy was applied to memory machines in [13] through the reconfiguration of the armature windings and the magnetizing coils. In [14], a WS strategy was utilized to stabilize the output voltage for a wind-photovoltaic hybrid generation system. In [15,16,17], the stator winding groups of PM machines were rearranged as various connection types by power electronic devices. In [15], a low-voltage inverter-fed MATRIX machine was proposed to expand the operating range and high efficiency area. Six winding groups were connected to inverters independently, which enabled the machine to operate at four modes by changing the winding configuration. The proposed circuit topology could avoid surge voltage during the WS process. Additionally, the torque reduction, due to flux linkage variation, can be compensated by simultaneously changing the applied current. In [16,17], a WS strategy was proposed to extend the speed range of a six phase non-salient pole PM machine by multi-mode operation. In the cumulative mode, each winding group of the machine was controlled by a three-phase inverter to provide the maximum torque. In the differential mode, the machine was controlled by an open winding configuration and the resultant MMF could be considered as the difference between the MMFs of two winding groups, which enabled the machine to operate at a higher speed. In addition, the proposed WS strategy utilized several thyristors and current regulators to avoid voltage spikes during the WS process. In [18], the winding turns changing was combined with the WS circuit given in [16] to improve the efficiency in a wide speed range and avoid the low torque in the differential mode. Besides, an alternative WS circuit with a single inverter and six bidirectional switches was proposed in [19] to realize the cumulative/differential switching as well. This WS circuit was improved in [20] by combining the cumulative/differential and wye/delta switching strategies together, achieving multi-mode operation.

As discussed above, the existing WS circuit topologies can effectively extend the speed range of PM machines. However, the design and optimization of the reconfigurable armature windings in the same stator still have many constraints, which may limit the resultant WS dynamic performance. The further improvement of the WS performance requires more complex circuits [18,19,20]. Additionally, the back-EMF distortion exists in some WS strategies, which increases torque ripples [16,17]. There is no related research about the WS controller design to automatically produce the WS signal according to the real-time operating conditions of PM machines.

This paper aims to propose a novel WS strategy based on the research work in [21] to extend the speed range of a dual-stator PM machine (DS-PMM) without applying negative d-axis current. The WS circuit and controller can be applied or provide design guidance for other WS strategies and specific applications. The investigated DS-PMM has an improved torque density [22]. When the WS strategy is applied, the back-EMF distortion from winding connection changes can be alleviated, since the inner winding and outer winding share the same phasor position. Compared with [21], another winding switching circuit is proposed for the DS-PMM, and the machine can operate with more types of winding connections. The mathematical model of the machine using WS strategy is established to reveal the characteristics of the machine at all the operating modes. A speed-based WS controller is proposed to execute the WS process. This paper is organized as follows. Firstly, the machine topology and the designed WS circuits are introduced, respectively. The principle of the designed WS circuits is illustrated via the simplified equivalent circuits of the machine windings in different modes. In addition, the torque–speed characteristics for the machine under different modes are analytically deduced to evaluate the performance of speed range extension and obtain the switching speed. A speed-based WS controller is then designed to generate the WS control signal and realize the multi-mode operation according to real-time operating conditions. A WS controller is developed to achieve simple and effective dynamic mode switching over an entire operating region. Finally, some experimental measurements on the DS-PMM prototype are carried out to validate the feasibility of the proposed strategy for the speed range extension.

2. Machine Topology and Winding Switching Principle

2.1. The Topology of the Investigated DS-PMM

The topology of the investigated DS-PMM is presented in Figure 1a, which is geometrically characterized by two different stators [22]. The outer stator has a similar structure to the conventional fractional-slot PM machine, and the inner stator is composed of six spoke-type PMs and auxiliary armature windings. The geometric conflicts between PM and armature winding existing in conventional DS-PMM counterparts can be alleviated in this machine. Meanwhile, the inner winding can further improve the output torque. Since the outer windings and inner windings essentially have the same phasor position, the back-EMF distortion from winding connection changes can be alleviated significantly. Figure 1b shows the assemblies of the manufactured DS-PMM prototype, which includes an inner stator, a rotor, and an outer stator. The main parameters of the prototype are tabulated in

Table 1. Main parameters of the inner and outer windings.

