Vehicle-Mounted SRM DITC Strategy Based on Optimal Switching Angle TSF

Abstract

Switched reluctance motors (SRMs) offer several advantages, including a magnet- and winding-free rotor, high mechanical strength, and exceptional output efficiency. However, the doubly salient pole structure and high-frequency switching power supply result in significant torque ripple and electromagnetic noise, which limit the application in the field of new energy vehicles. To address these issues, this paper proposes a direct instantaneous torque control (DITC) strategy based on an optimal switching angle torque sharing function (TSF). Firstly, an improved cosine TSF is designed to reasonably distribute the total reference torque among the phases, stabilizing the synthesized torque of SRM during the commutation interval. Subsequently, an improved artificial bee colony (ABC) algorithm is used to obtain the optimal switching angle data at various speeds, integrating these data into the torque distribution module to derive the optimal switching angle model. Finally, the effectiveness of the proposed control strategy is validated through simulations of an 8/6-pole SRM. Simulation results demonstrate that the proposed control strategy effectively suppresses torque ripple during commutation and reduces the peak current at the beginning of phase commutation.

1. Introduction

The switched reluctance motor (SRM) has garnered significant attention from researchers and enterprises in recent years due to its simple structure, adaptable control, broad speed regulation range, and robust fault tolerance [1,2,3]. Currently, the commonly used types of automotive drive motors include asynchronous motors, permanent magnet synchronous motors, and switched reluctance motors (SRMs) [4]. Although asynchronous motors and permanent magnet synchronous motors perform well in the field of new energy vehicles, their operation relies on permanent magnets, the main component of which is neodymium–iron–boron, which risks demagnetization in harsh environments. These shortcomings can lead to increased manufacturing costs and reduced reliability of vehicles [5]. Additionally, their overload capacity, speed range, and starting performance, which are key parameters, are also inferior to those of switched reluctance motors (SRM). Magnet-free motors, such as switched reluctance motors (SRMs) and synchronous reluctance motors, are gradually gaining the attention of researchers in the field of new energy vehicles. Compared with synchronous reluctance motors, switched reluctance motors have lower costs, better starting performance, and a wider speed range, making them more suitable for the frequent starts and stops, as well as the complex operating conditions, characteristic of new energy vehicles.

Researchers have already begun to apply switched reluctance motors (SRMs) to vehicles. For instance, Jaguar developed a hybrid electric vehicle that uses two SRMs for propulsion, achieving a 0–100 km/h acceleration time of just 3.4 s. Additionally, Toyota Motor Corporation in Japan, in collaboration with the Tokyo Institute of Technology, has developed an SRM drive system for the Toyota Prius. It has been verified that compared with permanent magnet motors of the same volume, electric vehicles equipped with SRMs exhibit superior performance [6]. However, SRMs exhibit significant torque ripple and noise during operation, which diminishes the comfort level of vehicles. Additionally, the drive process of SRMs requires frequent switching of the power state, leading to high current peaks during the conduction period and thus imposing higher performance demands on power switching devices. These drawbacks have constrained the application and development of SRMs in the field of new energy vehicles. Ongoing efforts to mitigate SRM torque ripple primarily concentrate on two avenues: motor body design and the improvement of SRM control strategies [7]. The latter approach is comparatively simple, cost efficient, and effective, allowing for customization based on specific requirements, thus positioning itself as the focal point of current research.

