Performance analysis of a novel outer rotor flux‐switching permanent magnet machine as motor/generator for vehicular and aircraft applications

Peyman Naderi, Electrical Engineering Department, Shahid Rajaee Teacher Training University, Lavizan, Tehran, Iran. Email: p.naderi@sru.ac.ir Abstract Herein, a novel study on outer rotor flux‐switching permanent magnet (OR‐FSPM) machines for motor/generator applications is presented. An improved magnetic equivalent circuit (MEC) is used for saturable machine model, and the performance analysis is presented in both dynamic and steady‐state cases. A flexible MEC‐based method is used, where the machines with arbitrary properties can be analysed. Moreover, the model accuracy can be tuned by selective parameters in the proposed method. It is shown that the machine can be used as a high efficiency 400 Hz Ground Power Unit (GPU) for aircraft application. Furthermore, the machine usage for in‐wheel application in the hybrid and electric vehicles (HVs and EVs) is analysed. Comparison with 2D and 3D finite‐element‐ method (FEM) shows the effectiveness and accuracy of the proposed MEC method, where shorter processing time is obtained compared with FEM.

with inner and outer rotors is presented in Ref. [18] as a GPU, and analysis is performed by FEM, but the obtained voltage regulation is not suitable. A novel structure for OR-FSM is presented in Ref. [19], where the Back-EMF analysis is performed by FEM, but the dynamic response and analytical method are lacked. The FEM-based method is the most investigated approach for modelling and analysis of electric machines which has been used many times by researchers. Although, the FEM is a powerful tool for the mentioned aim, it has some drawbacks such as intensive processing and large simulation time. Moreover, individual FEM-based programming is needed for each case study, which can cause some difficulties in the modelling and analysis. Magnetic Equivalent Circuit (MEC), is another powerful method for modelling and analysis of electric machines, where all of the harmonics effects can be modelled. The method was initially proposed by Ref. [20], but this has been used in many new researches thanks to its capability. As a recent work, a partitioned stator FSM is modelled in Ref. [21], where an improved MEC is proposed for the machine. Another new work is presented in Ref. [22] for OR-PMSM, where a flexible MEC is addressed. The presented MEC can be simply modified for many types of electric machines such as FSMs, and etc. This method is also used for Ladder-Secondary linear induction machine in Ref. [23]. This method is now used for this research for modelling and analysis of an OR-FSPM machine, where the machine capability for in-wheel application and ground power unit (GPU) is studied. The novelties herein can be summarized as follows: � Modelling of OR-FSPM by a flexible MEC method, based on the presented technique in Ref. [22]. � Dynamic simulation of OR-FSPM for in-wheel application. � Analysis of OR-FSPM as a GPU for aircraft application.

| PROPOSED OR-FSPM MACHINE
Structure of the studied OR-FSPM machine is shown in Figure 1, where a 28-pole 36-slot OR-FSPM is considered as a sample case in the figure. Considering n pm PMs, 2n pm poles are produced in the rotor.
Each PM is magnetized tangentially and is sandwiched by two magnetic materials, where a non-magnetic material is used as a pole insulator.
The machine principle can be found in Ref. [19], where the flux switching in the stator teeth is clarified.