Symbol	Quantity	Value
R1	Phase resistance of the outer winding	0.64 Ohm
R2	Phase resistance of the inner winding	0.55 Ohm
ψm1	PM flux linkage of the outer winding	0.009 Wb
ψm2	PM flux linkage of the inner winding	0.0129 Wb
N1	Outer winding turns	84
N2	Inner winding turns	72

. It can be found that the asymmetrical structure and the separately designed winding turns cause the outer and inner windings to have different PM flux linkages.

2.2. The Winding Switching Circuits

Two WS circuits for speed range extension of the DS-PMM are illustrated in Figure 2, which both include a three phase H-bridge inverter and two switch groups. Additionally, Figure 3 and Figure 4 exhibit different resultant winding configurations based on these two types of WS circuits, respectively. In the WS circuit type I, if all the switches in groups I and II are turned to point 0, the inner and outer windings are connected as shown in Figure 3a, which is termed T1M1. In this case, the PM flux linkages of the machine can be regarded as the sum of the two groups of windings, which can produce high torque at low speeds. If all the switches in group I are turned to point 0 and the switches in group II are turned to point 1, the inner windings are separately utilized, as shown in Figure 3b, which is termed T1M2. In this case, the equivalent PM flux linkage of the machine can be simply regarded as that of the inner winding. On the contrary, if all the switches in group I are turned to point 1, and the switches in group II are turned to point 0, the outer winding is separately utilized, as shown in Figure 3c, which is termed T1M3. Due to the asymmetrical structure of the investigated DS-PMM, the machine at T1M2 and T1M3 exhibit distinguished characteristics, which can be utilized to extend the operation region. In the WS circuit type II, if all the switches in group I are turned to point 0, and the switches in group II are turned to point 1, the inner and outer windings are connected as shown in Figure 4a, which is termed T2M1. In this case, the PM flux linkages of the machine can be regarded as the sum of the two groups of windings. If all the switches are turned to the same point, only the inner winding is utilized as shown in Figure 4b, which is termed T2M2. The PM flux linkage of the machine can be simply regarded as that of the inner winding. In addition, if all the switches in group I are turned to point 1 and the switches in group II are turned to point 0, the inner and outer windings are connected as shown in Figure 4c, which is termed T2M3. In this case, the PM flux linkages of the machine can be regarded as the difference of the two groups of windings, so that the FW can be achieved to extend the speed range.

2.3. Mathematical Model Analysis

According to the characteristics of the investigated DS-PMM, the inner and outer windings of the machine can be considered as two separated PM machines. Similar to the non-salient PM machine, the steady voltage equation of the inner and outer windings can be expressed in the same formation as:

$$\{\begin{array}{l}{u}_{dx}=R_x{i}_{dx}-\omega L_x{i}_{qx}\\ u_{qx}=R_x{i}_{qx}+\omega L_x{i}_{dx}+\omega {\psi }_{mx}\end{array},x=\alpha ,\beta$$

(1)

where the subscript x = α and β represents the outer winding and inner winding, respectively, R and L are phase resistance and inductance, u_d and u_q are d-axis and q-axis voltages, respectively, i_d and i_q are d-axis and q-axis currents, respectively, ω is electrical angular speed, and ψ_m is PM flux linkage. Since the two windings share the same phasor position and the induced voltages have no phase difference, the resultant voltage of the machine with WS circuit can be considered as the linear combination of the voltages of the outer and inner windings, expressed as:

$$\{\begin{array}{l}{u}_{d-ws}=c_{\alpha }{u}_{d\alpha }+c_{\beta }{u}_{d\beta }\\ u_{q-ws}=c_{\alpha }{u}_{q\alpha }+c_{\beta }{u}_{q\beta }\end{array}$$

(2)

where the WS factors c_α and c_β are dependent on the winding connections. By substituting (1) to (2), the steady voltage equation of the machine with WS circuit can be generally expressed as [15]:

$$\{\begin{array}{l}{u}_{d-ws}=\left(c_{\alpha }{R}_{\alpha }+c_{\beta }{R}_{\beta }\right)i_{d-ws}-\omega \left(c_{\alpha }{L}_{\alpha }+c_{\beta }{L}_{\beta }\right)i_{q-ws}\\ u_{q-ws}=\left(c_{\alpha }{R}_{\alpha }+c_{\beta }{R}_{\beta }\right)i_{q-ws}+\omega \left(c_{\alpha }{L}_{\alpha }+c_{\beta }{L}_{\beta }\right)i_{d-ws}+\omega \left(c_{\alpha }{\psi }_{m\alpha }+c_{\beta }{\psi }_{m\beta }\right)\end{array}$$

