Switched Reluctance Machines for Hybrid Electric Vehicles

Abstract ? This paper presents a procedure of determination of static characteristics of switched reluctance machines (SRMs). Calculations are realized for two SRM topologies including novel configuration with 8 stator and 14 rotor poles (SRM 8/14). This configuration is based on new pole design formula introduced recently. Flux linkage and static torque characteristics are calculated for different rotor positions and stator currents using two-dimensional finite element analysis (2D-FEA). Simulation results for new SRM 8/14 and conventional SRM 8/6 with the same number of phases and outer dimensions are presented and compared. This comparison shows that new configuration can have better torque density. Therefore, new design approach should be considered to make this type of machines a more attractive for high performance HEV’s (Hybrid Electric Vehicle’s) drives.

Index Terms – hybrid electric vehicle, static characteristics, switched reluctance machine

I. I NTRODUCTION

Air pollution, global warming and depletion of the World's petroleum resources are led to an increased interest for clean and efficient vehicles. HEVs, PHEVs (Plug-In HEVs) and FCVs (Fuel Cell Vehicles) have been typically proposed to replace ICEVs (Internal Combustion Engine Vehicles) in the near future. Electric drives are the core technology for HEVs. They have to fulfill vehicle characteristics (acceleration, gradeability, maximum speed and range), considering constraints such as vehicle volume, weight and payload and power source limits [1], [2]. The basic characteristics of an electric drive for HEVs are [3]-[7]:

? high torque and high power density;

? high torque at low speed for starting and hill climbing; ? high power at high speed for cruising;

? very wide speed range including low speed for urban

and high speed for highway driving;

? wide constant power operation capability, thus lowering

machine’s rated power;

? high efficiency over wide speed and torque ranges,

especially for regenerative braking; ? fast torque response;

? high intermittent overload capability for overtaking; ? low level of torque ripple and acoustic noise; ? fault tolerance operation;

S. Smaka is with University of Sarajevo, Faculty of Electrical Engineering, 71000 Sarajevo, Bosnia and Herzegovina (e-mail: ssmaka@etf.unsa.ba).

?. Ma?i ? is with University of Sarajevo, Faculty of Electrical Engineering, 71000 Sarajevo, Bosnia and Herzegovina (e-mail: smasic@etf.unsa.ba).

M. ?osovi ? is with University of Sarajevo, Faculty of Electrical Engineering, 71000 Sarajevo, Bosnia and Herzegovina (e-mail: mcosovic@etf.unsa.ba).

I. Salihbegovi ? is with Elektroprivreda BiH, Generation Department, 71000 Sarajevo, Bosnia and Herzegovina (e-mail: i.salihbegovic@elektroprivreda.ba).

high reliability and robustness for specific vehicular working environment; ? reasonable cost.

Additional characteristics are: good voltage regulation over wide speed generation; modular design; low level of electromagnetic interference (EMI) noise; widespread market acceptance [3], [4], [7].

SRMs have potential for vehicle propulsion due to several advantages [8]-[12]: low manufacturing cost owing to simple construction; concentric stator windings with short end-turn, thus reducing machine’s inactive part and copper losses; rotor does not have winding or PMs, it is highly mechanical robust and therefore suited for high speed operation; suitable torque-speed characteristic with long constant power range; high reliability due to absence of excitation source on the rotor, so there is no rotor winding failures, demagnetization or flying off of the PMs; fault tolerance operation due to low cross-coupling effects between phases; the major sources of heat are on the stator and therefore cooling is simpler; low maintenance; resilience to harsh operating condition.

Two major shortcomings of SRMs are acoustic noise generation and torque ripple. However, there are other disadvantages that can outweigh the advantages of SRMs in automotive applications [7], [9]: EMI noise generation; too many connections between machine and inverter; special inverter topology; nonlinear behavior, i. e. flux-linkage, inductance and torque characteristics are highly nonlinear functions of both rotor position and phase current; control is difficult and subtle.

There are primarily two approaches for reducing the acoustic noise generation. One method is to improve magnetic design of the machine [13]-[15]. Control approach is based on optimizing the selected parameters, such as the supply voltage and turn-on and turn-off angles [16]-[18]. Also, control [19], [20] and design [21]-[23] methods for torque ripple minimization are reported. There has been some success in overcoming these problems, but only at the expense of some output characteristics of the machine [4]. Comparative studies of the few major types of electric machines adopted or under consideration for HEVs traction system presented in [1], [3], [7], [11], [24], [25] shows:

? SRMs is comparable in power density and efficiency

with the Induction Machines (IMs) but Permanent Magnet Synchronous Machines (PMSMs) offers best power density and efficiency;

? SRMs are more expensive than IMs but less than

PMSMs despite price reduction of rare-earth magnets; ? reliability of SRMs is comparable to or even slightly

better than that for IMs and is better than that of the PMSMs;

? SRMs are behind IMs and PMSMs regarding

controllability.

