Sådhanå (2021) 46:67 Ó Indian Academy of Sciences

https://doi.org/10.1007/s12046-021-01603-6Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)

Design and performance analysis of a dual multiphase using finite element method

M SOWMIYA1,* and S HOSIMIN THILAGAR2

1 Department of Electrical and Electronics Engineering, College of Engineering Guindy, Anna University, Chennai 600 025, India 2 Department of Electrical and Electronics Engineering, College of Engineering Guindy, Anna University, Chennai 600 025, India e-mail: [email protected]; [email protected]

MS received 7 June 2020; revised 30 October 2020; accepted 8 March 2021

Abstract. A new Dual Stator Multiphase Phase Induction Motor (DSMIM) configuration is proposed and described in this paper. Steady state equivalent circuit of DSMIM is developed and its performance parameters are calculated. The efficiency curves plotted under different excitation modes of the machine assists in operating it at a better efficiency for wider load range. Thus, the proposed configuration can be utilized in Electric Vehicles (EV) to efficiently support a sudden load change during acceleration, cruising and uphill driving patterns. A Finite Element Method (FEM) based design of the machine is done using software. The elec- tromagnetic performance of DSMIM is analyzed through the flux patterns obtained at different excitation modes. Its electromechanical performance is studied by analyzing the current, and speed developed under load driven conditions. The article also proposes an ideology behind the mechanical arrangement of DSMIM for fabrication. The simulation results are included to illustrate the performance of DSMIM. The results are compared and validated with the analytical results obtained through equivalent circuit approach.

Keywords. DSMIM; Equivalent circuit; Efficiency curves; EV; FEM; Electromagnetic and electromechanical performance.

