A Comprehensive Performance Comparison between Segmental and Conventional Switched Reluctance Machines with Boost and Standard Converters

: This paper presents the comparisons between two types of switched reluctance machines (SRMs) and SRM converters. An SRM with a segmental rotor is compared with a conventional SRM (CSRM), and an SRM converter containing a passive boost circuit is compared with a conventional asymmetric half-bridge (AHB) converter. The segmental SRM has an asymmetric rotor with a segmented structure. The four rotor segments are made of steel laminations. Two segments are misaligned with the other two by 15 degrees. The torque ripple of the SRM with this structure is decreased, and the static torque is increased compared to a conventional SRM. The boost converter comprises a front-end circuit and a conventional AHB converter. The front-end circuit boosts the voltage level. The boosted voltage accelerates the rising and falling progress of the phase current. In this way, the SRM can obtain a greater speed and a smaller torque ripple. The comparison is conducted in simulation and validated through the experimental results. The experiment results have demonstrated that the segmental SRM obtains a maximum 7% torque ripple reduction at a low-speed range, compared to the CSRM. With the boost converter, both the CSRM and the segmental SRM can achieve a lower torque ripple and a higher maximum speed.


Introduction
Compared to other electric machine types, the switched reluctance machine (SRM) has advantages, such as a simple structure, robustness, high reliability, and a low manufacturing cost. These advantages make the SRM a promising candidate for electric vehicle (EV) applications. The high reliability of the SRM also makes it an attractive machine for other applications, such as off-shore renewable energy applications [1,2]. The SRM has the main disadvantage of high torque ripple at low speed. Extensive research has been performed to overcome this disadvantage.
The multi-stack configuration is a candidate solution for reducing the SRM torque ripple, including the three-stack SRM [3]. A multi-stack SRM is presented in [4] with axially misaligned rotor poles. A two-stack SRM with bidirectional startup capability has been proposed in [5]. The SRM introduced in [6] has obtained a 3 Nm increase for the average torque, compared to a Toyota Prius motor. Compared to conventional SRM (CSRM), the multi-layer SRM topology, which is presented in [7], has obviously reduced the output torque ripple. Compared to a CSRM, a two-layer SRM in [8] has a greater average torque and a lower torque ripple. Multi-stack SRMs have been demonstrated in [9,10] with the segmental rotor. The segmental rotor is shifted by 14 degrees mechanically.
A SRM structure with a segmental rotor has been presented in [11,12]. A much greater force density is possible for this structure [11]. The segmental rotor is made of several • A segmental SRM with a lower torque ripple has been compared to a CSRM. • A boost converter has been compared with a conventional AHB converter.

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The boost converter is tested with the segmental SRM and generates a higher maximum speed compared to the conventional AHB converter.

Comparison of the Segmental SRM and a Conventional SRM
The SRM with a misaligned segmented rotor is compared to a conventional SRM in this section. The SRM control system is presented in Figure 1. A PID controller is used for speed control. A hysteresis controller is used for current control. The converter is a conventional asymmetric half-bridge converter. Figure 2 presents the conventional converter circuit. The control model is implemented in MATLAB/Simulink™, and then Energies 2023, 16,43 3 of 18 the code generation capabilities of MATLAB™ are used to automatically generate efficient and optimized code for the microcontroller.

Comparison of the Segmental SRM and a Conventional SRM
The SRM with a misaligned segmented rotor is compared to a conventional SRM in this section. The SRM control system is presented in Figure 1. A PID controller is used for speed control. A hysteresis controller is used for current control. The converter is a conventional asymmetric half-bridge converter. Figure 2 presents the conventional converter circuit. The control model is implemented in MATLAB/Simulink™, and then the code generation capabilities of MATLAB™ are used to automatically generate efficient and optimized code for the microcontroller.  Table 1 lists the parameters of the conventional SRM.  Figure 3 illustrates the structure of the conventional SRM. The number of stator poles is 12, and the number of rotor poles is 8.