Traditional control methods, such as current chopping control (CCC), angle position control (APC), and voltage chopping control (VCC), indirectly regulate torque by managing current, angle, and voltage, respectively. This indirect control makes precise torque regulation challenging. In contrast, direct instantaneous torque control (DITC) [8,9] is a novel control strategy for SRMs that focuses on the instantaneous torque at any given moment. DITC has gained popularity among researchers globally due to its stable control performance, simplicity, and effective suppression of torque ripple. However, one limitation of DITC is the significant torque experienced during the commutation phase [10]. To address this issue, the torque sharing function (TSF) [11,12,13] is proposed to the total reference torque of SRM reasonably among the phases, thereby reducing ripple during commutation. While traditional TSF strategies can effectively reduce torque ripple within the commutation interval, they do not account for torque tracking capabilities of the conducting and non-conducting phases during this interval period [14,15]. To further reduce torque ripple during commutation, this paper introduces an SRM-DITC control strategy based on a switching angle TSF. This strategy reshapes the cosine TSF, optimizes the switching angles at various conditions using an artificial bee colony (ABC) algorithm with a crossover operator, and integrates these optimized angles into the TSF module to achieve optimal reference torque for each phase. This improves the accuracy of the actual motor torque and achieves the objective of suppressing torque ripple. The effectiveness of the proposed control strategy is validated by simulation.

2. SRM Mathematical Model

SRMs inherently possess strong non-linear characteristics due to effects such as core magnetic hysteresis and eddy currents, which lead to larger control errors and higher difficulty levels. Analyzing the mathematical model of SRMs and establishing finite element models can aid in understanding the principles behind torque pulsation and enhance the precision of control strategies.

A distinctive feature of SRM is that, while in operation, the magnetic flux follows the path of least magnetic reluctance, known as the “principle of minimal magnetic reluctance” [16]. The input electrical energy is divided between consumption and conversion into magnetic field energy.

The magnetic flux linkage ${\psi }_k$ of the k-th phase winding of the motor can be expressed as a function of the winding current $i_k$ and the rotor position angle $\theta$, which can be expressed as follows:

$${\psi }_k\left(\theta ,i_k\right)=L_k\left(\theta ,i_k\right)i_k$$

(1)

Neglecting the effect of mutual inductance between phases, the voltage balance equation for SRM can be determined as follows:

$$U_k=R{i}_k+{\displaystyle \frac{d{\psi }_k}{dt}}=R{i}_k+{\displaystyle \frac{\mathsf{\partial }\psi \left(i_k,\theta \right)}{\mathsf{\partial }{i}_k}}{\displaystyle \frac{d{i}_k}{dt}}+{\displaystyle \frac{\mathsf{\partial }\psi \left(i_k,\theta \right)}{\mathsf{\partial }\theta }}{\displaystyle \frac{d{i}_k}{dt}}$$

(2)

The mechanical balance equation for the motor can be expressed as follows:

$$T_k=J{\displaystyle \frac{d\omega }{dt}}+T_L+F\omega$$

(3)

where $T_k$ represents the electromagnetic torque of the k-th phase; $\omega$ represents the rotor angular velocity; $J$ represents the moment of inertia; $T_L$ represents the load torque; and $F$ represents the damping coefficient.

Based on the principle of electromechanical energy conversion, the current $i$ and the electromagnetic torque $T_e$ of the mechanical system are interconnected through the magnetic field’s storage $W_f$ and co-energy $W^{\prime }$ [17]. Utilizing the principle of virtual displacement, the electromagnetic torque can be represented as the partial derivative of the co-energy with respect to the angular position between the motor’s stator and rotor, as expressed in the following equation:

$$T_e\left(i,\theta \right)={\displaystyle \frac{\mathsf{\partial }{W}^{\prime }\left(i,\theta \right)}{\mathsf{\partial }\theta }}=-{\displaystyle \frac{\mathsf{\partial }{W}_f\left(\psi ,\theta \right)}{\mathsf{\partial }\theta }}$$

(4)

$$W^{\prime }={\displaystyle \frac{1}{2}}i\psi ={\displaystyle \frac{1}{2}}L{i}^2$$

(5)

Substituting Equation (5) into Equation (4) results in the expression as follows:

$$T_e={\displaystyle \frac{1}{2}}{i}^2{\displaystyle \frac{\partial L}{\partial \theta }}$$

(6)