1. Introduction Motor (PMSM), Switched (SRM) and Brushless DC motor (BLDC) [12, 13]. PMSM, BLDC and Induction motors (IM) are the giant utilization in many of SRM inherently enjoy the features of high power density the industrial applications. It is acclaimed for its com- and high torque to current ratio which are considered to be mendable features such as simplicity, ruggedness and reli- the primary necessities of a [14, 15]. These ability. Significant efforts have been taken to suppress the features also made them as the strong competitors in trac- shortcomings of an IM by various modifications in its tion industry. PMSM and BLDC motor require rare earth design and constructional arrangement [1, 2]. Certain materials for its construction. The difficulties faced with noticeable modifications made IMs extensively used in unavailability and unstable cost of the rare earth materials traction application [3, 4]. In spite of the fact that a traction stirred research towards a magnet free configuration. SRMs motor should sufficiently develop enough starting torque to are considered to be a better suited magnet free configu- overcome vehicle inertia, it is also vital that it should ration in traction application but it greatly suffers from operate at a better efficiency for wider load range [5–9]. A torque ripple and acoustic noise [16–19]. Such undesir- span of research in improving the starting torque of squirrel ability once again directed research towards the renovation cage induction motors sprang up with the development of of IMs in order to acquire its beneficial utilization in trac- deep bar and double cage induction motor configurations. tion application. Both exhibited an appreciable performance in developing a A Multiphase Induction Motor (MIM), whose number of high starting torque due to the distributed leakage reactance phases is usually greater than three, was conceived with the in its core but failed in performing at a better effi- necessity of high power and reliability demands. It gained ciency for wider load range [10, 11]. This aspect pushed popularity with the growth and expansion of power elec- deep bar and double cage induction motors behind other tronic drives [20, 21]. Its stator windings are shifted sym- traction motors such as Permanent Magnet Synchronous metrically by 360 o/ number of phases and it could operate with a reduced current per phase without increasing the *For correspondence voltage per phase. It is also featured with lower dc link 67 Page 2 of 11 Sådhanå (2021) 46:67 current harmonics, reduced torque pulsations and increased Steady state equivalent circuit approach is a well-estab- torque to current ratio with reference to its three-phase lished conventional method to analytically arrive at the counterpart. Increased fault tolerance with the failure of one machine parameters and performance characteristics [26]. or two phases is a major aspect for its wider utilization in This kind of analysis helps out in identifying the perfor- submarines, rail traction, avionics and automobiles [22, 23]. mance of the machine before being designed or fabricated. Due to these entrancing features, MIM grabbed its attention Finite Element Method (FEM) is the most popular and an in Electric Vehicle (EV) applications. Later the concept of extensively used advanced numerical method that assists in load sharing and torque producing capability headed its structural, thermal, vibration, electromagnetic and elec- importance in EV. In order to satisfy this, a Dual Stator tromechanical analysis of any complex geometry. The Winding Induction Motor (DSWIM) which includes a simple and result oriented approach towards analyzing the secondary stator winding in addition to the existing primary electromagnetic and electromechanical performance of a stator winding was proposed. The two sets of insulated machine with FEM based software such as MAGNET, stator winding are wound in the same stator core and are ANSYS, COMSOL etc. made FEM a versatile tool in excited separately by two inverters depending upon the load machine designing [27, 28]. demand. This configuration is facilitated with an effective The paper is organized to present the development of torque and speed control [24] but it suffers from saturation steady state equivalent circuit and efficiency curves for of the entire stator core even at lesser load demand i.e. even DSMIM along with an enlightenment to its utilization in at the excitation of any one of the two stator windings. This EV in Section 2. Design of DSMIM and an ideology for its results in improper stator core utilization, development of mechanical arrangement is presented in Section 3. FEM more iron loss and efficiency deterioration [25]. based simulation analysis is carried out in MAGNET This paper proposes a novel Dual Stator Multiphase software to study and analyze its electromagnetic and Induction Motor (DSMIM) which stands apart from other electromechanical performances in Sections 4.1 and 4.2 traction motors in its constructional arrangement. It is respectively. The simulation results depicted at different developed with the aim of incorporating the benefits of excitation modes are validated with the analytical results MIM and DSWIM in a single configuration. It consists of obtained through equivalent circuit approach in Section 4. two separate stator cores namely the inner stator core and the outer stator core. Each core involves an individual set of multiphase stator winding wound separately over its slots. 2. Equivalent circuit analysis of DSMIM The outer stator is of higher power rating which supports a higher load demand and the inner stator is of lower power Equivalent circuit approach is a traditional tool used in rating which supports a lesser load demand. As the load predicting the performance of any electrical machine. The demand increases more than the rated load demand of the constructional approach adapted for building the equivalent individual when excited separately then both the circuit of a MIM is similar to that of a conventional three stator could be excited simultaneously. To facilitate this phase induction motor [29, 30]. The steady state equivalent selective excitation, the machine is featured with a stator circuit of DSMIM is given in figure 1. This circuit is selection switch. This switch assists in shifting the excita- developed such that all parameters of inner stator and rotor tion between the two stators or bring both stators under are referred to the outer stator. The outer and inner stators 0 excitation based on the load demand. Thus, with two are represented as two stator impedances Zs1 and Z s2 individual stator arrangement this configuration satisfies the concept of load sharing and high torque production. It paves way for proper stator core utilization by localized core saturation at minimal load conditions which helps in minimization of iron losses. A hollow squirrel cage rotor is housed between the two stators. The configuration is expected to generously include the advantages of MIM to make it more specifically applicable in places where better efficiency and reliability are demanded. The proposed DSMIM is claimed to be a well potent traction unit in EV application since it makes the vehicle to operate with a better efficiency at its various load changing conditions like acceleration, cursing and uphill movement. This improves the overall energy efficiency of the vehicle and in turn improves its fuel economy and drive range. Prior to the discussions on design and fabrication it is customary to develop the equivalent circuit of DSMIM to study, analyze and predict its static or dynamic behavior. Figure 1. Steady state equivalent circuit of DSMIM. Sådhanå (2021) 46:67 Page 3 of 11 67 respectively. The air gap between the outer stator and the rotor is represented by the magnetizing reactance jXm1 and the air gap between the inner stator and the rotor is repre- 0 sented by the magnetizing reactance jX m2. These two windings are connected in parallel with the rotor impedance 0 Z r through the control switches S1 and S2. The control switches facilitate the excitation of the inner and outer stator separately. Based on the switching arrangement three different modes of excitation can be achieved in DSMIM. Mode I correspond to outer stator excitation with switch S1 Figure 3. Thevinin’s equivalent circuit of DSMIM under dual turned on and S2 turned off. Mode II correspond to inner stator excitation. stator excitation with switch S2 turned on and S1 turned off. Mode III correspond to dual stator excitation with both the switches turned on. It is also interesting to note that under Where, the values of Vth and Zth are given by equation dual excitation mode the equivalent circuit appears as two (3) and equation (4) respectively. parallel connected motors with a common rotor. Thus, the ð jj 0 Þ machine is designed in such a way that it could be ener- Vs jXm1 jXm2 V ¼ 0 0 ð3Þ th ð jj Þþð jj Þ gized by either of the stators or both simultaneously Zs1 Zs2 jXm1 jXm2 depending upon the power and efficiency demands.  ¼ jj 0 þ jj 0 ð Þ The equivalent circuit during mode I and mode II is Zth Zs1 Zs2 jXm1 jXm2 4 similar to the conventional steady state equivalent circuit of 0 a five-phase induction motor. Therefore, the torque devel- Load impedance ZL is equal to the rotor impedance Z r oped under these modes is given by equation (1). and it is given by equation (5).