Comparison of the Segmental SRM and a Conventional SRM
The SRM with a misaligned segmented rotor is compared to a conventional SRM in this section. The SRM control system is presented in Figure 1. A PID controller is used for speed control. A hysteresis controller is used for current control. The converter is a conventional asymmetric half-bridge converter. Figure 2 presents the conventional converter circuit. The control model is implemented in MATLAB/Simulink™, and then the code generation capabilities of MATLAB™ are used to automatically generate efficient and optimized code for the microcontroller.  Table 1 lists the parameters of the conventional SRM.  Figure 3 illustrates the structure of the conventional SRM. The number of stator poles is 12, and the number of rotor poles is 8.  Table 1 lists the parameters of the conventional SRM.  Figure 3 illustrates the structure of the conventional SRM. The number of stator poles is 12, and the number of rotor poles is 8.  Table 2 lists the parameters of the segmental SRM. The number of phases is six. The segmental SRM has two phases working simultaneously. This means that the working   Table 2 lists the parameters of the segmental SRM. The number of phases is six. The segmental SRM has two phases working simultaneously. This means that the working phase ratio is 1/3. It is the same as the conventional three-phase SRM. Figure 4 shows the structure of the segmental SRM. The segmental SRM has a fully pitched (FP) winding configuration. The winding distributes symmetrically with a pitch of 30 degrees.  Figure 3. Structure of the conventional SRM. Table 2 lists the parameters of the segmental SRM. The number of phases is six. The segmental SRM has two phases working simultaneously. This means that the working phase ratio is 1/3. It is the same as the conventional three-phase SRM. Figure 4 shows the structure of the segmental SRM. The segmental SRM has a fully pitched (FP) winding configuration. The winding distributes symmetrically with a pitch of 30 degrees.   The rotor is made of four segments and one rotor core. The material of the segments is silicon steel. The material of the rotor core is aluminum. Two segments are shifted by 15 degrees with respect to the other two. This misalignment makes sure that the maximum torque point of the present phase is in line with the zero torque point of the next phase. The torque ripple of the SRM will be reduced in this configuration.

Finite Element Analysis and Simulink™ Simulation Comparison
The SRMs are simulated using the finite element method (FEM). The software Simcenter MAGNET™ has been used to run the FEM simulation with static performance. The static computation takes around 30 min. The static simulations of the torque performance for the two SRMs are performed. Figure 5 shows the static torque simulation results for the conventional SRM. The dashed line presents the sum of the positive torque. It shows that the torque ripple for the conventional SRM is 6.54 Nm and 97% to the average torque, which is 6.60 Nm. Figure 6 shows the static simulation results of the torque for the segmental SRM. It can be seen that the average static torque of the segmental SRM is higher than the conventional SRM. The torque ripple is 11.26 Nm, and the average torque is 23.92 Nm. Compared to the conventional SRM, the segmental SRM has a lower torque ripple ratio, which is 47% to the average torque, and has a higher average static torque.
15 degrees with respect to the other two. This misalignment makes sure that the maximum torque point of the present phase is in line with the zero torque point of the next phase. The torque ripple of the SRM will be reduced in this configuration.

Finite Element Analysis and Simulink™ Simulation Comparison
The SRMs are simulated using the finite element method (FEM). The software Simcenter MAGNET™ has been used to run the FEM simulation with static performance. The static computation takes around 30 min. The static simulations of the torque performance for the two SRMs are performed. Figure 5 shows the static torque simulation results for the conventional SRM. The dashed line presents the sum of the positive torque. It shows that the torque ripple for the conventional SRM is 6.54 Nm and 97% to the average torque, which is 6.60 Nm. Figure 5. Static simulation results of torque performance for the conventional SRM with 97% torque ripple to the average torque, edited from [30]. Figure 6 shows the static simulation results of the torque for the segmental SRM. It can be seen that the average static torque of the segmental SRM is higher than the conventional SRM. The torque ripple is 11.26 Nm, and the average torque is 23.92 Nm. Compared to the conventional SRM, the segmental SRM has a lower torque ripple ratio, which is 47% to the average torque, and has a higher average static torque. Dynamic simulations are performed for the two types of SRM to compare the torque ripple. Based on the static characteristics, MATLAB/Simulink™ software is em- Figure 5. Static simulation results of torque performance for the conventional SRM with 97% torque ripple to the average torque, edited from [30].
The SRMs are simulated using the finite element method (FEM). The software Simcenter MAGNET™ has been used to run the FEM simulation with static performance. The static computation takes around 30 min. The static simulations of the torque performance for the two SRMs are performed. Figure 5 shows the static torque simulation results for the conventional SRM. The dashed line presents the sum of the positive torque. It shows that the torque ripple for the conventional SRM is 6.54 Nm and 97% to the average torque, which is 6.60 Nm.  Figure 6 shows the static simulation results of the torque for the segmental SRM. It can be seen that the average static torque of the segmental SRM is higher than the conventional SRM. The torque ripple is 11.26 Nm, and the average torque is 23.92 Nm. Compared to the conventional SRM, the segmental SRM has a lower torque ripple ratio, which is 47% to the average torque, and has a higher average static torque. Dynamic simulations are performed for the two types of SRM to compare the torque ripple. Based on the static characteristics, MATLAB/Simulink™ software is em- Figure 6. Static simulation results of the torque performance for the segmental SRM with 47% torque ripple to the average torque, edited from [30].
Dynamic simulations are performed for the two types of SRM to compare the torque ripple. Based on the static characteristics, MATLAB/Simulink™ software is employed to perform the dynamic simulation. The Simulink™ simulation runs very quickly and generates a result within several minutes. Figure 7 demonstrates the simulated torque waveforms at 500 rpm for the two types of SRMs. It shows that the torque ripple for the segmental SRM is 1.58 Nm, and it is 2.9 Nm for the conventional SRM. ployed to perform the dynamic simulation. The Simulink™ simulation runs very quickly and generates a result within several minutes. Figure 7 demonstrates the simulated torque waveforms at 500 rpm for the two types of SRMs. It shows that the torque ripple for the segmental SRM is 1.58 Nm, and it is 2.9 Nm for the conventional SRM.

