Performance Analysis of a Modular E-Shaped Stator Hybrid Excited Flux Switching Motor With Flux Gaps

This paper proposes a new modular hybrid excited flux switching motor (MHEFSM) with flux gaps, adding the fault-tolerant capability to the proposed motor. The proposed motor uses an E-Shaped stator, as the middle teeth of E-core produce fault-tolerant capability, and in C-core, this capability is eradicated. The no-load flux linkage is calculated by the magnetic network model (MNM) to reduce time and disk storage. The drawback of the constant flux linkage of PM motors is overcome by employing field excitation (FE). The FE helps in regulation flux at higher speeds. The motor leading geometry variables are optimized by using Genetic Global Optimization (GGO). The GGO helped in refining the structure of the motor and has improved the flux linkage by 68.17%, average torque and torque density by 62.39% each, reduced torque ripples by 20.69%, and cogging torque by 18.48%. The volume of permanent magnet (PM) in the proposed MHEFSM is reduced by 36.24%, and 48.49% higher average torque and torque density is obtained compared to the state of art motor proposed in the literature. Furthermore, a 3D analysis of the proposed MHEFSM is done to further evaluate the electromagnetic performance.


I. INTRODUCTION
Electrical motors with PM materials play a vital role in academia and industries concerning their characteristically high torque density, power density, and efficiency. PMs are traditionally placed on the rotating part of the motor, which causes demagnetization, poses a risk of PMs breaking, and necessitates the use of mechanical supporting sleeves [1], [2]. In the conventional synchronous motor design, Field Excitation Sources (FES) are located on their rotor, which requires commutator brushes for their operation. Because of the rotor's simple and robust structure, improved heat dissipation, The associate editor coordinating the review of this manuscript and approving it for publication was Qinfen Lu . greater reliability and brushless operation, transferring the excitation sources from rotor to stator have recently received considerable attention [3]. Flux Switching Motor (FSM) accommodates excitation sources (PM and field winding) along with armature winding on the static part (stator), and the rotor is free from these excitation sources, which makes the rotor robust and simple [4], [5]. Although both the Doubly Salient PM Motor (DSPMM) and the Flux Reversal PM Motor (FRPMM) also have simple and robust rotor structures; however, the torque density of the PMFSM is higher due to bi-polar flux linkage, whereas the flux linkage of the DSPMM and FRPMM is unipolar which causes lower torque density [6]. Additionally, FSM provides more power density, sinusoidal back electromotive force (EMF) and high efficiency [7]. Moreover, due to the simple and robust rotor structure, FSM is suited for high-speed operation.
FSM are divided into three groups according to their excitation sources: PM excited FSM (PMFSM) [8], field excited FSM (FEFSM) [9], and hybrid excited FSM (HEFSM) [10]. PM excited FSM provides high torque density and efficiency on account of high magnetic-energy rare-earth PMs. The availability of rare-earth PM materials is reducing with time, due to which its cost is rising. Due to the rare-earth material characteristics of the PMs, minimum utilization of the PMs is an essential requirement of the future. FEFSM uses DC excitation sources (electromagnet) as a counterpart of the PM. Field Excitation (FE) is low-cost, and its magnetic field strength and direction are controllable. HEFSM utilizes both PM and FE as main flux sources. HEFSM utilizes relatively less PM volume than PMFSM and decrease in the torque density and efficiency are fulfilled by the FE source. The advantages of both PMFSM and FEFSM are integrated into HEFSM, such as better flux weakening and enhancing performance, high torque density and high efficiency [11]. FE winding can be accommodated at different locations: wrapping on the PMs, in the armature slot or assigning a separate slot. Twisting the FE winding on PMs makes the topology a series hybridized one, which limits the flux modulation capability. While placing FE winding in the armature slot reduces the space for armature winding. Allocating separate slots to FE winding limits the position of PMs and armature winding slots [12]. So, the main goal of researchers is to propose a HEFSM with the best utilization of space for all the excitation sources.
Generally, FSM is doubly salient structured and produces numerous problems, including high cogging torque, more torque ripples, and high magnetic flux leakage. Many HEFSM topologies were proposed in literature recently [13], [14], [15], [16], [17], [18], [19]. In [13], the flux regulation principle of three different topologies was presented based on the PM positioning. Among all, the middle-PM machine has the lowest flux regulation. In [14], a bearing-less HEFSM is examined, and a new technique for minimizing cogging torque is developed, namely the right angle chamfering scheme of the PM. Design of different parameters like optimum tooth width, coupling of magnetic flux of winding and PM, and optimum torque of HEFSM is challenging and time-consuming. In [15], a new variable structure magnetic network model method was proposed that greatly decreases the time necessary for HEFSM design. A consequent pole HEFSM was proposed in [19] with a flux bridge to prevent flux leakage from the stator. The authors in [20] proposed the HEFSM design, aiming for a high filling factor and efficiency. Flat wires, thin PMs, and a pair of FE coils are used in this design, which improves the filling factor while also lowering the motor's cost. The capability of HEFSM to regulate the flux is investigated in [21] using various PM materials. This investigation shows that ferrite PMFSM has a wide range of flux modulation capability while NdFeB PM gives better flux density with a limited range of flux regulation capability. A consequent pole HEFSM is analyzed in [22], where flux leakage is minimized by introducing a flux bridge in the stator and placing PMs with opposite magnetization to the leakage flux.
The design of the FSM with a lower mutual to self-inductance ratio results in reliable functioning and great fault tolerance. Fault tolerance of two designs, PMFSM and twisted rotor multi-tooth PMFSM are analyzed and compared in [23]. Multi-tooth FSM gives high fault tolerance capability, high torque density, and better efficiency. In [7], the fault tolerance capability of an E-core modular FSM is compared with its conventional double layer counterpart, which concludes that high fault tolerance and better demagnetization withstand capability are provided by the E-core modular FSM. E-core modular structure is also compared to C-core and E-core design, where E-core still gives promising faulttolerant capability.
In this paper, a modular stator hybrid excited flux switching motor (MHEFSM) is proposed. Concentrated type winding for both FE and armature are used, which are wound across the middle tooth of the E-shaped stator. PMs with alternating polarities are also placed at the tips of middle teeth. This paper is organized as follows, section II presents the design and operating principle of the proposed MHEFSM, section III presents the genetic optimization, FEM based performance of the proposed motor is analyzed in section IV, while the fault-tolerant capability of the proposed motor is discussed in section V. Section VI presents the comparison of proposed motor with state of the art motor and section VII concludes the paper.