(3)

Assuming that the equivalent resistance R_ws, inductance L_ws, and PM flux linkage ψ_m-ws of the machine at each mode satisfy:

$$\{\begin{array}{l}{R}_{ws}=c_{\alpha }{R}_{\alpha }+c_{\beta }{R}_{\beta }\\ L_{ws}=c_{\alpha }{L}_{\alpha }+c_{\beta }{L}_{\beta }\\ {\psi }_{m-ws}=c_{\alpha }{\psi }_{m\alpha }+c_{\beta }{\psi }_{m\beta }\end{array}$$

(4)

Then, (3) can be rewritten as:

$$\{\begin{array}{l}{u}_{d-ws}=R_{ws}{i}_{d-ws}-\omega L_{ws}{i}_{q-ws}\\ u_{q-ws}=R_{ws}{i}_{q-ws}+\omega L_{ws}{i}_{d-ws}+\omega {\psi }_{m-ws}\end{array}$$

(5)

It can be found that the general voltage equation of the machine with WS circuit is the same as that of conventional PM machines. Besides, the machine at each mode can be considered as an individual PM machine with different parameters, which are related to the WS factors c_α and c_β.

Table 2. Characteristics of each mode using WS circuits.

WS Circuit	Mode	S1S2S3S4S5S6	ψm (Wb)	(cα, cβ)
Type I	T1M1	000000	0.022	(1, 1)
	T1M2	000111	0.0129	(1, 0)
	T1M3	111000	0.009	(0, 1)
Type II	T2M1	000111	0.022	(1, 1)
	T2M2	000000 (111111)	0.0129	(1, 0)
	T2M3	111000	0.0039	(1, −1)

presents the main characteristics of the studied machine using the above-mentioned two kinds of WS circuits, including the switch state, the resultant PM flux linkage, and the WS factors (c_α, c_β) of each mode.

3. The WS Strategy for Speed Range Extension

Based on the above analysis in Section 2, the proposed two types of WS circuits both enabled the studied DS-PMM to operate at three modes. Since the machine at each mode can be considered as an individual PM machine, the voltage equation of each mode could be expressed as:

$$\{\begin{array}{l}{u}_{di}=R_i{i}_{di}-{\omega }_i{L}_i{i}_{qi}\\ u_{qi}=R_i{i}_{qi}+{\omega }_i{L}_i{i}_{di}+\omega {\psi }_{mi}\end{array},i=1,2,3$$

(6)

where the subscript i = 1, 2 and 3 represent the operating modes M1, M2 and M3 of the machine when the WS circuit is utilized. If the i_d = 0 control method is applied to the machine at each mode, (6) can be simplified as:

$$\{\begin{array}{l}{u}_{di}=-{\omega }_i{L}_i{i}_{qi}\\ u_{qi}=R_i{i}_{qi}+{\omega }_i{\psi }_{mi}\end{array}$$

(7)

The operating region of the machine at each mode is always restricted by the current and voltage limitations of the connected inverter as:

$$\{\begin{array}{l}{i}_{qi}\le I_{\lim }\\ {\left({\omega }_i{L}_i{i}_{qi}\right)}^2+{\left(R_i{i}_{qi}+{\omega }_i{\psi }_{mi}\right)}^2\le U_{\lim }^2\end{array}$$

(8)

When the machine operates at a low speed within the voltage limitation, the maximum output torque of each mode on the operating region boundary only relies the current limitation as:

$$T_i=1.5p{\psi }_{mi}{I}_{\lim }$$

(9)

where p indicates the number of pole pairs. However, due to the voltage limitation, the output torque in (9) can only be maintained below the base speed, where the current and voltage limitations are both reached as:

$$\{\begin{array}{l}{i}_{qi}=I_{\lim }\\ {\left({\omega }_i{L}_i{i}_{qi}\right)}^2+{\left(R_i{i}_{qi}+{\omega }_i{\psi }_{mi}\right)}^2=U_{\lim }^2\end{array}$$

(10)

Then the base speed at each mode can be obtained by solving (10) and expressed as:

$${\omega }_{bi}=\frac{-R_i{\psi }_{mi}{I}_{\lim }+\sqrt{U_{\lim }^2\left(L_i^2{I}_{\lim }^2+{\psi }_{mi}^2\right)-L_i^2{R}_i^2{I}_{\lim }^4}}{\left(L_i^2{I}_{\lim }^2+{\psi }_{mi}^2\right)}$$