0 0 0 0 0 Z ¼ R þ jX ð Þ ¼ 5 2 Rr ð Þ r r r 5 Te Ir 1 xs s 0 On substituting the equations of Vth, Zth and Z r in 0 0 The equation of rotor current Ir under dual excitation equation (2) the rotor current Ir under dual excitation can cannot be the same as that in a conventional five phase be represented by equation (6). induction motor. Hence the developed equivalent circuit is ð þ 0 Þ simplified with an interest of determining the equation of 0 Vth Zs1 Zs2 I ¼ 0 ð6Þ r ð þ 0 Þ rotor current through Thevinin’s approach. Under Mode III Zs1Zs2 1 Xr the two control switches are kept closed. This modifies the Therefore, the torque developed by the DSMIM under equivalent circuit as in figure 2. Further it is simplified into dual stator excitation is obtained through equation (7) Thevenin’s equivalent circuit as shown in figure 3. From 0 0 0 figure 3 the rotor current Ir can be calculated as in equation 2 2 5 V ðZs1 þ Z Þ R (2) T ¼ th s2 r ð7Þ e x ð 0 ð þ 0 ÞÞ2 s s Zs1Zs2 1 Xr 0 ¼ Vth ð Þ I 0 2 Equation (7) exhibits the dependency of developed tor- r Z þ Z th r que upon the parameters of both outer and inner stator windings. It is also important to note that the torque developed in mode III can be enhanced only by a syn- chronized five phase dual stator excitation because such excitation increases flux density and aids in acquiring rotating fluxes that lie in phase to each other. These fluxes go hand in hand to develop the net torque. In other words, net torque Te developed by DSMIM under dual excitation will be the vector sum of the torque Te1 developed by the outer stator excitation and the torque Te2 developed by the of inner stator excitation as represented in equation (8).