Switched Reluctance Machines for Hybrid Electric Vehicles

S. Smaka, ?.Ma?i ?, M.?osovi ?,I.Salihbegovi ?

XIX International Conference on Electrical Machines - ICEM 2010, Rome

978-1-4244-4175-4/10/$25.00 ?2010 IEEE

The first prototype of SRM for EV (Electric Vehicle) applications was built during the 1980s [4]. Various SRM prototypes, designed and built during last two decades for propulsion of heavy and light full and mild HEVs, are presented in [4], [8], [10], [26]-[31]. All presented configurations are regular three phases (6/4, 12/8 and 24/16) or four phases (8/6) SRMs. To the author’s best knowledge, SRM was not used as traction motor for commercially available vehicles, until now. Nevertheless, a few prototypes of heavy and light full HEVs with SRM-based propulsion system are reported in [10] and [26].

This paper will investigate the potential of the SRM 8/14 configuration for vehicle traction. A 2D-FEA model with refined mesh and reliable nonlinear material properties will be used to obtain the static characteristics of this machine. Flux linkage and static torque of SRM 8/14 will be compared with static characteristics of prototype SRM 8/6 reported in [32]-[34]. These two machines are characterized by the same external dimensions and used materials. Main motor's data for SRM 8/6 and magnetization characteristic of the lamination's material are given in [32]-[34].

II. C OMPUTATION OF S TA TIC C HARACTERISTICS Proper design evaluation and the optimization of SRMs require at least 2D magnetic field analysis done for different positions of the rotor defined by angle θ and phase currents i . The static characteristics of SRM are defined as flux linkage look-up table Ψ(θ,i) and electromagnetic torque look-up

table T(θ,i) for one motor’s phase.

The computation of the flux linkage look-up table Ψ(θ,i) is the first step in performance prediction of the SRM. To complete this task, magnetic field equations must be solved, taking into account saturation effects. The 2D magnetostatic field simulator solves nonlinear Poisson’s field equation for the scalar values of the magnetic vector potential A in

Cartesian coordinates: ()()(,)?????????+?=?????????????A A B B J x y x x y y νν, (1) where are: ν(B ) – the magnetic reluctance, J (x ,y ) – scalar

value of current density.

After A is computed, the magnetic flux linkage can then be computed using the relationships:

11(,) =?=?=?∑

∫

G G n

ph k k k V N l i J A dV A S I S

Ψθ, (2)

where are: I – winding excitation current, G

J – source current

density, G A – magnetic vector potential, N ph – number of

turns per phase windings, l – machine axial length, S – area

for phase winding, A k and S k – scalar values of magnetic

vector potential and area of the k th element, n – number of

elements for area of one winding.

Magnetic coenergy W co (θ,i ) can be calculated on the basis of flux linkage Ψ(θ,i ) characteristics using numerical integration [35]: .0(,)(,) ==∫

co const W i i di θθΨθ. (3) The electromagnetic torque T(θ,i) about the axis of rotation is calculated from the system’s coenergy W co with respect to the angular displacement θ for different rotor

positions and winding excitation current i :

(,)

(,) =?=

?co i const W i T i θθθ

. (4) III. SRM S C ONFIGURATIONS

SRMs are typically designed as regular machines in which the rotor and stator poles are symmetrical about their centerlines and equally spaced around the rotor and stator circumference. Various combinations of stator and rotor poles and number of phases are employed.

Reference [12] presents the design of novel SRM 6/10 and introduces a pole design (PD) formula:

22r s N N =?, (5) where N r is the number of rotor poles, N s is the number of stator poles having one tooth per pole and N s > 4 (N s is even number).

Although SRMs with higher number of rotor poles than stator poles are well known [36], several novel combinations of the stator-rotor poles can be proposed using a newly defined PD formula. SRM 8/14 is 4-phase configuration with number of rotor poles calculated according to (5). This

machine has maximum torque zone of 12,857° mechanical and effective torque zone comparable to rotor poles arc since stator poles are wider than rotor poles. Stroke angle is ε = 6,428° mechanical (90° electrical) and absolute overlap ratio is equal to 2. Number of strokes per revolution is S = 56.

For a comparative evaluation of new SRM 8/14 with the SRM 8/6, the air gap width, stator outer and inner diameter, rotor outer diameter, shaft diameter, stack length and lamination material are kept the same for both these machines. Fig. 1 shows SRM 8/6 and SRM 8/14 cross sections. Both rotors are shown in unaligned position with respect to the phase A.