Experimental Validation and Comparison
Experiments are conducted to validate and to compare the SRMs. Figure 8a shows the converter hardware of the conventional converter for the conventional SRM. There are PCBs for the power supply, controller, and converter for each phase.

Experimental Validation and Comparison
Experiments are conducted to validate and to compare the SRMs. Figure 8a shows the converter hardware of the conventional converter for the conventional SRM. There are PCBs for the power supply, controller, and converter for each phase. Figure 8b shows the hardware of the converter for the segmental SRM. The power supply board is used to provide a DC voltage supply for the sensors, microcontroller, and the switch drivers modules. The controller board contains the controller chip and sensor ports. Each phase has an independent driver board. The switches, driver modules, and heat sinks are installed on the phase winding driver boards.

Experimental Validation and Comparison
Experiments are conducted to validate and to compare the SRMs. Figure 8a shows the converter hardware of the conventional converter for the conventional SRM. There are PCBs for the power supply, controller, and converter for each phase. Figure 8b shows the hardware of the converter for the segmental SRM. The power supply board is used to provide a DC voltage supply for the sensors, microcontroller, and the switch drivers modules. The controller board contains the controller chip and sensor ports. Each phase has an independent driver board. The switches, driver modules, and heat sinks are installed on the phase winding driver boards.     Figure 10 displays the measured torque ripple percentage comparison with different speeds for the two types of SRM [30]. It demonstrates that the segmental SRM has a lower torque ripple at the low-speed range, compared to the conventional SRM. Figure 11 displays the measured torque waveform at 2000 rpm and a 1.24 Nm torque load. It shows that the segmental SRM has a lower torque ripple with 0.13 Nm, compared to the conventional SRM with a 0.21 Nm torque ripple.    Figure 10 displays the measured torque ripple percentage comparison with different speeds for the two types of SRM [30]. It demonstrates that the segmental SRM has a lower torque ripple at the low-speed range, compared to the conventional SRM.

Section Conclusions
Compared to the conventional SRM, the simulation and experimental results show that the segmental SRM generates a lower torque ripple at different speeds.
In this section, the CSRM is compared with the segmental SRM driven by the conventional converter. Tests were performed, both in simulation and experimentally. The results prove that the torque ripple ratio for the segmental SRM is lower below the rated speed, with a maximum of 7%, while at the rated speed, torque ripple improvement is not ensured.

Simulation and Experiment Comparison of the Boost Converter and Conventional Converter
A boost converter for the SRM is presented in this section. It is compared to a conventional converter.
The boost converter comprises a conventional asymmetric half-bridge (AHB) converter with a fronted-end boost circuit. The fronted-end circuit is a passive boost circuit. It is made of a diode and a capacitor. Once the phase winding is turned off, the capacitor stores the current flowing back from the phase winding and boosts the capacitor voltage. When the phase winding is turned on for the next stroke, the capacitor will energize it first. The boost capacitor voltage can accelerate the energizing progress.  Figure 12 presents the different modes for the conventional AHB converter. At the excitation mode in Figure 12a, all switches are turned on and the phase winding is energized by the DC source voltage. The phase current increases. At the free-wheeling mode in Figure 12b, the switch on the upper arm is turned off and the current loop is completely within the converter. At the demagnetization mode in Figure 12c, both switches are turned off and the phase current decreases and charges to the DC source. ventional converter.