(11)

As the speed increases, and exceeds ω_bi, the working points on the operating region boundary are obtained on the voltage limitation ellipse. Then, the corresponding torque and speed should satisfy:

$$\{\begin{array}{l}\left(L_i^2{\omega }_i^2+R_i^2\right)i_{qi}^2+2R_i{\psi }_{mi}{\omega }_i{i}_{qi}+{\psi }_{mi}^2{\omega }_i^2=U_{\lim }^2\\ T_i=1.5p{\psi }_{mi}{i}_{qi}\end{array}$$

(12)

By solving (11), the operation region boundary of the machine at each mode when ω_i > ω_bi can be expressed as:

$$T_i\left({\omega }_i\right)=1.5p{\psi }_{mi}{i}_{qi}\left({\omega }_i\right)=1.5p{\psi }_{mi}\frac{-B_i\left({\omega }_i\right)+\sqrt{B_i^2\left({\omega }_i\right)-4A_i\left({\omega }_i\right)C_i\left({\omega }_i\right)}}{2A_i\left({\omega }_i\right)}$$

(13)

where A_i(ω_i), B_i(ω_i) and C_i(ω_i) are:

$$\{\begin{array}{l}{A}_i\left({\omega }_i\right)=L_i^2{\omega }_i^2+R_i^2\\ B_i\left({\omega }_i\right)=2R_i{\psi }_{mi}{\omega }_i\\ C_i\left({\omega }_i\right)={\psi }_{mi}^2{\omega }_i^2-U_{\lim }^2\end{array}$$

(14)

In order to calculate the switching speed in the WS strategy easily, (12) can be also written as a function of ω_i:

$$\left(\frac{4L_i^2{T}_i^2}{9p^2{\psi }_{mi}^2}+{\psi }_{mi}^2\right){\omega }_i^2+\frac{4R_i{T}_i}{3p}{\omega }_i+\frac{4R_i^2{T}_i^2}{9p^2{\psi }_{mi}^2}-U_{\lim }^2=0$$

(15)

By solving (15), the speed on the boundary at each mode can be expressed as:

$${\omega }_i\left(T_i\right)=\frac{-E_i\left(T_i\right)+\sqrt{E_i^2\left(T_i\right)-4D_i\left(T_i\right)F_i\left(T_i\right)}}{2D_i\left(T_i\right)}$$

(16)

where D_i(T_i), E_i(T_i) and F_i(T_i) are:

$$\{\begin{array}{l}{D}_i\left(T_i\right)=\frac{4L_i^2{T}_i^2}{9p^2{\psi }_{mi}^2}+{\psi }_{mi}^2\\ E_i\left(T_i\right)=\frac{4R_i{T}_i}{3p}\\ F_i\left(T_i\right)=\frac{4R_i^2{T}_i^2}{9p^2{\psi }_{mi}^2}-U_{\lim }^2\end{array}$$

(17)

According to (9) and (12), the operating region boundary of the machine at each mode can be directly calculated in the whole speed range. Figure 5 shows the torque–speed curves of the machine at the three operating modes. In the mode M1, the machine could produce the largest torque, but its speed range is limited due to the relatively large PM flux linkage. When the machine operates at M2 or M3, the speed range is extended as the PM flux linkage reduces. The mode M3 produces the smallest torque but widest speed range. Generally, the overall operating envelop of the machine can be considered as a combination of the operating regions in the three modes for each WS circuit. This indicates that the operating region can be significantly extended using WS strategy. In order to achieve the multi-mode operation for the machine online, a speed based on WS control strategy is proposed. The torque–speed curves of two adjacent operating modes intersect at P and Q in Figure 5. The speed values of these two intersections are labeled as ω_P and ω_Q, which can be regarded as the transition speed of the two adjacent operating modes to maximize the operating region and simplify the WS process when it is applied to the machine. According to (14), the switching speed ω_P and ω_Q can be calculated as:

$$\{\begin{array}{l}{\omega }_P={\omega }_1\left(T_1\right)=\frac{-E_1\left(T_1\right)+\sqrt{E_1^2\left(T_1\right)-4D_1\left(T_1\right)F_1\left(T_1\right)}}{2D_1\left(T_1\right)}\\ T_1=1.5p{\psi }_{m2}{I}_{\lim }\end{array}$$