Due to the complex non-linearity of the magnetic circuit within a SRM, elucidating the interrelations among flux linkage, inductance, current, and rotor position angle poses a significant challenge in accurately modeling SRMs [18]. This study employs finite element simulation to capture the electromagnetic properties of SRMs for a more precise model. The instantaneous torque for each phase is determined using a lookup table approach. Figure 1 illustrates the structure of an 8/6 four-phase SRM. The SRM rotor rotates clockwise, and, during finite element simulation, the initial state is defined as the alignment of the rotor’s slot axis l₁ with the stator winding axis of phase A–A1. The terminal state is when the rotor has rotated clockwise to align the adjacent rotor slot axis l₂ with the stator winding of phase A–A1. This process captures the electromagnetic force exerted on a single-phase rotor pole by the stator winding over one cycle. Throughout this process, the mechanical angular rotation of the rotor is 60°. Figure 2, generated using Maxwell 2D 2022 R1 software, depicts the torque behavior of SRM. It indicates that an increase in current leads to a corresponding rise in higher electromagnetic torque at the same rotor position.

3. DITC Strategy

Traditional control strategies typically regulate torque indirectly through the adjustment of current, voltage, or flux linkage. In contrast, DITC strategy is capable of instantaneously detecting SRM at any given moment. It directly utilizes this instantaneous torque as the control objective, leading to improved suppression of torque ripple.

Figure 3 illustrates the system block diagram of DITC strategy, comprising a SRM, power converter, torque estimation module, and torque hysteresis controller. The primary focus of DITC is the real-time torque output. The fundamental concept involves utilizing the torque hysteresis controller to appropriate switching signals by comparing the instantaneous torque with the reference torque and the rotor position angle. This process continuously adjusts the switching states of each phase to regulate the instantaneous torque. The operational sequence involves obtaining the reference torque using an outer loop speed computing the variance between the reference torque and the actual torque, utilizing the torque hysteresis controller to produce control signals based on this torque discrepancy for governing the power converter’s switching behavior, thereby managing the motor torque.

Although DITC strategy effectively suppresses torque ripple, substantial torque ripple still persists in the motor’s commutation zone. To improve stability in this region, TSF was introduced. TSF rationally allocates the total reference torque, generated by the outer speed loop, to each phase during commutation. This ensures a constant total motor torque and significantly reduces torque ripple. At any given moment, the sum of TSFs for each phase winding must equal 1 (Equation (7)):

$$\left\{\begin{array}{c}{\displaystyle \sum _{k=1}^i{f}_k\left(\theta \right)=1}\\ 0\le f_k\left(\theta \right)\le 1\end{array}\right.$$

(7)

where $i$ represents the number of phases of SRM and $f_k\left(\theta \right)$ represents TSF for the k-th phase.

Commonly employed TSFs encompass linear, exponential, cosine, and quadratic forms. The single-phase reference torque, which is obtained from TSF, can be determined as follows:

$$T_{ref}\left(k\right)=T_{ref}\times f_k\left(\theta \right)$$

(8)

where $T_{ref}\left(k\right)$ represents the reference torque for the k-th phase and $T_{ref}$ represents the total reference torque.

To guarantee that the effective torque generated by individual phase windings of SRM closely follows the reference torque established by the TSF is essential to limit the rate of change of TSF. This study proposes the utilization of a cosine TSF, which can be represented as follows:

$$f_k\left(\theta \right)=\left\{\begin{array}{cc}{\displaystyle \frac{1}{2}}-{\displaystyle \frac{1}{2}}\cos {\displaystyle \frac{\pi }{{\theta }_{ov}}}\left(\theta -{\theta }_{on}\right),& {\theta }_{on}\le \theta \le {\theta }_{on}+{\theta }_{ov};\\ 1,& {\theta }_{on}+{\theta }_{ov}\le \theta \le {\theta }_{off};\\ {\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}\cos {\displaystyle \frac{\pi }{{\theta }_{ov}}}\left(\theta -{\theta }_{off}\right),& {\theta }_{off}\le \theta \le {\theta }_{off}+{\theta }_{ov};\\ 0,& other.\end{array}\right.$$

(9)

where ${\theta }_{on}$, ${\theta }_{ov}$, and ${\theta }_{off}$ represent the turn-on angle, commutation overlap angle, and turn-off angle, respectively. The cosine TSF curve is shown in Figure 4.