Conventional Converter
The boost converter comprises a conventional asymmetric half-bridge (AHB) converter with a fronted-end boost circuit. The fronted-end circuit is a passive boost circuit. It is made of a diode and a capacitor. Once the phase winding is turned off, the capacitor stores the current flowing back from the phase winding and boosts the capacitor voltage. When the phase winding is turned on for the next stroke, the capacitor will energize it first. The boost capacitor voltage can accelerate the energizing progress. Figure 12 presents the different modes for the conventional AHB converter. At the excitation mode in Figure 12a, all switches are turned on and the phase winding is energized by the DC source voltage. The phase current increases. At the free-wheeling mode in Figure 12b, the switch on the upper arm is turned off and the current loop is completely within the converter. At the demagnetization mode in Figure 12c, both switches are turned off and the phase current decreases and charges to the DC source.  Figure 13 presents the circuit of the boost converter and its different modes. A front-end circuit with a diode, a switch, and a capacitor are connected to the conventional AHB converter [31]. The switch SRA is used to switch for the selection of regenerative mode and motoring mode for the electric machine. When the electric machine is running in motoring mode, the switch SRA is turned off. When the electric machine is running in regenerative mode, the switch SRA is turned on. Once the switch SRA is on, the boost converter works as a conventional AHB converter. In this paper, the SRM is running in motoring mode and the switch SRA is turned off.  Figure 13 presents the circuit of the boost converter and its different modes. A frontend circuit with a diode, a switch, and a capacitor are connected to the conventional AHB converter [31]. The switch SR A is used to switch for the selection of regenerative mode and motoring mode for the electric machine. When the electric machine is running in motoring mode, the switch SR A is turned off. When the electric machine is running in regenerative mode, the switch SR A is turned on. Once the switch SR A is on, the boost converter works as a conventional AHB converter. In this paper, the SRM is running in motoring mode and the switch SR A is turned off. Boost excitation mode in Figure 13: During this mode, the voltage level of the boost capacitor CA is greater than the DC source . The diode DA is turned off. The phase winding is energized by the capacitor CA.

Boost Converter
DC excitation mode in Figure 13: During this mode, the voltage level of the boost capacitor CA is same as or lower than the DC source voltage level VDC. The diode DA will be turned on by the voltage difference from the DC source voltage to the capacitor voltage. The phase winding is energized by the DC source.
Freewheeling mode in Figure 13: During this mode, the switch on the upper arm is Boost excitation mode in Figure 13: During this mode, the voltage level of the boost capacitor C A is greater than the DC source V DC . The diode D A is turned off. The phase winding is energized by the capacitor C A .
Energies 2023, 16, 43 9 of 18 DC excitation mode in Figure 13: During this mode, the voltage level of the boost capacitor C A is same as or lower than the DC source voltage level V DC . The diode D A will be turned on by the voltage difference from the DC source voltage to the capacitor voltage. The phase winding is energized by the DC source.
Freewheeling mode in Figure 13: During this mode, the switch on the upper arm is turned off. The current loop is completed within the converter.
Demagnetization mode in Figure 13: During this mode, all the switches are switched off. The current flows back to the boost capacitor C A . The voltage level of the capacitor is boosted. The energy is stored in the capacitor. Once the switches turn on for the next stroke, the winding will firstly be energized by the voltage-boosted capacitor C A . With the help of the boosted voltage, the rising and falling time of the phase current will be decreased. It helps the SRM to output a greater average torque and a smaller torque ripple ratio. The calculation method in detail is published in [31]. Figure 14 presents the simplified circuit model during Mode 4 [31]. In this paper, the phase winding resistance R is 0.07 ohm and is neglected. Boost excitation mode in Figure 13: During this mode, the voltage level of the boost capacitor CA is greater than the DC source . The diode DA is turned off. The phase winding is energized by the capacitor CA.
DC excitation mode in Figure 13: During this mode, the voltage level of the boost capacitor CA is same as or lower than the DC source voltage level VDC. The diode DA will be turned on by the voltage difference from the DC source voltage to the capacitor voltage. The phase winding is energized by the DC source.
Freewheeling mode in Figure 13: During this mode, the switch on the upper arm is turned off. The current loop is completed within the converter.
Demagnetization mode in Figure 13: During this mode, all the switches are switched off. The current flows back to the boost capacitor CA. The voltage level of the capacitor is boosted. The energy is stored in the capacitor. Once the switches turn on for the next stroke, the winding will firstly be energized by the voltage-boosted capacitor CA. With the help of the boosted voltage, the rising and falling time of the phase current will be decreased. It helps the SRM to output a greater average torque and a smaller torque ripple ratio. The calculation method in detail is published in [31]. Figure 14 presents the simplified circuit model during Mode 4 [31]. In this paper, the phase winding resistance R is 0.07 ohm and is neglected. The equation group (1) expresses the equivalent circuit model.
where, u L (t) is the phase voltage, L(t) is the inductance of the phase winding, i(t) is the phase current, u C (t) is the boost capacitor voltage, Φ is the phase winding magnetic flux linkage, and C is capacitance of the capacitor C A .