Te ¼ Te1 þ Te2 ð8Þ Therefore, during mode III it is essential to have a syn- chronized five phase excitation at the dual stator windings Figure 2. Equivalent circuit of DSMIM under dual stator of DSMIM. This could be achieved by two identical five excitation. phase voltage source inverters with separate DC input 67 Page 4 of 11 Sådhanå (2021) 46:67 sources. Providing a synchronized Pulse Width Modulation Table 2. Equivalent Circuit Parameters of DSMIM. (PWM) to the two inverter switches helps in developing a synchronized five phase output voltage. Such voltage is free Operating modes Parameters (X) from even and sub- harmonic waves and its symmetrical I II III control enables speed control of DSMIM [31]. The electrical specifications considered for the design of Stator resistance Rs 18.2 37.9 8.2 DSMIM are listed in table 1. The traditional analytical Stator reactance Xs 52.6 72.1 52.9 Outer magnetizing reactance Xm1 247 – 227 approach involved in a no load and is 0 Inner magnetizing reactance Xm2 – 365 230 adapted for acquiring the equivalent circuit parameters. The 0 Rotor resistance Rr 8.41 13.3 8.41 parameters are calculated for all the three modes of Rotor reactance X 0 19.5 30.7 38.5 DSMIM and listed in table 2. Performance characteristics r of the machine shall be studied analytically using the tab- ulated equivalent circuit parameters. Torque and efficiency of DSMIM are calculated under rated load conditions and listed in table 5 in section 4. In order to explore the maximum efficiency load points, effi- ciency curves of the machine under all three excitation modes are plotted as shown in figure 4. The plot is drawn between percentage efficiency and the per unit values of output power calculated by considering 1.5 HP as the base power. It shows that under dual excitation the machine operates at a maximum efficiency of 85% at 80% full load i.e. 80% of 1.5 HP. As the load demand drops either the inner or the outer stator alone is excited and the machine now runs as a single stator five phase induction motor. A maximum efficiency of 84% is attained at 90% full load i.e. 90% of 1 HP under outer stator excitation and a maximum efficiency of 82% is attained at 80% full load i.e. 80% of 0.5 HP under inner stator excitation. Thus, the DSMIM tend to operate with a higher efficiency at various load points. Figure 4. Efficiency curves of DSMIM under the three excita- In an EV there are three basic driving patterns such as tion modes. acceleration, cursing and uphill movement. During accel- eration the vehicle requires high power to displace itself from rest. Cruising is the vehicle’s free running condition Let us now consider the proposed DSMIM being oper- over level roads which require only a minimal amount of ated as a traction motor under acceleration, cruising and power. Power demand of the vehicle reaches to its maxi- uphill movement with load demands assumed to be 0.5 p.u, mum when it is subjected to uphill movement. Any traction 0.2 p.u and 0.7 p.u respectively. The selection of stator motor could sufficiently satisfy these variations in power excitation during each driving pattern is represented in demand but how efficiently it does matters. Because an table 3. efficient operation of a traction motor at various load points At T = t1 the vehicle is considered to accelerate with load highly assist in energy saving and in turn increases the demand of 0.5 p.u. From the efficiency curve plot in fig- driving range of EV. The proposed DSMIM configuration ure 4 it is observable that this load demand could be sat- is claimed to operate with better efficiency at different load isfied by either exciting the outer stator or both the stators. points by changing the stator excitation. But the machine operates at a higher efficiency only on exciting the outer stator. At T = t2 the vehicle is considered to cruise with a minimal load demand of 0.2 p.u. This load demand can be satisfied by any of the three excitation Table 1. DSMIM specification. modes. But the machine operates at a higher efficiency only Rating Outer stator Inner stator on exciting the inner stator. Thus, the excitation is now shifted to inner stator alone. At T = t3 the vehicle moves Rated power (P) 1 HP 0.5 HP over uphill with a further raise in load demand up to 0.7 p.u. Supply voltage (V) 230 V 230V This load demand can only be satisfied by dual stator No. of phases (n) 5 5 excitation as the load demand now exceeds the rated load of No. of poles (p) 4 4 Rated speed (N) 1440 rpm 1440 rpm the inner and outer stator. Therefore, depending upon the Frequency (f) 50 Hz 50 Hz driving patterns and its load demand, excitation of stator shall be selected to make the machine operate at a higher Sådhanå (2021) 46:67 Page 5 of 11 67

Table 3. Excitation Mode Selection in DSMIM under EV Driving Patterns.

Time interval T (Sec) EV driving pattern Load demand P0 (p.u) Excitation t1 Acceleration 0.5 Outer stator t2 Cruising 0.2 Inner stator t3 uphill Movement 0.7 Dual stator