4. Improved TSF Strategy

The use of TSF strategy improves the generation of single-phase reference torque, leading to a reduction in torque ripple to a certain degree. However, as the generation of single-phase reference torque relies on a predetermined function, it fails to account for the effect of motor torque characteristics and neglects the challenges faced by each phase accurately tracking the reference torque. Therefore, this approach results in elevated peak currents at specific positions throughout the commutation interval and persists in exhibiting torque ripple concerns.

4.1. Improved TSF

As indicated by Equation (6), the torque generated by the motor is directly proportional to the square of the current and the rate of change of inductance. The SRM control method based on the cosine-type TSF always results in unequal increases in torque during the conduction phase and unequal decreases in torque during the turn-off phase within the commutation zone, leading to torque fluctuations during this period [19].

In Figure 4, when the rotor of the k-th phase moves to ${\theta }_{on}$ where it has been energized, it is completely misaligned with the stator, resulting in a very small, nearly 0 rate of change in inductance relative to the rotor position angle $\theta$. According to Equation (6), if the rotor winding is to track the reference torque, it requires a substantial current, leading to the total torque being lower than the total reference torque. When the k-th phase rotor moves to ${\theta }_{off+ov}$ near alignment with the stator, the inductance is higher, the rate of change of current is lower, and the rate of change of inductance is very low, resulting in diminished torque generation capability. If the motor operates at low speed or light load, at the stator–rotor alignment position, the phase current of the output phase can smoothly reduce to 0, effectively controlling torque ripple. However, if the motor operates at high speed or under heavy load, under TSF control strategy, it becomes challenging for the phase current to drop to 0 at the stator–rotor alignment position. If the rotor position exceeds ${\theta }_{off+ov}$ but the winding still has residual current, the phase winding operates in a region where the rate of change of inductance is negative, thereby generating negative torque opposite to the direction of the reference torque, causing significant torque ripple.

To address these issues, this paper proposes a more precise segmentation of the conduction intervals for each phase winding in TSF and devises a TSF based on the operational area of each phase rotor winding. By analyzing the ratio of torque to current, a higher torque-to-current ratio [20] indicates a stronger torque generation capability for that phase, and vice versa. In Figure 5, the rotor position angle is resegmented. In the conduction interval $\left({\theta }_{on},{\theta }_{on}+{\theta }_{ov}\right)$ of the k-th phase rotor winding, when the torque-to-current ratio of the k-th phase rotor winding is equal to that of the (k − 1)th phase rotor winding, it is set to ${\theta }_{on}+{\theta }_c$; in the turn-off interval $\left({\theta }_{off},{\theta }_{off}+{\theta }_{ov}\right)$ of the k-th phase rotor winding, when the torque-to-current ratio of the k-th phase rotor winding is equal to that of the (k + 1)th phase rotor winding, it is set to ${\theta }_{off}+{\theta }_c$. The entire operating interval of the k-th phase winding is divided into five parts to design TSF (Equation (10)).

This method establishes a boundary based on the point where the torque-to-current ratios of the conducting and turn-off phases coincide within the commutation interval. It allows the phase with superior torque generation capacity to improve torque output, thereby offsetting torque fluctuations resulting from insufficient torque tracking.