MATLAB/Simulink™ Simulation and Comparison
A MATLAB/Simulink™ simulation is conducted to compare the boost converter and the conventional converter. Figure 15a illustrates the simulation results of the DC source voltage, the phase current, and the phase voltage, with a conventional converter at 3000 rpm speed and 1.07 Nm load. The DC source voltage is 72 V. It can be seen that the phase voltage is not boosted, and it is the same voltage level as the DC source voltage. Figure 15b shows the simulation results of the boost capacitor voltage, phase current, and phase voltage for the boost converter at 3000 rpm speed and 1.07 Nm load. It shows that the voltage of the boost capacitor is increased from 72 V to 107 V. Figure 16 presents the simulated torque waveforms at 500 rpm. It shows that the SRM outputs a lower torque ripple with the boost converter, compared to the conventional converter. The torque ripple comparison with different speeds is published in [31]. Compared to the conventional converter, the SRM with the boost converter generates a lower torque ripple at low-speed ranges [31]. Figure 15a illustrates the simulation results of the DC source voltage, the phase current, and the phase voltage, with a conventional converter at 3000 rpm speed and 1.07 Nm load. The DC source voltage is 72 V. It can be seen that the phase voltage is not boosted, and it is the same voltage level as the DC source voltage. Figure 15b shows the simulation results of the boost capacitor voltage, phase current, and phase voltage for the boost converter at 3000 rpm speed and 1.07 Nm load. It shows that the voltage of the boost capacitor is increased from 72 V to 107 V.  Figure 16 presents the simulated torque waveforms at 500 rpm. It shows that the SRM outputs a lower torque ripple with the boost converter, compared to the conventional converter. The torque ripple comparison with different speeds is published in [31]. Compared to the conventional converter, the SRM with the boost converter generates a lower torque ripple at low-speed ranges [31]. shows that the voltage of the boost capacitor is increased from 72 V to 107 V.  Figure 16 presents the simulated torque waveforms at 500 rpm. It shows that the SRM outputs a lower torque ripple with the boost converter, compared to the conventional converter. The torque ripple comparison with different speeds is published in [31]. Compared to the conventional converter, the SRM with the boost converter generates a lower torque ripple at low-speed ranges [31].

Experimental Validation and Comparison
Experimental tests are conducted to validate the boost converter. Figure 17 presents the measured boost capacitor voltage V C , phase current I ph , and phase voltage V ph 3000 rpm speed and 1.07 Nm load. It shows that the voltage of the boost capacitor is increased from 72 V to 120 V.