(18)

$$\{\begin{array}{l}{\omega }_Q={\omega }_2\left(T_2\right)=\frac{-E_2\left(T_2\right)+\sqrt{E_2^2\left(T_2\right)-4D_2\left(T_2\right)F_2\left(T_2\right)}}{2D_2\left(T_2\right)}\\ T_2=1.5p{\psi }_{m3}{I}_{\lim }\end{array}$$

(19)

It should be noted that if the machine operates around the switching speed, it is necessary to utilize a hysteresis controller to avoid frequent WS operation, as shown in Figure 5b. Assuming the WS occurs between the operating mode Mx and Mx + 1, and the switching speed is ω_sw, when the speed increases beyond ω_sw + Δω, the operating mode Mx switches to Mx + 1 and when the speed decreases below ω_sw − Δω, the operating mode Mx + 1 switches to Mx.

Figure 6 shows the schematic diagram of the WS strategy for the DS-PMM based on current vector control. In Figure 6, the inner and outer windings of the machine are connected to the inverter via the proposed WS circuit, which enables the machine to operate at three independent operating modes. As the speed increases, the WS controller generates a switch signal based on the real-time speed to the WS circuit to reconfigure the winding connection of the machine. It should be noted that if the machine operates around the transition speed, it is necessary to utilize a hysteresis controller to avoid frequent WS operation.

4. Experimental Validation

Figure 7 shows the test rig for experimentally validating the WS strategy for the investigated DS-PMM. A servo motor connected with a rectifier and a DC load could provide a load torque to the machine under test. The real-time torque and speed data could be captured by an HBM T20WN torque meter and the data acquisition unit. Figure 8 presents the hardware implementation of the controller for the machine. STM32F407 was used as the main control unit to execute the control algorithm. FDA59N30 was selected to construct the three phase H-bridge inverter and the DC link voltage was 24 V. The two types of WS circuits described in Figure 2 could be implemented, based on the hardware module, as shown in Figure 8, with corresponding wiring connection patterns. Since the power rate of the machine was small, mechanical switches, such as the relay groups in Figure 8, could be utilized to validate the feasibility of the proposed WS strategy. The ON/OFF state of all the switches in the switch groups could be separately controlled via the control port.

Figure 9 shows the measured no-load back-EMF of the DS-PMM prototype in the three operating modes with different WS circuits. It was found that each winding mode had different magnitudes of back-EMFs. That is to say, the proposed WS strategy could adjust the PM flux linkage of the machine to realize FW and extend the speed range. In addition, it should be noted that the proposed WS strategy for DS-PMM would not lead to the phase shift of back-EMFs in different coils, which was superior to the corresponding electromagnetic performance in [13]. That is to say, no compensation was required for the d-axis position when the WS strategy was applied to the DS-PMM.

Since the two types of WS circuits had similar FW performance and the output torque of the prototype at T2M3 was too small to measure, the type I WS circuit was utilized to implement the WS strategy in the experimental validation. Figure 10 shows the measured torque–speed curves of the DS-PMM prototype in three operating modes with the type I WS circuit. The machine in T1M1 provided the largest output torque but its speed range was limited. As the machine was switched to T1M2, the out torque reduced, while the speed range extended. Additionally, the maximum speed could be achieved when the machine was switched to T1M3. On the other hand, the torque–speed curves intersected at P and Q in Figure 10. It was found that the speeds at P and Q were 500 rpm and 1000 rpm, respectively, which were selected as the transition speeds between the two adjacent modes of the WS strategy for the DS-PMM prototype.

Figure 11 shows characteristics of the no-load back-EMF during the WS process, and the WS trigger signal indicated the beginning of the switching process. In Figure 11a, the peak-to-peak value of line voltage was reduced from 25.2 V to 14.8 V when the machine was switched from T1M1 to T1M2 at 500 rpm. Similarly, when the machine was switched from T1M2 to T1M3 at 1000 rpm, the line voltage was reduced from 29.4 V to 20.8 V. According to these no-load experimental results, it could be concluded that the WS circuit could realize the winding reconfiguration in 20 m and the proposed WS strategy for DS-PMM had an effective flux adjustment capability.