$$f_k\left(\theta \right)=\left\{\begin{array}{cc}{\displaystyle \frac{1}{2}}-{\displaystyle \frac{1}{2}}cos{\displaystyle \frac{\pi }{{\theta }_{ov}}}\left(\theta -{\theta }_{ov}\right),& {\theta }_{on}\le \theta \le {\theta }_{on}+{\theta }_{ov};\\ 1-{\displaystyle \frac{T_{ek-1}}{T_{ref}}},& {\theta }_{on}+{\theta }_c\le \theta \le {\theta }_{on}+{\theta }_{ov};\\ 1,& {\theta }_{on}+{\theta }_{ov}\le \theta \le {\theta }_{off};\\ 1-{\displaystyle \frac{T_{ek+1}}{T_{ref}}},& {\theta }_{off}\le \theta \le {\theta }_{off}+{\theta }_c;\\ {\displaystyle \frac{1}{2}}+{\displaystyle \frac{1}{2}}cos{\displaystyle \frac{\pi }{{\theta }_{ov}}}\left(\theta -{\theta }_{off}\right),& {\theta }_{off}+{\theta }_c\le \theta \le {\theta }_{off}+{\theta }_{ov};\\ 0,& other.\end{array}\right.$$

(10)

4.2. Angle Optimization

By adjusting the switching angles of SRM, it is possible to alter the current waveform during the conduction period of a single phase [21,22,23], consequently regulating the motor’s output torque. The identification of the most effective switching angles to minimize torque variation across different speed conditions is essential for mitigating SRM torque fluctuations. Therefore, this study utilizes an ABC algorithm in conjunction with a crossover operator to optimize the switching angles at various motor speeds. Resultant optimal switching angle data is then incorporated into the torque distribution module, establishing an optimal switching angle module aimed at further reducing torque ripple.

The ABC algorithm is a swarm intelligence algorithm first proposed by Karaboga et al. [24]. Compared with the commonly used genetic algorithm (GA), the ABC algorithm has fewer parameters, lower complexity, a reduced likelihood of getting trapped in local optima, faster convergence speed, and better stability. In the ABC algorithm, the number of leader bees is set equal to the number of follower bees. The position of a food source represents a feasible solution, and the quantity of pollen at a food source represents the fitness value of the solution. Leader bees locate food sources and communicate this information with follower bees, who select food sources to exploit based on a roulette wheel strategy. If a new solution has a higher fitness value than an existing one, it replaces the old solution; otherwise, the old solution is retained. If a solution fails to improve after a predefined maximum number of updates, the food source is abandoned, and scout bees are deployed to randomly generate a new food source. This iterative process continues until the optimal solution is obtained.

The ABC algorithm initializes its parameters, with key parameters including the number of food sources SN, the maximum number of updates allowed for a single food source limit, the maximum number of iterations MaxIt, and the acceleration coefficient α. Initially, SN food sources are randomly generated, and a specific feasible solution is randomly generated as follows:

$$v_{ij}=x_{ij}+r\left(x_{ij}-x_{kj}\right)$$

(11)

where $v_{ij}$ represents the new position; $x_{ij}$ represents the original position; $x_{kj}$ represents the position of a randomly selected neighboring food source; $r$ represents a random number uniformly distributed between [−1, 1]; $k=\left\{1,2,\cdots ,BN\right\}$ ($BN$ is the population size); and $j=\left\{1,2,\cdots ,n\right\}$ ($n$ is the dimension).

The leader bees disseminate information regarding food sources to the follower bees, who subsequently employ Equations (12) and (13) to choose a food source using a roulette wheel mechanism. Equation (11) is utilized to randomly create a new food source position in proximity to the current one, followed by a comparison of the food source qualities at the original new positions. If the quality of the food source at the new position is superior, the new position is retained.

$$p_i={\displaystyle \raisebox{1ex}{$fi{t}_i$}\!\left/ \!\raisebox{-1ex}{${\displaystyle \sum _{n=1}^{BN}fi{t}_n}$}\right.}$$

(12)

$$fi{t}_i=\left\{\begin{array}{cc}{\displaystyle \frac{1}{1+f_i}},& f_i\ge 0\\ 1+\left|f_i\right|,& f_i<0\end{array}\right.$$

(13)

where $fi{t}_i$ represents the fitness value of the current food source position.