Experimental Validation and Comparison
Experimental tests are conducted to validate the boost converter. Figure 17 presents the measured boost capacitor voltage VC, phase current Iph, and phase voltage Vph 3000 rpm speed and 1.07 Nm load. It shows that the voltage of the boost capacitor is increased from 72 V to 120 V. Different speeds are tested to analyze the torque ripple. Figure 18 illustrates the comparison between the measured torque ripples. It shows that the conventional SRM output has a lower torque ripple percentage with the boost converter, compared to the conventional converter.  Different speeds are tested to analyze the torque ripple. Figure 18 illustrates the comparison between the measured torque ripples. It shows that the conventional SRM output has a lower torque ripple percentage with the boost converter, compared to the conventional converter. Figure 17. Measured phase voltage (75.2 V/div), phase current (20 A/div), and boost capacitor voltage (75.2 V/div) with the boost converter at 3000 rpm and 1.07 Nm load.
Different speeds are tested to analyze the torque ripple. Figure 18 illustrates the comparison between the measured torque ripples. It shows that the conventional SRM output has a lower torque ripple percentage with the boost converter, compared to the conventional converter. The boost converter boosts the winding terminal voltage. It helps the SRM output a higher power with a higher maximum speed.
The induced electromotive force (EMF) of the SRM is expressed in Equation (2), which is referenced from equation (1.18) of [32]: where is the induced EMF, is the phase current, ( , ) is the phase inductance depending on the rotor position and phase current, and is the rotor electrical speed. The boost converter boosts the winding terminal voltage. It helps the SRM output a higher power with a higher maximum speed.
The induced electromotive force (EMF) of the SRM is expressed in Equation (2), which is referenced from equation (1.18) of [32]: where e is the induced EMF, i is the phase current, L(θ, i) is the phase inductance depending on the rotor position and phase current, and ω m is the rotor electrical speed. With the boost converter, more voltage is available to compensate for a higher EMF; hence, a higher speed and/or a higher current can be reached, as of Equation (2). The increased speed is visible in Figure 19. This increased no-load maximum speed is combined with an increase of current, compensating for the increased friction and windage losses. With the boost converter, more voltage is available to compensate for a higher EMF; hence, a higher speed and/or a higher current can be reached, as of Equation (2). The increased speed is visible in Figure 19. This increased no-load maximum speed is combined with an increase of current, compensating for the increased friction and windage losses. Figure 19 presents the experimental results of the maximum speed test. To remove the electromagnetic noise, a moving average filter is applied to the speed sensor, which is an encoder [33]. The conventional SRM has been tested with the same maximum phase current, which is 34 A, but with different converters. The measured results show that the maximum speed with the conventional converter is about 3550 rpm, and it is 3800 rpm with the boost converter. The experimental results show that boost converter has increased the maximum speed of the conventional SRM by 7%.

Section Conclusions
In this section, a comparison is performed between the boost converter and the conventional converter as drives for the conventional SRM. Unfortunately, the comparison between converters did not result in a significant torque ripple improvement for the boost converter for a certain speed range. This is probably due to the increase of the current ripple, which is caused by the increase of the phase voltage. However, the no-load maximum speed was improved.  Figure 19 presents the experimental results of the maximum speed test. To remove the electromagnetic noise, a moving average filter is applied to the speed sensor, which is an encoder [33]. The conventional SRM has been tested with the same maximum phase current, which is 34 A, but with different converters. The measured results show that the maximum speed with the conventional converter is about 3550 rpm, and it is 3800 rpm with the boost converter. The experimental results show that boost converter has increased the maximum speed of the conventional SRM by 7%.

Section Conclusions
In this section, a comparison is performed between the boost converter and the conventional converter as drives for the conventional SRM. Unfortunately, the comparison between converters did not result in a significant torque ripple improvement for the boost converter for a certain speed range. This is probably due to the increase of the current ripple, which is caused by the increase of the phase voltage. However, the no-load maximum speed was improved.

Comparison of the Boost Converter and the Conventional Converter with the Segmental SRM
In this section, the boost converter in Figure 13 is compared to the conventional converter in Figure 2, with the segmental SRM.

Segmental SRM with the Conventional Converter
The conventional converter in Figure 2 is tested with the segmental SRM. The torque ripple test and maximum speed test have been simulated and tested experimentally, and then compared with the boost converter.

Segmental SRM with the Boost Converter
The boost converter in Figure 13 is tested with the segmental SRM. The torque ripple test and maximum speed test have been implemented to compare the boost converter with the conventional converter.
The analytical method is used to calculate the turn-off angle for the boost converter. After the turning off of the phase winding, the phase current in Figure 20a is calculated with (3). The boost capacitor voltage in Figure 20b is calculated with (2). The torque in Figure 20c is calculated with (5). The analytical method is used to calculate the turn-off angle for the boost converter. After the turning off of the phase winding, the phase current in Figure 20a is calculated with (3). The boost capacitor voltage in Figure 20b is calculated with (2). The torque in Figure 20c is calculated with (5). With the calculated torque waveform, the average torque for the turning off period can be calculated. The turn-off angle is selected with the highest average output torque. A full table scan method is applied to calculate the optimized turn-off angle [31]. The details of the scan method have been introduced in [31]. Figure 21 shows the calculated turn-off angle table. The current controller calculates the turn-off angle with this table. With the calculated torque waveform, the average torque for the turning off period can be calculated. The turn-off angle is selected with the highest average output torque. A full table scan method is applied to calculate the optimized turn-off angle [31]. The details of the scan method have been introduced in [31].  With the calculated torque waveform, the average torque for the turning off period can be calculated. The turn-off angle is selected with the highest average output torque. A full table scan method is applied to calculate the optimized turn-off angle [31]. The details of the scan method have been introduced in [31]. Figure 21 shows the calculated turn-off angle table. The current controller calculates the turn-off angle with this table.