efficiency. The selection mechanism is facilitated by a design is 1.5 HP. The inner stator is constructed with a programmable switch termed as the stator selection switch. lesser diameter and material than the outer stator and hence By sensing the load current the switch is programmed to it is considered that the motor delivers a rated mechanical estimate the load demand and accordingly shift the exci- power output of 0.5 HP, 1.0 HP and 1.5 HP with the inner, tation modes. This illustration justifies that the proposed outer, and dual excitations respectively. DSMIM can be considered as a well potent traction motor The two stator cores are constructed by laminated sheets in improving the performance of an EV. of Si steel stacked together with a stack factor of 0.9. Dynamic performance of DSMIM with high degree of Choice of specific electric loading, magnetic loading, L/s accuracy can be studied through its design and structural ratio and winding factor are fixed for both the stators sep- analysis using Finite Element Method. This method arately. An optimal value is chosen for magnetic and requires a sound knowledge over the characterization of electric loading as it greatly influences the total iron and machine under study [32]. Physical geometry, choice of copper losses in the machine. The L/s ratio is fixed on the material, winding distribution, electromagnetic property, choice of achieving a better efficiency [33]. By fixing the nature of instantaneous current and flux distribution is the flux densities at various parts of the magnetic circuit the key information prerequisite to successfully proceed with stator core, stator slot, rotor core, rotor bar and end ring design and construction of the machine. dimensions are calculated and listed in table 4. Based on the above tabulated design parameters, the five- phase dual stator induction motor is designed using 3. Design and construction of DSMIM MAGNET software. The design procedure involved is discussed in the following sections. The cross-sectional quadrant view of DSMIM is shown in figure 5. Its construction includes two electrically isolated stators with a hollow squirrel cage rotor housed in between. 3.1 Design of dual stator There are two air gaps, one between the outer stator and the The inner and outer stator model developed in MAGNET is rotor and the other between the inner stator and the rotor. shown in figure 6. The space between inner and outer stator Under the excitation of any one of the stators, this config- is utilized for fixing the hollow squirrel cage rotor uration exhibits an operation similar to that of a conven- tional five phase induction motor. A traditional design procedure is adopted in designing the proposed configura- Table 4. Design parameters of DSMIM. tion. The rated power of the DSMIM considered in the Parameters Outer stator Inner stator Stator bore diameter (mm) 146 115 Gross iron length (mm) 61.9 61.9 No. of stator slots 40 40 Stator teeth width (mm) 4 3.5 Stator slot depth (mm) 13 16 Stator core depth (mm) 18.5 14.5 Slot opening (mm) 0.2 0.2 Air gap length (mm) 0.35 0.3 Rotor outer diameter (mm) 145.3 Rotor inner diameter (mm) 115.3 No. of rotor slots 42 Rotor slot pitch (mm) 10.8 Rotor bar length (mm) 80 Bar cross sectional area (mm2)119 2.5 End ring mean diameter (mm) 131 Figure 5.. Dual stator five phase induction motor drive. End ring cross sectional area (m2) 12.5 9 6 67 Page 6 of 11 Sådhanå (2021) 46:67

stator teeth. Semi closed slots are most prevalent in smaller machines. Since efficiency is chosen as a major concern both the inner and outer stators of our case study are designed with semi closed slots. Length of air gap creates an impact upon the pulsation losses, magnetic pull, cooling, loading capacity and power factor of a machine [36]. The outer and inner air gap lengths in the case study are considered to be 0.35mm and 0.3 mm respectively.

3.2 Design of hollow squirrel cage rotor The hollow squirrel cage rotor model developed in MAG- NET is shown in figure 8. It involves a Si steel rotor core with copper bars embedded within the closed rotor slots. Figure 6. Dual stator 2D model. The rotor bars are short circuited by end rings as in the case of a conventional type squirrel cage rotor. Closed rotor slot arrangement helps in achieving a circumvented by inner and outer air gaps. The winding smooth rotor surface at the air gap. Number of rotor slots is arrangement patterns of both the stators are the same and it chosen in proper combination with stator slots to avoid is represented by the winding distribution diagram shown in unpredictable hooks and cusps in torque speed character- figure 7. Mush winding is chosen for the design. It is a type istics [37, 38]. Cross sectional area of the rotor bar and end of single layer winding preferred for small induction motors ring are so chosen to attain a rotor resistance that meets the having circular conductors. The number of phases in both torque and efficiency demands. the stators is five and therefore the phase difference between the windings is 720 and phase spread is 36°. The coils are short pitched by one slot with a chording angle of 3.3 Mechanical arrangement of DSMIM 18°. Both stators involve four poles and ten slots corre- The mechanical arrangement of DSMIM is not analogous sponding to each pole. to a conventional IM. Proper alignment of the rotor core in- In the winding distribution diagram, the five phase coils between the two stators with respect to a definite central are represented by five different colors. In and out in it axis is the most significant aspect of this design to avoid represents the entering and leaving ends of the coil that eccentricity in standstill and rotary conditions [39, 40]. passes through the slots. The number of stator slots is Also, it is quite delicate to fix the shaft with the hollow chosen as a multiple of number of phases. Also, it is rotor located in between the two stators. Considering these selected appropriately to fix the weight, cost and opera- intricacies, the longitudinal view of the mechanical tional characteristics of the motor [34, 35]. arrangement of DSMIM is proposed as shown in figure 9. Slot depth and slot width that decides the area of the slot It clearly depicts that at drive end, the shaft is clamped are so chosen to attain a perfectly parallel flux path at the along with a disc like arrangement termed as holder. The holder is designed with a shaft hole at its center and two elevated concentric rings along its circumference. The diameter of the inner and outer ring is so chosen to firmly