| MODELLING APPROACH OF OR-FSPMS MACHINE
The proposed MEC in Ref. [22] is considered herein. The used MEC for OR-FSPM machines is shown in Figure 2, where all the model details are clarified in the figure. It is notable that the presented MEC in Ref. [22] was proposed by authors for OR-PMSMs with radially magnetized PMs, and the MEC-based equations are clarified in Ref. [21]. Some minor modifications are necessary because of tangentially magnetized PMs, instead to radially type. The air-gap permeances are shown in Figure 3, where the air-gap fluxes are modelled by linear conductances (G ij for 1 ⩽ i ⩽ nr, and 1⩽ j ⩽ ns) [20][21][22]. The used MEC accuracy can be tuned by tuneable defined parameters in Table 1. In addition, the machine properties and tuneable parameters are listed in the table. Noticing to Figure 1, the number of obtained flux tubes in the defined MEC can be written as Table 2. Moreover, the flux tubes geometries are shown in Figure 4, and the relative reluctance should be computed by Equation (1). The μ r (b) is a function for core nonlinearity model, where μ r (b) ≈ 1 should be considered for the air and PMs flux tubes. A new flexible function for relative permeability is considered, where the core non-linearity curve fitting can be performed by selective parameters (a, b, and (c). These parameters can be tuned experimentally for the best fitting of the magnetization curve on the actual material curve.
The proposed function is written in Equation (2) as well as some various curves are shown in Figure 5. In the considered MEC, there are two MMF sources for the flux production, as shown in Figure 2. One for the rotor magnets (Fi j , i = 1, 2, 3),   -245 and the other for stator windings (Fs i ). The mentioned sources are written in Equation (3), where the li pm is the length of the PMs flux tubes in the ith zone. Moreover, W s is the turn map matrix of the stator windings.

| SOLVING PROCEDURE
Dynamic model of the OR-FSPM machine can be obtained by solving of the presented MEC equations. The minimum number of equations in both magnetic and electric types should be obtained. In the next part, the general form of the mentioned equations are defined in matrix form.

| Magnetic equations
Based on the Kirchoff's current and voltage laws (KVL and KCL), the general form of the magnetic equations can be written as Equations (4)- (13), where the details of the equations can be found in Ref. [22]. In addition, some of the details are written in Appendix A for clarification of the used equations. These equations are in non-linear algebraic type, where the nonlinearity is due to the core saturation (see Equation (1)).

| Electric and mechanical equations
Electric and mechanical equations are in linear differential type. In these equations, the winding configuration (Y, Yn, or Δ  (14). Moreover, the equations should be converted to algebraic time-stepping form. The converted equations are written in Equations (14) and (15), where the details are written in Refs. [21,22]. In Equation (14), the Mc is the turn function of windings, and in Equation (15), the τ e , τ l , J, and D denotes produced torque, load torque, shaft moment of inertia, and shaft damping coefficient, respectively. It is notable that the output torque in a MEC-based method is computed by the airgap Co-Energy computation as written in Equation (17) [20].

| SIMULATION RESULTS
Simulation results are presented in this section for two following purpose.
� The machine dynamic as motor/generator for in-wheel application in the electric and hybrid vehicles. � The machine dynamic as a 400 Hz generator for GPU application in the aircrafts.
The core non-linearity is modelled by a = 3684, b = 1.027, and c = 0.811 for Steel À 1010 À 2DFSO À 950 core B À H curve fitting [24]. The above-mentioned parameters are obtained based on the actual magnetization curve after a try and error procedure. It is considerable that the proposed function in Eq. (2) is a flexible technique for various B À μ r curve fitting based on the actual material curve (see Figure 5). It is notable that, Δt = 25 μs is used as the time step in the solving procedure.

| OR-FSPM as in-wheel motor
Two different machines with tabulated parameters in Table 3 are considered for simulation, where a 44-pole/48-slot (44/48) and a 28-pole/36-slot (28/36) OR-FSPM machines are considered. It is notable that the synchronous value is the rotational speed in these machines which can be defined by  (19) is considered for the simulated manoeuvres ( Figure 6).
The torque, speed, and stator currents for both machines are shown in Figure 6a,b. Moreover, the obtained B-H curve for a given flux tube (first flux tube in eighth zone), and the airgap flux density at a sample moment for 28/36 machine are shown in Figure 6c. As can be seen in Figure 6c, the saturation effect is modelled with acceptable accuracy, hence the nonlinear B-H curve for the considered element is observable. Moreover, the air-gap flux density of the 28-pole machine is shown in the figure. However, the space and time harmonics effects are visible in the air-gap flux, but a 28-pole sinusoidal component is obtained as fundamental component.