Comparison in the Simulink Simulation
A Simulink simulation has been applied to compare the torque ripple ratio of the segmental SRM between with the conventional converter and with the boost converter. Figure 23 presents the simulated torque waveforms of the segmental SRM at 500 rpm. It shows that compared with the SRM working with a conventional converter, the SRM with the boost converter produces a lower torque ripple. The torque ripple with the conventional converter is 1.58 Nm. Additionally, it is 1.27 Nm with the boost converter. The simulated torque ripple is reduced by 19.6%.

Comparison in the Simulink Simulation
A Simulink simulation has been applied to compare the torque ripple ratio of the segmental SRM between with the conventional converter and with the boost converter. Figure 23 presents the simulated torque waveforms of the segmental SRM at 500 rpm. It shows that compared with the SRM working with a conventional converter, the SRM with the boost converter produces a lower torque ripple. The torque ripple with the conventional converter is 1.58 Nm. Additionally, it is 1.27 Nm with the boost converter. The simulated torque ripple is reduced by 19.6%. segmental SRM between with the conventional converter and with the boost converter. Figure 23 presents the simulated torque waveforms of the segmental SRM at 500 rpm. It shows that compared with the SRM working with a conventional converter, the SRM with the boost converter produces a lower torque ripple. The torque ripple with the conventional converter is 1.58 Nm. Additionally, it is 1.27 Nm with the boost converter. The simulated torque ripple is reduced by 19.6%.

Comparison in Experimental Tests
Experiments have been performed to validate the performance of the boost converter with the segmental SRM. Figure 24 presents the measured boost capacitor voltage VC, phase current Iph, and phase voltage Vph of the segmental SRM with the boost converter with 3000 rpm and 1.07 Nm torque load. The capacitor voltage VC is boosted from 72 V to 85 V.

Comparison in Experimental Tests
Experiments have been performed to validate the performance of the boost converter with the segmental SRM. Figure 24 presents the measured boost capacitor voltage V C , phase current I ph , and phase voltage V ph of the segmental SRM with the boost converter with 3000 rpm and 1.07 Nm torque load. The capacitor voltage V C is boosted from 72 V to 85 V.  Figure 25 presents the measured torque ripple waveforms of the segmental SRM with two types of converters. The torque ripple value of the conventional converter is 0.14 Nm, which is 13% to the average torque; and it is 0.07, which is 6.5% with the boost converter. The experimental torque ripple is reduced by 6.5%.
Torque (Nm) Figure 24. Measured phase voltage (40 V/div), phase current (10 A/div), and boost capacitor voltage (40 V/div) with 3000 rpm and 1.07 Nm torque load. Figure 25 presents the measured torque ripple waveforms of the segmental SRM with two types of converters. The torque ripple value of the conventional converter is 0.14 Nm, which is 13% to the average torque; and it is 0.07, which is 6.5% with the boost converter. The experimental torque ripple is reduced by 6.5%.
The boost converter boosts the voltage, and it can increase the maximum speed of the SRM. The experiment has been conducted to validate the increase of the maximum speed with the boost converter. Figure 26a presents the maximum speed with the boost converter, which is 4979 rpm. Figure 26b shows the maximum speed of the segmental SRM with the conventional converter. It reaches 4836 rpm. Compared to the conventional converter, the maximum speed of the segmental SRM with the boost converter is increased by 2.9%. Figure 24. Measured phase voltage (40 V/div), phase current (10 A/div), and boost capacitor voltage (40 V/div) with 3000 rpm and 1.07 Nm torque load. Figure 25 presents the measured torque ripple waveforms of the segmental SRM with two types of converters. The torque ripple value of the conventional converter is 0.14 Nm, which is 13% to the average torque; and it is 0.07, which is 6.5% with the boost converter. The experimental torque ripple is reduced by 6.5%. The boost converter boosts the voltage, and it can increase the maximum speed of the SRM. The experiment has been conducted to validate the increase of the maximum speed with the boost converter. Figure 26a presents the maximum speed with the boost converter, which is 4979 rpm. Figure 26b shows the maximum speed of the segmental SRM with the conventional converter. It reaches 4836 rpm. Compared to the conventional converter, the maximum speed of the segmental SRM with the boost converter is increased by 2.9%.