II. DESIGN AND OPERATING PRINCIPLE
The proposed MHEFSM double salient structural topology is depicted in Fig. 1, where three pairs of E-shaped stator cores are placed at 120 • from each other. Radially magnetized PMs with alternating polarization directions are housed at the apex of the E-shaped stator cores' middle pole. Stator modules are alternately separated by an angular distance of 4 • and 6 • degrees. This separation helps to improve the fault-tolerant  capability of the proposed MHEFSM. Armature and field winding is coiled over the E-shaped stator core's central leg. Each armature phase is composed of two set of coils. The geometry parameters are denoted in Fig. 2 and given in Table 1.
The operating principle of proposed MHEFSM is based on no-load flux linkage, which is evaluated using magnetic network model (MNM) initially to save time of computation and disk storage. The MNM helps in finding the suitable coil combination and no-load flux linkage. Based on the flux linking path given in Fig. 3, two permeance networks are generated shown in Fig. 4. As MNM models all parts of the motor so it gives accurate no-load flux in terms of precision. The formulations of MNM are based on authors own published work [22]. After MNM, the proposed motor is design in JMAG v. 20.1 to validate the mathematical analysis via Finite Element Method (FEM). The no-load flux linkage obtained by MNM and FEM are compared in Fig. 5. The results reveal a small error between two. The time and storage comparison is made in Table 2. The MNM significantly reduces the drive storage and time as compared to FEM. Both the MNM and FEM are done using Lenovo system having 8 GB RAM, Intel(R), Core(TM) i5-8500 CPU 3.00GHz.

