As a new electric excitation machine, EEDSVRM is widely used in popular fields such as aerospace and electric vehicles because of its simple structure and high robustness. However, due to its structural characteristics, VRM has problems such as excessive torque pulsation, which affects operating performance. Therefore, it is necessary to consider the machine structure and optimize the design of the machine to find the optimal combination of structural parameters to make the EEDSVRM achieve the best operating performance, which is of great benefit to the large-scale application of VRM in industry. The optimization design of EEDSVRM ontology was researched in ^{[16][17][18][19][20][21]}[16,17,18,19,20,21]. There are many types of EEDSVRM ontology optimization designs, which can be roughly divided into five types: novel machine topology-based optimization, finite element simulation-based optimization, mathematical analysis-based optimization, intelligent algorithm-based optimization, and multiple fusion-based optimization. These five optimization design methods have their own characteristics. It is relatively time-consuming to propose new machine topology optimization and finite element optimization. Although mathematical formula analysis meets the requirements of real-time optimization, the optimization accuracy is still insufficient compared to finite element. Multi-objective optimization using intelligent algorithms can improve optimization efficiency. The optimization method of multiple fusion combines the advantages of multiple optimization methods and greatly improves the optimization efficiency as well as reduces the optimization cost.

2. Basic Topologies, Principles, and Performances

2.1. WFDSM

According to the machine excitation mode, the Doubly Salient Machine (DSM) can be divided into three categories, as follows: the Wound-field Doubly Salient Machine (WFDSM), which is shown in Figure 1a; the Doubly Salient Permanent Magnet Machine (DSPM); and the Hybrid Excitation Doubly Salient Machine (HEDSM), as shown in Figure 2 ^[22][23][24][22,23,24]. Compared with DSPM and HEDSM, WFDSM does not use permanent magnets for excitation. Instead, it only relies on the DC power supply to provide the excitation source. In this way, the magnetic flux of the machine can be controlled by adjusting the amplitude of the excitation current and the risk of irreversible demagnetization of the machine can be avoided. Therefore, the WFDSM can be used in harsh environments and has a strong magnetic flux adjustment capability.

Figure 2. (a) DSPM machine [22]. (b) HEDSM machine [23].

The working mode of WFDSM is different from DSPM and HEDSM, which adopt permanent magnet excitation because of the DC excitation mode. When current flows into the excitation winding, a magnetic field is established inside the machine. The magnetic flux generated by the main magnetic field passes through the yoke and magnetic poles of the stator and rotor and penetrates the entire magnetic circuit of the machine. When the machine rotor is driven to rotate by the prime mover, the flux linkage of the armature winding changes with the rotor position, resulting in a symmetrically induced potential. Unlike the permanent magnet excitation, the air gap magnetic field remains constant, which results in poor output voltage regulation and fault demagnetization capabilities. In WFDSM, the main magnetic flux of the machine can be controlled by adjusting the excitation current to affect the output voltage. The external uncontrollable rectifier circuit is shown in Figure 3 [25], where e_Af, e_Bf, e_Cf, and e_Df are the induced voltages of windings A, B, C, and D; W_A, W_B, W_C, and W_D are the windings A, B, C and D; R_A, R_B, R_C, and R_D are the self-resistance of the armature windings of A, B, C, and D; and R is the external load.

Figure 3. Full bridge rectifier circuit [25].

2.2. SRM

The stator and rotor of SRM are salient pole structures. As shown in Figure 1b, the salient pole of the stator is wound with armature winding, while there is no excitation winding. The magnetic flux moves along the path of minimum reluctance. When the stator and rotor poles are aligned, the air gap reluctance is the smallest. On the contrary, when the cogging is aligned, the air gap reluctance of the machine is the largest. Therefore, SRM follows the principle of minimum reluctance and the magnetic field is distorted to produce electromagnetic torque. Due to its simple structure, stable operation, and wide speed regulation range, it is widely used in aerospace, electric vehicle, and other fields. SRM have two-phase, three-phase, and multi-phase structures, and the stator and rotor also have different pole slot matching combinations. Generally speaking, if the multi-phase structure is adopted, the torque ripple of SRM is relatively small [26]. The relationship between the pole slot and phase number of SRM is as follows:

$$\{\begin{array}{c}{L}_{min{}_{}(N_S,N_r)=m{N}_r\begin{array}{c}\\ L_{min{}_{}(N_S,N_r)>N_S>N_r\begin{array}{c}\end{array}}\end{array}}\end{array}$$ (1)

where $L_{min{}_{}}$ is the least common multiple of the number of poles of the stator and rotor, m is the phase number of SRM, and $N_S$ and $N_r$ represent the number of poles of the stator and rotor, respectively.

The pole slot between the stator and rotor of SRM is shown in

The pole slot between the stator and rotor of SRM is shown in

Table 1

. The most common one is the three-phase 12/8-pole machine, as shown in

Figure 1b. Increasing the number of poles of SRM can reduce the torque ripple and vibration problems caused by SRM to a certain extent ^[27].

b. Increasing the number of poles of SRM can reduce the torque ripple and vibration problems caused by SRM to a certain extent [27].