Section Conclusions
In this section, the conventional converter was compared to the boost converter, with the segmental SRM. Simulations and experiments were performed for the comparison. The simulation results showed that the segmental SRM produces a 19.6% lower torque ripple with the boost converter, compared to the conventional converter. The experimental results presented that the segmental SRM reaches a 6.5% lower torque ripple with the boost converter, compared to the conventional converter. The experimental results also showed that the maximum speed of the segmental SRM was improved by 2.9% with the boost converter.

Discussion
As reported in the scientific literature, the multi-stack SRM is often designed as a 3D structure. It makes the manufacturing of the SRM more difficult. In this study, the 3D multi-stack structure is simplified to a 2D design structure, with misalignment between the stacks. This simplification is achieved with the short flux structure, fully pitched winding, and misaligned rotor segments. The 2D structure is easier to analyze with FEM simulations and is easier to manufacture.
When reviewing the current state of the art, some boost converters with parallel type capacitors are reported. One main problem there, is that the parallel capacitor is shared with all the SRM phases. It makes the operational behavior of each phase mixed, due to the shared capacitor. In contrast, with the design presented in this article, the parallel capacitor works independently for each phase. It makes the voltage equation of each phase straightforward, and makes it possible to calculate the voltage curve with analytical differential equations.
A part of the torque ripple in this paper is generated with the current control method, which is the hysteresis current control method. Because the phase inductance of the SRM is changing with the rotor position, it makes the transfer function of the current

Section Conclusions
In this section, the conventional converter was compared to the boost converter, with the segmental SRM. Simulations and experiments were performed for the comparison. The simulation results showed that the segmental SRM produces a 19.6% lower torque ripple with the boost converter, compared to the conventional converter. The experimental results presented that the segmental SRM reaches a 6.5% lower torque ripple with the boost converter, compared to the conventional converter. The experimental results also showed that the maximum speed of the segmental SRM was improved by 2.9% with the boost converter.

Discussion
As reported in the scientific literature, the multi-stack SRM is often designed as a 3D structure. It makes the manufacturing of the SRM more difficult. In this study, the 3D multi-stack structure is simplified to a 2D design structure, with misalignment between the stacks. This simplification is achieved with the short flux structure, fully pitched winding, and misaligned rotor segments. The 2D structure is easier to analyze with FEM simulations and is easier to manufacture.
When reviewing the current state of the art, some boost converters with parallel type capacitors are reported. One main problem there, is that the parallel capacitor is shared with all the SRM phases. It makes the operational behavior of each phase mixed, due to the shared capacitor. In contrast, with the design presented in this article, the parallel capacitor works independently for each phase. It makes the voltage equation of each phase straightforward, and makes it possible to calculate the voltage curve with analytical differential equations.
A part of the torque ripple in this paper is generated with the current control method, which is the hysteresis current control method. Because the phase inductance of the SRM is changing with the rotor position, it makes the transfer function of the current openloop system difficult to calculate. As a result, a simple control method, the hysteresis control method, is selected for this research. The hysteresis current controller generates a high-current ripple, which contributes to the torque ripple.
The torque waveforms are measured on the shaft of the experimental motor setup. The torque reconstruction method can be performed to observe the torque waveforms at the air gap. The details of the method can be found in [30].
The analytical method in this paper can be used for future work. In the present work, the analytical method is used for the turn-off period of the switches conducting the current of the SRM's phases. For future research, it would be an interesting topic to apply this analytical method to the entire current conduction period of the SRM.

Conclusions
In this paper, a segmental SRM was compared to a CSRM, and a boost converter was compared to a conventional converter. The rotor of the segmental SRM is made of silicon steel segments and an aluminum shaft. The boost converter comprises a passive boost circuit and a conventional AHB converter. Simulation and experiment results were conducted to verify the design of the motor and its drive system.
With the conventional AHB converter, the simulation results at 500 rpm showed that the torque ripple value of the segmental SRM equals 1.58 Nm, while it is 2.9 Nm for the CSRM. The experiment results presented that the torque ripple of the segmental SRM is 7% lower than the CSRM, with the conventional converter.
The boost converter has been validated with the simulation and experiment results. The experiment showed that the phase voltage has been boosted from 72 V to 120 V. The experiment results of the boost converter with the CSRM illustrated that the boost converter produced a lower torque ripple at a certain speed range. Furthermore, the no-load maximum speed with the boost converter was improved by 7%.
The experimental results of the boost and conventional converters with the segmental SRM have demonstrated that the torque ripple of the segmental SRM can be reduced by up to 6.5% with the boost converter. The maximum speed of the segmental SRM can be improved by up to 2.9% with the boost converter.