If a food source exhibits no improvement in fitness after a certain number of generations, it is considered abandoned. Additionally, the leading bee at the current food source transitions into a scout bee, which uses Equation (14) to explore new food sources randomly:

$$x_{ij}=x_j^{\min }+rand\left[0,1\right]\left(x_j^{\max }-x_j^{\min }\right)$$

(14)

where $x_j^{\max }$ and $x_j^{\min }$ represent the upper and lower bounds of the j-th dimensional component, respectively.

The search process, which includes leader bees, follower bees, and scout bees, is iterated until the algorithm terminates either upon reaching the maximum number of iterations or when the optimal solution of the population satisfies the predetermined accuracy criterion.

To improve the global optimization capability of the ABC algorithm, this study introduces a crossover operator inspired by GAs into the ABC framework. Crossover operations facilitate the exchange of segments of values within parental encodings to create new individuals. This process enables a more comprehensive distribution of solutions across the search space, thereby increasing the probability of discovering superior global optima and reducing the risk of the algorithm converging to local optima. Within the algorithm, a uniform random number ranging from 0 to 1 is generated for each component. If this random number is below a predefined value cr, the new value is accepted; otherwise, the current value is preserved.

In order to verify the problem-solving capability of the improved ABC, four standard test functions were selected for testing, and the specific forms of the functions are shown in

Table 1. Standard test functions.

Function	Function Expression	Dimensionality	Search Range
Sphere	$f(x)={\displaystyle \sum _{i=1}^n{x}_i^2}$	10	[−100, 100]
Shubert	$f(x)=1+{\displaystyle \frac{1}{4000}}{\displaystyle \sum _{i=1}^n{x}_i^2}-{\displaystyle \prod _{i=1}^n\cos (\frac{x_i}{\sqrt{i}})}$	10	[−300, 300]
Rastrigin	$f(x)=10n+{\displaystyle \sum _{i=1}^n\left\{x_i^2-10\cos \left[2\pi \left(x_i\right)\right]\right\}}$	10	[−10, 10]
Schwefel	$f(x)=418.9829d-{\displaystyle \sum _{i=1}^n{x}_i}\sin \left(\sqrt{\left|x_i\right|}\right)$	10	[−500, 500]

.

To compare the solution capabilities of the algorithms, particle swarm optimization (PSO), the ABC, and the improved ABC were used to solve the aforementioned four test functions. Each algorithm was run under the same conditions. The tests were conducted on MATLAB, with the maximum number of iterations set uniformly to 500, resulting in the function value convergence curves, as shown in Figure 6.

From Figure 6, it can be observed that under the test of four standard test functions, the improved ABC demonstrates faster convergence speed and higher solution accuracy compared with the ABC and PSO, and it addresses the issue of the ABC algorithm’s tendency to get trapped in local optima.

The primary objective of this study is to reduce the torque ripple rate, with the algorithm’s flowchart in Figure 7. The torque ripple rate [25] is defined in Equation (15):

$$T_{ripple}={\displaystyle \frac{T_{\max }-T_{\min }}{T_{av}}}$$

(15)

where $T_{\max }$ represents the maximum torque; $T_{\min }$ represents the minimum torque; and $T_{av}$ represents the average torque.

The DITC system incorporates the optimal switching angle TSF module, leading to improvements in the control system (Figure 8). By refining the cosine TSF expression based on the SRM non-linear model and its electromagnetic properties, the improved TSF maximizes the torque production capacity of motor phase winding. It globally optimizes the conduction and turn-off angles of each phase while considering various constraints, thereby effectively reducing torque ripple and peak currents. The initial phase involves utilizing finite element methods to derive motor torque and inductance characteristics for modeling purposes. This approach replaces the traditional DITC torque estimation technique with motor torque characteristics to mitigate control inaccuracies stemming from the non-linear motor model.