| Steady-state characteristic
Steady-state torque and power of the machines are obtained based on various initial rotor position (θ 0 ). In all cases, the constant synchronous value is considered as rotor speed and the written input voltages in Equation (14) are considered as Equation (20). ð20aÞ As can be seen in Figure 7, 23 and 5.4 kW are obtained as the rated power for 44 and 28 poles machines, respectively. It is important to note that the 28-pole machine dimensions are small compared with the 48-pole type. Therefore, the rated power is obtained less for the 28-pole machine compared with the 48-pole type.

| OR-FSPM as GPU
GPU is another suggestion of OR-FSPM machine usage which is proposed in this research for first time. It is shown that the -249 machine can be used as a 400 Hz generator with acceptable voltage regulation. Therefore, performance of the 44/48 machine is analysed as a 120 v rms , 400 Hz generator under various loading cases. The machine parameters are listed in Table 4, and general schema of the machine usage as a GPU is shown in Figure 8. A three-phase RL branch is considered as the electrical load. Considering v s = 0, the written R, and L matrices in Equation (14) should be defined as Equation (21), where L n = 10,000 H is used in Equation (21a) for Y connection modelling of the stator windings [21,22]. Simulation results of the designed GPU under various ohmic loads and n = 1091 rpm are shown in Figure 9. Figure 9a shows the output phases voltages under no-load and full load cases. Moreover, the windings currents and machine input power are shown in Figure 9b. In addition, the curves of the output voltage and machine power under various ohmic loads are shown in Figure 9c. As can be observed in Figure 9a,b, three-phase 400 Hz voltage is produced as the GPU output voltage. Moreover, in Figure 9c, 5.3% voltage regulation is obtained. To evaluating of the designed GPU performance under RL load, two sample loading cases with fixed |Z| ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi R 2 þ L 2 :ω 2 p ¼ 5 are considered in the next evaluation. Simulations are performed with two different load branches. Once, with R = 5 Ω, L = 0H, and the other under R = 2.5 Ω, L = 100μH load branches which means to 5 Ω loading with 1, and 0.707 power factors, respectively. The results are shown in Figure 10, where lower voltage amplitude is obtained with RL load.  Table 3 is modelled, and the results are compared in terms of processing duration time and methods accuracy. It is notable that the half symmetrical model in the xy surface is used for both 2D and 3D analyses, where half axial symmetry is additionally applied for 3D-FEM model, as shown in Figure 11a

| Validation and comparison by 3D-and 2D-FEM
The machine structure and the obtained speed curve in the 3D Maxwell environment are shown in Figure 11a,b, where the applied mesh and the flux density at a sample moment (t = 0.1 s) are shown. Figure 11c shows the flux density at a sample moment in 2D environment. Moreover, comparison between the obtained results by the used MEC method and the 3D-FEM is performed in Figure 12a, where the speed, torque, and windings currents under the defined load torque in Equation (22) are compared. Moreover, to analysis of the proposed method capability in the saturation model, the obtained B-H curve for a sample flux tube are compared. Figure 12b shows the actual B-H curve of the used material (Steel-1010-2DFSO-950), which is presented for the mentioned core in Ansoft/Maxwell as well as the obtained curve for R8 1 is compared in Fig. f12c, where one half of the steady-state B8 1 is considered. Noticing to the results, there are acceptable agreement between the obtained results. The processing time duration for 10 ms simulation is tabulated in Table 5, where very shorter processing time is obtained by the MEC compared with both 2D-FEM and 3D-FEM.

| CONCLUSION
In this research, a known flexible MEC method is represented for a novel OR-FSPM machine model for first time. The machine performance for in-wheel applications in the EV and HEVs is analysed as well as the machine capability for GPU application is studied, where the machine performance as a 400 Hz generator is introduced. Saturation effect is modelled by a novel method, where the B-H curve of all the materials can be tuned by selective parameters. As a considerable paper novelty, the presented method can be used for all the OR-FSPM machines with various properties and dimensions. Moreover, the model accuracy can be tuned for a given machine simulation. Performed validation by 2D and 3D FEM-based analyses showed the model accuracy, whereas very shorter processing time is obtained by MEC.  -251