According to the description of the proposed WS strategy and the test results in Figure 10, the WS operations at the working point A and B were selected to exhibit the on-load WS performance for the DS-PMM prototype at 500 rpm and 1000 rpm, respectively. Figure 12 shows the on-load WS transient characteristics from T1M1 to T1M2 at 500 rpm with a constant torque of 0.8 Nm. In Figure 12a, the trigger signal indicated the beginning of the WS process. Due to the reduction of PM flux linkage, the phase current of the machine increased after the WS operation. However, the line voltage was obviously reduced when the machine was switched to T1M2, which enabled the machine to maintain the torque at a higher speed. In Figure 12b, it was found that the switching transient process caused a drop in torque and speed variation. However, the WS operation could complete in a very short time and the machine torque and speed recovered to 0.8 Nm and 500 rpm. The torque characteristics during the switching process should be further investigated to improve the switching performance.

Figure 13 shows the on-load WS transient characteristics when the machine was switched from T1M2 to T1M3 at 1000 rpm with a constant torque of 0.4 Nm. In Figure 13a, the trigger signal indicated that beginning of the WS process. Due to the reduction of PM flux linkage, the phase current of the machine increased when the machine was switched to T1M3. Additionally, the line voltage was kept almost constant after the WS operation, since the working points at T1M2 and T1M3 were both beyond the constant torque region, and the machine voltage reached the limitation. However, according to the torque–speed curves in Figure 10, the machine at T1M3 achieved a higher speed. When the machine operated at 1000 rpm, it was found that the switching transient process also caused torque and speed variations, as shown in Figure 13b. However, the WS operation could be completed in a very short time, and the machine torque and speed recovered to 0.4 Nm and 1000 rpm.

Figure 14 shows the torque and speed curves of the DS-PMM prototype when it accelerated to 1200 rpm, using the proposed WS strategy. As the speed increased, the WS controller was triggered once the speed exceeded 500 rpm to reconfigure the winding connection and switch the machine from T1M1 to T1M2. Then, when the speed was over 1000 rpm, the machine switched from T1M2 to T1M3. The experiment carried out in the reversed speed rotation had similar results. Although the WS operation caused a drop in torque and speed variations, the speed range of the machine was effectively extended without applying a negative d-axis current.

5. Comparisons and Discussions

Figure 15 shows the comparison between the conventional d-axis current, based on the FW method, and the proposed WS strategy, based on the simulation model. The machine accelerated to about 1600 rpm in 6 s with a torque of 0.2 Nm using these two methods, respectively. With the conventional method, the d-axis current is kept as zero when it rotates at a low speed. The line voltage increases when the machine speeds up. When it reaches the voltage limitation, a negative d-axis current is applied to keep the line voltage within the voltage limitation. If the speed is further increased, more d-axis current for FW is required, which causes a significant increase of phase current. With the proposed WS strategy, the WS is performed according to the speed, as discussed in Section 3. Although the WS process causes a drop in torque during the switching transient, the line voltage of the machine can be obviously reduced, which ensures the line voltage is always within the voltage limitation. Then, the d-axis current is kept as zero during the whole acceleration process while the q-axis current increases due to the reduction of PM flux linkage. According to the simulation results in Figure 15g,h, when the machine operated at 1600 rpm and 0.2 Nm, the peak-to-peak value of phase current was about 5.4A for the WS strategy, which was smaller than that of the conventional method (7A). The smaller phase current always means less copper loss. That is to say, the WS strategy had a better performance at this working point, since it had less copper loss. However, when the machine operated at a lower speed or had a larger output torque, the q-axis current increase of the WS strategy would be larger than the d-axis current increase of the conventional method. Thus, the proposed WS strategy tended to have a better performance at a higher speed and a lower torque. On the other hand, although the WS strategy requires a complex hardware implementation, the control algorithm is much simpler, since there is no need to calculate the target d-axis current in real-time.

6. Conclusions

A novel WS strategy is proposed for the speed range extension of a DS-PMM. Two WS circuits were designed to enable the machine to operate at three different modes, respectively. According to the measured back-EMFs in different winding connection modes, there was no phase change of the investigated machine using WS and the back-EMF distortion could be alleviated. Besides, the effectiveness of these two WS circuits for speed range extension was verified by measured torque–speed curves. A speed-based WS controller was designed to automatically generate the switch signal according to the torque–speed characteristics in different modes, which could obtain simple and effective dynamic mode switching over an entire operating region. The transient WS experimental results validated that the proposed WS controller is able to achieve the online multi-mode operation for speed range extension. It is necessary to further study the torque characteristics, as well as the pulsating torque mitigation method during the WS transient. It would also be interesting to investigate sensor-less control for the machine with WS in the future.