III. GENETIC OPTIMIZATION
The Genetic Global Optimization (GGO) method is used to optimize the various design parameters of the proposed MHEFSM. Variations in design parameters improve the performance, such as electromagnetic (EM) torque and cogging torque of the proposed design of MHEFSM. GGO improves the performance of the examined design by adjusting the size of design parameters such as the stator yoke radial length, stator pole thickness, PM dimensions, PM position, rotor tooth thickness, and so on. Some design parameters, such as stator outer diameter, air gap, stack length, and module separator width, are kept constant in this analysis. GGO significantly improves the performance of the proposed MHEFSM by investigating the parameter's optimum dimensions. The flow of the methodology used during GGO is depicted in Fig. 6.
GGO is accomplished by using JMAG software's builtin genetic algorithm. The number of generations simulated are 15, which consumed 88 hours. Specification of the PC is 64-bit operating Lenovo system Intel(R), Core(TM) i5-8500 CPU with 3.00 GHz, 8 GB RAM, 3,000 Mhz.
Targets of the optimization are; Objective Function : max(T avg , T D ) and Constraints :  where In (3), T avg , T EM and T cog represents average torque, electromagnetic torque and cogging torque, respectively. In (4), T D represent electromagnetic torque per volume of the proposed MHEFSM, whereas T Max and T Min , used in (5) represents maximum and minimum values of the torque.
The convergence plot of objective function is shown in Fig. 7. The varying parameters are investigated, and their response in terms of EM torque and torque ripples are depicted in Fig. 8 and Fig. 9. Fig. 8a to 8e show the optimum value of the objective function at stator yoke of value 4.22 mm, stator middle tooth thickness of value 8.23 mm, the thickness of the end poles of the E-shaped stator core value 4.61 mm, PM position with value 1.33 mm, and PM radial length of value 7.88 mm, respectively. Similarly, the rotor of the proposed MHEFSM is also optimized through GGO, where the effect of different rotor parts dimensions is presented in the Fig. 9. Fig. 9a and Fig. 9b presents optimum values of the objective function at a rotor tooth thickness value of 6.09 mm and a shaft radius value of 14.08 mm. The ranges, initial and optimum design parameter values obtained after optimization are listed in Table 3.
To summarize, the proposed MHEFSM performance is significantly enhanced by using GGO through FEM. This analysis reveals that the EM torque response achieves a global value of 5.83 Nm, while the toque tipples are optimized to 1.15 Nm at the optimum values of the geometry varying parameters. The quantitative improvement in all performance indices is provided in Table 4.

IV. PERFORMANCE ANALYSIS USING FEM
The performance of the proposed MHEFSM is examined utilizing initial and optimum design parameters through 2D and 3D FEM. The flux lines distribution patterns due to PM, FE and overall throughout the proposed MHEFSM geometry   are presented in Fig. 10. The other performance indices are explained in the following subsections.

A. NO-LOAD FLUX LINKAGE AND FLUX REGULATION
The three-phase no-load armature flux linkage over one pole pitch of the initial, optimized, and 3D topology of MHEFSM is shown in the Fig. 11a. The flux linkage is improved by 68% after optimization. The 3D analysis validates the 2D analysis. Harmonics in the flux linkage of both the initial design and optimized design of MHEFSM are illustrated in Fig. 11b. The ability to adjust the magnetic flux is an essential characteristic of the HEFSM, which reflects the influence of the field excitation on the magnetic field. The impact of field excitation on the PM flux linkage is provided in Fig. 12,   and the impact of FE on overall flux linkage is shown in Fig. 13 which reveals that the proposed motor is capable of weakening flux at higher speeds. Fig. 14 reveals that the proposed motor works as a PM motor in the absence of field excitation and achieves 5.12Nm average torque. This average torque can be decreased and increased by 34.18% and 30.86%, respectively, by changing field current.

B. BACK-EMF
The back-EMF of the proposed design is shown in Fig. 15 at the rated speed of 500 rpm. If the amplitude of the phase back-EMF increases, this means that the flux focusing improves. Fig. 15 depicts that after GGO, the amplitude of back-EMF has increased from 78.73V to 121.96V, which is a 54.91% increment from its initial value.

C. COGGING TORQUE
The cogging torque is calculated at no-load when the armature current is zero. The cogging torque causes ripples in the instantaneous torque. The cogging torque of the proposed MHEFSM is minimized after GGO. Furthermore, 3D analysis is conducted, and the response of initial, optimized and 3D cogging torque is plotted in Fig. 16.

D. ELECTROMAGNETIC TORQUE
The instantaneous torque is calculated under loaded conditions, i.e., when the armature current is applied. The average torque of the proposed MHEFSM is improved by 62.39% after GGO, as shown in Fig. 17. The 3D analysis is done to validate the 2D analysis. The ripples rate in the 3D analysis is a bit higher due to the end effects. In Fig. 18, the average torque with varying armature current density is observed at different field current densities.