Figure 7. Mush winding distribution diagram. Figure 8. Hollow squirrel cage rotor 2D model. Sådhanå (2021) 46:67 Page 7 of 11 67 encase the hollow rotor body. The holder thus establishes a As the number of poles chosen for the design equals to mechanical contact between the hollow rotor and shaft. four for both the stators, the flux pattern developed under Insulation is made at the inner surface of the rings in order all the three modes of operation exhibits four closed paths to electrically isolate the holder from the rotor. During each concealing ten stator slots. The direction of the field stator excitation the torque developed rotates the rotor flux can be reversed by reversing the excitation to the field along with the holder attached to it. This arrangement windings. From figure 10 and figure 11 during individual smoothens the way for shaft rotation at the drive end. The excitation of the outer and inner stator windings the flux holder should also ensure that the position of rotor is fixed produced links the rotor and the unexcited stator by passing precisely with respect to the central axis so as to maintain through the inner and outer air gaps. This pattern of flux the air gap lengths and avoid eccentricity. It is important to linkage illustrates an increased reluctance offered to the note that the holder material chosen for the design should flux path. Only the useful flux linked with the rotor assists be characterized with less mechanical strength to avoid its in developing the net torque. Also, the pattern significantly influence over the moment of inertia of rotor. indicates the increased total leakage reactance of the pro- posed model during individual excitation than a conven- tional single stator induction motor. 4. FEM results and discussion During dual excitation the flux pattern developed is obtained as in figure 12. It illustrates the formation of four DSMIM considered for the case study is modeled three poles in both the stators with its flux path linking the outer dimensionally in MAGNET. Its electromagnetic and elec- stator, outer air gap, rotor, inner air gap and the inner stator. tromechanical performances are obtained through simulat- The shaded plot obtained through the simulation also ing the model in 2D static and transient solvers. The results reveals that the maximum flux density region occurs at the are depicted and discussed in the following sections. pole formation region of the stator teeth. The value of maximum flux density equals to 1.907 wb/m2 which lies within the maximum flux density limit of the stator core 4.1 Electromagnetic performance material used. Operational analysis of DSMIM and its electromagnetic performance greatly depends on the number, size and type 4.2 Electromechanical performance of the finite elements chosen. The proposed configuration’s 3D design involves 5, 21,967 triangular meshes created for Electromechanical performance study helps in analyzing the complete 3600 geometry with the default element size the transient characteristics of a machine. The DSMIM setup in the software. The DSMIM is made to operate in design is investigated under load driven conditions. It is three different modes by exciting the outer and inner stator carried out by providing an external load torque as input to five phase windings separately and concurrently with a five- graphically obtain the corresponding electromagnetic tor- phase power supply of 230V rms. The flux patterns que and speed developed as outputs. The design is simu- developed and distributed over its 2D geometrical view lated in transient 2D motion solver for 1000 ms under all during the excitation of the outer, inner and dual excitation three excitation modes. The rated per phase current are shown in figure 10, figure 11 and figure 12 respectively.

Figure 9. Longitudinal view of the mechanical arrangement in Figure 10. Flux developed due to outer stator excitation. DSMIM. 67 Page 8 of 11 Sådhanå (2021) 46:67

Figure 13. Rated per phase current of DSMIM under outer stator excitation.

Figure 11. Flux developed due to inner stator excitation.

Figure 14. Torque developed by DSMIM under outer stator excitation.