In Figure 8, $n_{ref}$ and $n$ represent the reference speed and actual speed, respectively; $T_{ref}$ represents the total reference torque; $T_{Aref}$, $T_{Bref}$, $T_{Cref}$, $T_A$, $T_B$, and $T_C$ represent the reference and actual torques of phases A, B, and C, respectively; $\theta$ represents the rotor position angle; while ${\theta }_{on}$ and ${\theta }_{off}$ represent the optimal turn-on and turn-off angles, respectively. The speed controller generates $T_{ref}$ based on the difference between $n_{ref}$ and $n$. The optimal angle module outputs ${\theta }_{on}$ and ${\theta }_{off}$ to the torque distribution module based on the current actual speed. TSF then rationally distributes the total reference torque to each phase. The hysteresis controller generates switching signals based on the difference between the actual torque and the reference torque of each phase, thereby controlling the switching state of the power converter and the actual torque of the motor.

5. Results

To validate the effectiveness of the control strategy proposed in this paper, an SRM control system simulation model was developed (Figure 8). The motor model utilizes lookup tables, incorporating magnetic linkage and torque data obtained from RMxprt and Maxwell 2D modules in Ansys Electronics. This data is imported into the lookup table (2D) module to complete the non-linear modeling of SRM. Additionally, the torque data is used to compute the actual torque of SRM by referencing the motor’s current and rotor position angle during operation. The structural parameters of SRM are detailed in

Table 2. SRM structural poarameters.

Parameter	Value
Number of stator and rotor stages	8/6
Rated power	4 kW
Rated speed	1500 r/min
Frictional loss	12 W
Stator external/internal diameter	120/74.5 mm
Rotor external/internal diameter	74/30 mm
Embrace factor	0.5
Stacking factor	0.95
Steel type	DW360_50
Core length	65 mm

.

To verify the performance of the DITC strategy proposed in this paper, traditional DITC strategies were selected as the comparison object for simulation. The following two sets of simulation were designed to validate the effectiveness of the improved DITC system under constant speed and variable speed conditions:

Simulation 1: To compare the performance of the traditional DITC strategy with the DITC strategy proposed in this paper, an analysis was conducted on the torque ripple and phase currents of the SRM when it reaches a stable speed.

Figure 9 and Figure 10, respectively, present the torque and phase current waveforms of the SRM under a load of 10 Nm, when stabilized at 300 r/min, for both the traditional DITC strategy and the DITC strategy proposed in this paper. The simulation results indicate that the total torque ripple of the traditional DITC strategy during stable operation is 9.34%, while the total torque ripple of the DITC strategy proposed in this paper is 8.35%, which is a reduction of 10.59% compared with the traditional DITC strategy. Additionally, the peak current of each phase for the traditional DITC strategy during stable operation is 48.20 A, whereas for the DITC strategy proposed in this paper, it is 38.24 A, representing a reduction of 20.66% compared with the traditional DITC strategy.

Figure 11 and Figure 12, respectively, illustrate the torque and phase current waveforms of the SRM under a load of 10 Nm, when stabilized at 600 r/min, for both the traditional DITC strategy and the DITC strategy proposed in this paper. According to the simulation results, the total torque ripple of the traditional DITC strategy during stable operation is 10.92%, while the total torque ripple of the DITC strategy proposed in this paper is 8.71%, which represents a reduction of 20.24% compared with the traditional DITC strategy. Concurrently, the peak current of each phase for the traditional DITC strategy during stable operation is 48.83 A, whereas for the DITC strategy proposed in this paper, it is 39.47 A, indicating a reduction of 19.17% compared with the traditional DITC strategy.

Figure 13 and Figure 14, respectively, present the torque and phase current waveforms of the SRM under a load of 10 Nm, when stabilized at 1000 r/min, for both the traditional DITC strategy and the DITC strategy proposed in this paper. The simulation results indicate that the total torque ripple of the traditional DITC strategy during stable operation is 12.89%, while the total torque ripple of the DITC strategy proposed in this paper is 10.35%, which is a reduction of 19.70% compared with the traditional DITC strategy. Additionally, the peak current of each phase for the traditional DITC strategy during stable operation is 47.78 A, whereas for the DITC strategy proposed in this paper, it is 37.04 A, representing a reduction of 22.48% compared with the traditional DITC strategy.