E. TORQUE AND POWER VERSUS SPEED CURVES
The torque-speed and power-speed characteristics plots are shown in Fig. 19. The proposed MHEFSM maintains a constant torque region up to the speed of 784.49 rpm and achieves a maximum power of 565.28W. At speed beyond    784.49 rpm, the torque decreases to maintain constant power operation. The efficiency of the proposed MHEFSM at different regions under torque-speed curve is calculated and is shown in Fig. 20. It can be observed that the proposed motor has better efficiency of 82.38% in region II which is its feasible region of operation.

V. FAULT TOLERANCE
Fault tolerance of an electric machine is evaluated in terms of self-inductance and mutual inductance of the armature coil with itself and other adjacent phase coils. A high fault-tolerant machine must have magnetic, thermal, and physical separation between phase coils [24]. Due to the magnetic isolation of the coils, the healthy component of the motor remains independent from magnetic coupling with the faulty component. This section examines the self and mutual inductance of the proposed MHEFSM's armature coils.

A. INDUCTANCE COMPUTATION IN STATOR PART
Magnetic coupling between two phases of armature coils is reduced by inserting non-magnetic materials in the middle of E-shaped stator core parts modules. After linkage of the flux from the rotor component, stator flux remains inside the stator module due to the isolation of the stator module by a non-magnetic part. Inductance is calculated by following two steps; unsaturated case and saturated case. PM and FE coils portions are made air at unsaturated conditions, and DC with appropriate current density J c is injected into armature coils. At saturated condition, J c is injected to both armature and FE coil. In addition, PMs are also made active with appropriate direction. Basic relations for calculating self-inductance and mutual-inductance used in [22] and [25] are where L A represents self-inductance of phase A coil, A is linkage flux of phase A coil, A slot is the area of armature coil slot, N is the number of turns of armature coil, φ A is the A-phase coil flux and S f is the coil filling factor. In (7), L AB represents mutual inductance in coil B due to coil A, B is flux linkage in coil B, and φ B is the coil B flux. The same relations are used for calculating the self-inductance of B and C phase coils. In addition, L BC and L AC are calculated using (7).
Since the A-phase contains two coils, their inductance is calculated using the sum of the self-inductance of the individual coil.
Similarly, the cumulative inductance of B-phase and C-phase coil sets are taken into count. At saturated conditions,  both the excitation sources are made active, and the effect of the coils in terms of inductance on itself and between the coils are investigated. Expression for calculating self-inductance and mutual inductance changes by including the effect of excitation sources.
where (PM +FE) is the linkage flux due to PM and FE. The self-inductance and mutual-inductance of the proposed MHEFSM are calculated through the above equations are shown in Fig. 21 and Fig. 22, respectively. Fig. 21 shows self-inductance, while mutual-inductance under saturated and unsaturated condition is shown in Fig. 22.
The average value of mutual-inductance under unsaturated condition is −0.00245 mH while under saturated condition is −0.00589 mH, which is negligible compared to the self-inductance of the proposed motor. This investigation demonstrates that the proposed MHEFSM's self-inductance value is substantially higher than the mutual-inductance value, indicating that the coils have minimal influence on one another. This study further confirms that the proposed MHEFSM is a fault-tolerant.

VI. COMPARISON WITH STATE-OF-THE-ART DESIGN
After the complete analysis of the proposed motor, the comparison is made with the state of art topology. The leading dimension of both the topologies and magnetic material type is kept the same. The excitation conditions of the proposed motor are used the same as the state-of-the-art model. An Ecore stator is used compared to the C-core of the conventional topology. Furthermore, the best utilization of PM helps in achieving high torque and power density.

VII. CONCLUSION
A three-phase MHEFSM is proposed with flux gaps in the stator, which helps in flux focusing and fault-tolerant capability. The MNM reduces time and disk storage in the initial analysis of the proposed motor. GGO is used to globally optimize the geometry parameters of the proposed motor and achieve an optimal value of the objective function. FEM is used to analyze the 2D and 3D electromagnetic performance at no-load and loaded conditions. Torquespeed and power-speed graphs are obtained to analyze the performance of the motor at higher speeds. The fault-tolerant capability of the proposed motor is tested via calculation of self and mutual inductance method. Finally, the proposed motor is compared with the state-of-the-art model. The comparison unveils that the proposed design achieves higher torque and power density under the same dimensions and excitation conditions.