Table 1. Common pole slot fit combination of the stator and rotor of SRM.

2.3. EEFSM

Identical to the excitation method of DSM, in addition to EEFSM that uses only direct current for excitation, FSM also includes a flux-switching permanent magnet machine (FSPM) that uses permanent magnets for excitation and a hybrid flux-switching machine (HEFSM) in which permanent magnets and direct current are used for excitation at the same time. The topology of FSPM and HEFSM are shown in Figure 4. Although FSPM is considered to be the latest stator excited reluctance machine ^[28], the permanent magnets used for excitation inevitably encounter demagnetization problems. It is because of the ability to achieve magnetic field adjustment and fault demagnetization under high temperature and harsh operating environments that EEFSM has attracted increasing attention and become one of the research highlights in the VRM field. Figure 1c shows the most widely used 12/10 pole for EEFSM.[28]，用于励磁的永磁体不可避免地会遇到退磁问题。正是由于能够在高温和恶劣的工作环境下实现磁场调节和故障退磁，EEFSM越来越受到关注，成为VRM领域的研究亮点之一。图1c 显示了 EEFSM 使用最广泛的 12/10 极。

Figure 4. (a) FSPM ^[12]. (b) HEFSM ^[5].图 4. ( a ) FSPM [ 12 ]。( b ) HEFSM [ 5 ]。

As shown in Figure 1c, it can be seen that there are 12 salient pole silicon steel cores on the stator. Slots are made on the stator teeth and the field windings are embedded in them. The excitation currents of the adjacent two sets of stator slots are opposite to each other.如在所示图1中C，可以看出，存在于定子12的凸极硅钢芯。在定子齿上开槽，励磁绕组嵌入其中。相邻两组定子槽的励磁电流是相反的。

Compared with conventional SRM, EEFSM can work in a full cycle and both its torque density and power density are higher, which makes it more suitable for applications with high performance requirements such as aerospace and offshore wind power.与传统的SRM相比，EEFSM可以全周期工作，扭矩密度和功率密度都更高，更适合航空航天、海上风电等高性能要求的应用。

With the periodic change of the overlapping area between the rotor pole and stator teeth, the air gap magnetic conductivity in the main magnetic circuit also changes, resulting in the magnetic linkage and back electromotive force in the phase winding, changing with the rotor position, which realizes the so-called “flux switching”, as shown in Figure 5. Reasonably designing the pole slot fit of FSPM and optimizing the structural size of the machine can make the waveform of the flux linkage and back EMF close to the sine wave.随着转子磁极与定子齿重叠面积的周期性变化，主磁路中的气隙导磁率也发生变化，导致相绕组中的磁联动和反电动势随转子位置而变化，从而实现了所谓的“磁通切换”，如图5所示。合理设计FSPM的极槽配合，优化整机结构尺寸，可使磁链和反电动势波形接近正弦波。

Figure 5. (a) Maximum forward position of flux linkage. (b) Maximum reverse position of flux linkage.图 5. ( a ) 磁链的最大前向位置。( b ) 磁链的最大反向位置。

2.4. Dissimilarity and Commonness of the Three Kinds of Variable Reluctance Machines

The three kinds of machines belong to the category of electrically excited variable reluctance machines, which have both dissimilarities and commonness. Commonalities are described below.

(1)

Electromagnetic torque is generated by the principle of minimum reluctance.

(2)

The stator and rotor adopt salient pole structures, also known as a double salient pole machine. There are no windings on the rotor and both the field winding and armature winding are on the stator poles.

(3)

The armature winding of the reluctance machine adopts centralized winding and uses less copper, thus the resistance of the armature winding is relatively small and the copper loss is also small.

(4)

All three types of VRM are excited by DC, which avoids the irreversible demagnetization defect of permanent magnet excitation at high temperature.

Furthermore, the three EEDSVRMs of WFDSM, SRM, and EEFSM also have various characteristics. Traditional SRM can only output power when the rotor slides out of the stator poles, while WFDSM and EEFSM can be connected to either a half-bridge rectifier circuit or a full-bridge rectifier circuit. When an external half-bridge rectifier circuit is connected, it can only work when the rotor slides in or slides out of the stator poles, which can only be output in half a cycle. However, when an external full-bridge rectifier circuit is connected, WFDSM and EEFSM will output voltage whether the rotor slides in or slides out of the stator poles. The process that the rotor completes from sliding in to sliding out of the stator poles is called a full cycle. Therefore, SRM can only work in a half cycle, while WFDSM and EEFSM can output power in a full cycle. Compared with WFDSM and EEFSM, the half-cycle working mode makes SRM output power density and torque density at a relatively low rate. Both SRM and WFDSM have unipolar magnetic flux linkage, while EEFSM can switch the magnetic flux to make the magnetic flux linkage present positive and negative bipolarly. Although the excitation windings on WFDSM and EEFSM are both placed on the stator poles, there are still some differences in the placement of the windings. The excitation windings of WFDSM are directly embedded in the stator slots, while EEFSM is slotted on the stator teeth to place the excitation windings.