As shown in

Table 3. Comparison of simulation results before and after improvement.

Speed	Torque Ripple		Peak Current
	DITC	Improved DITC	DITC	Improved DITC
300 r/min	9.34%	8.35%	48.20 A	38.24 A
600 r/min	10.92%	8.71%	48.83 A	39.47 A
1000 r/min	12.89%	10.35%	47.78 A	37.04 A

, the simulation results are compared between the traditional DITC strategy and the DITC strategy proposed in this paper. Based on the simulation results, it can be observed that the DITC strategy proposed in this paper has a smaller torque ripple than the traditional DITC strategy during stable operation of the system. Moreover, it effectively suppresses the peak current value at the beginning of phase commutation, which can significantly reduce the losses in the system’s power devices and extend their service life.

Simulation 2: To compare the dynamic performance of the traditional DITC strategy with the DITC strategy proposed in this paper, a simulation analysis of the total torque of the SRM under accelerating and decelerating conditions was conducted.

The motor load is set to 10 Nm, with an initial speed of 600 r/min. At a time of 0.5 s, the speed suddenly changes to 1000 r/min. Comparing Figure 15 and Figure 16, when the motor reaches the rated speed and is affected by the speed change, both systems can respond quickly and exhibit ideal waveforms. The torque ripple of the traditional DITC strategy after being affected by the speed change and stabilizing again is 13.19%, while the torque ripple of the DITC strategy proposed in this paper after being affected by the speed change and stabilizing again is 10.44%.

The motor load is set to 10 Nm, with an initial speed of 1000 r/min. At a time of 0.5 s, the speed suddenly changes to 600 r/min. Comparing Figure 17 and Figure 18, when the motor is affected by a speed change while reaching the rated speed and stabilizing, both systems can respond quickly and display ideal waveforms. The torque ripple of the traditional DITC strategy after being affected by the speed change and stabilizing again is 10.83%, while the torque ripple of the DITC strategy proposed in this paper after being affected by the speed change and stabilizing again is 8.60%.

According to the simulation results, under the condition of sudden speed change, both the traditional DITC strategy and the DITC strategy proposed in this paper can quickly return to stable operation within a very short time, demonstrating that the system’s operational characteristics have strong robustness against parameter variation disturbances. However, the DITC strategy proposed in this paper exhibits a smaller torque ripple and better torque ripple suppression after being affected by the speed change and stabilizing again, compared with the traditional DITC strategy.

In summary, under the control of the DITC strategy proposed in this paper, the SRM exhibits good torque pulsation suppression across different speed conditions, and the current peak values at the beginning of conduction are also suppressed. This contributes to improving the handling stability and comfort of SRM when applied to new energy vehicles. Additionally, in response to sudden speed changes, the DITC strategy presented in this paper can react quickly and maintain torque pulsation suppression, playing a positive role in dealing with the complex and variable conditions of new energy vehicles.

6. Conclusions

This study focuses on addressing the issue of significant torque ripple in the commutation zone of SRMs and proposes a DITC strategy based on the optimal switching angle TSF. The improved TSF aims to optimize utilization of the rotor’s torque generation capacity in the commutation zone by establishing a model for the optimal switching angle under various speed conditions. This approach is designed to reduce torque ripple and minimize peak currents during commutation. Based on the simulation results, the improved DITC strategy demonstrates significant suppression of torque ripple in the SRM commutation zone. Compared with the traditional DITC strategy, the torque ripple rate is reduced by 10.59% and 19.70% under low-speed and high-speed conditions, respectively. Furthermore, the improved DITC strategy effectively mitigates the peak currents at the beginning of phase conduction, reducing them by 20.66% and 22.48% in low-speed and high-speed conditions, respectively, compared with the traditional strategy. Moreover, this strategy excels in dynamic performance, rapidly adapting to sudden operational changes and maintaining effective torque ripple suppression after stabilization.