Under mode II the rated power of DSMIM is 0.5 HP and Figure 12. Flux developed due to dual stator excitation. therefore its rated load torque is calculated to be 2.5 Nm. This load demand is met by exciting the inner stator alone. The rated per phase current Ia1 developed in the inner stator waveform developed under inner and outer stator excita- winding is shown in figure 15 and the corresponding torque tions are depicted up to 500 ms for better clarity. developed is shown in figure 16. Under mode I the rated power of DSMIM is 1 HP and From figure 15 the RMS value of the rated per phase therefore its rated load torque is calculated to be 5 Nm. This current Ia2 is observed to be equal to 0.52 A. From figure 16 load demand is met by exciting the outer stator alone. The it is noticeable that the torque developed under the inner rated per phase current Ia1 developed in the outer stator stator excitation settles at 650 ms with an average rated winding is shown in figure 13 and the corresponding torque torque of 2.56 Nm and a torque ripple of 15.1 %. From developed is shown in figure 14. simulation results of rated current, torque and speed the From figure 13 the RMS value of the rated per phase efficiency of DSMIM under inner stator excitation is cal- current Ia1 is observed to be equal to 1.02 A. From figure 14 culated to be 79.7%. it is noticeable that the torque developed under the outer Under mode III the rated power of DSMIM is 1.5 HP and stator excitation settles at 600 ms with an average rated therefore its rated load torque is calculated to be 7.4 Nm. torque value of 5.21 Nm and a torque ripple of 24.6 %. This load demand can only be met by simultaneously From simulation results of rated current, torque and speed exciting the inner and outer stators. The total rated current the efficiency of DSMIM under outer stator excitation is developed under this mode will be the addition of the calculated to be 82.5 %. current developed in the outer and inner stator excitations. Sådhanå (2021) 46:67 Page 9 of 11 67

The net torque developed under this mode is depicted in figure 17. From figure 17 it is observed that, the torque developed on exciting the outer and inner stators settles at 610 ms at 7.31 Nm. The torque ripple is calculated to be 8.6 %. From simulation results of rated current, torque and speed the efficiency of DSMIM under inner stator excitation is cal- culated to be 81.6 %. It is observable from the simulation results of torque that the average torque developed under dual excitation is greater than the average torque developed under single stator excitation. It is due to the synchronized five phase excitation of the dual stators under this mode as discussed in section 2. Also, it is important to note from the simu- Figure 15. Rated per phase current of DSMIM under inner stator lation results that the average torque developed under dual excitation. excitation mode is almost equal to the sum of average developed under single stator excitation mode. The percentage torque ripple during dual excitation mode is observed to be lesser than in the other two modes. It is because of the involvement of two sets of five phase stator winding with a synchronized voltage excitation. The five stator windings are spatially displaced by 360°/5 = 72°. This displacement neutralizes the fifth harmonic flux wave produced by each of the five phases winding with one another. Therefore, the synchronized five phase voltages provided at the stator windings are devoid of 5th harmonic, even harmonic and sub harmonic waves and so it greatly reduces the space harmonic fluxes developed at the inner and outer air gaps. The hollow rotor mounted in between the two air gaps is now subjected to a lesser air gap flux harmonic and hence the developed harmonic rotor current Figure 16. Torque developed by DSMIM under inner stator which is responsible for the production of torque ripple is excitation. also lesser. It is noticeable from figure 12 that the flux pattern obtained during dual excitation is much smoother at the air gap and evenly distributed all over the motor geometry resulting in the development of torque with lesser ripple as depicted in figure 17. The average angular speed of DSMIM is obtained by measuring the angle at which the rotor rotates in a second and hence it is represented in degree/sec. Approximately 1 degree/ sec = (1/6) rpm. From the electrical specification as mentioned in table 1 the rated speed developed by the configuration is 1440 rpm i.e. 8640 deg/sec. Since the simulation is carried out by applying an external load equal to the rated load that corresponds to all three modes, the DSMIM develops a rated speed which is the same at all three modes of operation as depicted in figure 18. The speed output settles at a value of 8542 deg/sec i.e. 1423 rpm at 650 ms with a steady state error of 1.13%. A comparative analysis is carried out between the rated average torque and efficiency obtained analytically through Figure 17. Torque developed by DSMIM under dual stator equivalent circuit approach and FEM software. The calcu- excitation. lated torque an efficiency values are listed in table 5. 67 Page 10 of 11 Sådhanå (2021) 46:67

machine were calculated through equivalent circuit approach and the simulation results of FEM. The compar- ative analysis carried out between the results exhibit an error of less than 5 %. Thus, the promising features and the results revealed from simulation flourishes the utilization of DSMIM in an EV application.

References

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