Fig. 1. SRM 8/6 and SRM 8/14 Cross Sections SRM 8/14 has a narrower stator and rotor poles compared to SRM 8/6. Stator and rotor poles arcs are chosen in order

to enable production of starting torque in every position and

to ensure that there is no overlapping between stator and

rotor poles in the unaligned position. Effective overlap ratio

is slightly greater than 1,2. Total cross sectional area of

stator and rotor laminations is about 13 % lesser for SRM

8/14 and this machine has lower mass, resulting in reduced production cost. Also, SRM 8/14 has bigger space between adjacent stator poles. This additional stator slot area offered

by SRM 8/14 can be used for incorporating a higher number

of winding turns or/and increasing cross sectional area of

conductors. This can improve machine’s torque capabilities

and thermal behavior. A A ′ A A ′ B C D B ′C ′D ′B C D B ′ C ′ D ′

IV. S TATIC C HARACTERISTICS OF SRM 8/6 AND SRM 8/14 A. Configurations with the same Ampere-turns

The results of static characteristics calculation for SRM 8/6 and SRM 8/14 with the same number of turns per phase winding are given in this section.

Fig. 2 shows flux linkage characteristics of SRM 8/6 as a function of winding excitation currents i and for four rotor positions defined by electrical degrees. Angle θ = 0° represents unaligned position and angle θ = 180° depicts aligned position between axes of stator poles of excited phase and rotor poles.

Fig. 2. Flux Linkage Characteristics for Various

Currents and Rotor Positions – SRM 8/6

Fig. 3 shows static torque characteristics of SRM 8/6 for three winding excitation currents and one electrical cycle.

Fig. 3. Static Torque Characteristics for Various

Currents and Rotor Positions – SRM 8/6

Characteristics shown in Fig. 4 and Fig. 5 are the flux linkage and static torque profiles of SRM 8/14.

Fig. 4. Flux Linkage Characteristics for Various

Currents and Rotor Positions – SRM 8/14

Fig. 5. Static Torque Characteristics for Various Currents and Rotor Positions – SRM 8/14

From the flux linkage characteristics shown in Fig. 2 and Fig. 4 is clear that the area enclosed between curves for unaligned (0°) and aligned position (180°) is smaller for the SRM 8/14. In other words, the ratio of the aligned to unaligned inductance is reduced for this machine mainly due to smaller clearance between pole-corners in the unaligned position (increased unaligned inductance). The area between 0° and 180° curves in Fig. 2 and Fig. 4 gives the maximum work done for one stroke of the motor, so as a consequence of smaller area SRM 8/14 has reduced static torque. This can be verified by comparing torque profiles shown in Fig. 3 and Fig. 5. SRM 8/14 produces about 8 % lower peak torque for rated current 6 A. Peak torque reduction is even bigger for higher currents due to saturation of stator and rotor pole tips of SRM 8/14. Also, it can be observed that instantaneous torque at most positions is higher for SRM 8/6 than that of SRM 8/14. Therefore, for current 6 A average torque for one stroke is 11 % lower for SRM 8/14. However, the advantage of the larger N r is a smaller stroke angle, so SRM 8/14 needs 2,33 times more strokes than SRM 8/6 to complete one mechanical revolution. This can be advantage in dynamic and quasistatic states since average torque increases with the number of strokes [12]. But the reduction in available conversion energy tends to offset the increase in the number of strokes per revolution, and the core losses may be higher than those of the SRM 8/6 because of the higher switching frequency.

B. Configurations with different Ampere-turns

SRM 8/14 has the additional winding space due to smaller stator poles width, so this machine has the ability to

incorporate more turns per phase winding. SRM 8/14 configuration investigated in this section has 50 more winding turns per phase (about 11 % more). Also, the conductor cross sectional area is increased. SRM 8/14 has copper round-shaped conductors with diameter equal to 0,767 mm (20,5AWG) while SRM 8/6 has 0,683 mm conductor diameter (21,5AWG). Phase resistances of both machines are calculated on the basis of main stator geometry dimensions and conductor’s diameter. Phase resistances of SRM 8/14 and SRM 8/6 are 3,19 Ω and 3,64 Ω, respectively.

Static torque characteristics of SRM 8/14 with more

winding turns and 20,5AWG wire are shown in Fig. 6. Fig. 7 shows static torque profiles for this SRM 8/14 and SRM 8/6 from 2 A to 6 A and 0° to 180° electrical. Comparisons of static torque characteristics are summarized and presented in Table I. From the Table I it can be observed that the SRM

8/14 produces up to 17,1 % higher peak torque and up to

Rotor Position (Electrical Degree)

T o r q u e (N e w t o n M e t e r )

Phase Winding Current (Ampere)

F l u x L i n k a g e (W e b e r )

Phase Winding Current (Ampere)

F l u x L i n k a g e (W e b e r )

Rotor Position (Electrical Degree)

T o r q u e (N e w t o n M e t e r )

22,5 % higher average torque. Also, it is clear that SRM 8/14 is much more saturated than SRM 8/6 thus improvements of torque production of novel configuration are reduced at higher currents. This is expected since SRM 8/14 has smaller stator and rotor poles area.

Fig. 6. Static Torque Characteristics for Various Currents and Rotor Positions – SRM 8/14 with more winding turns and 20,5 AWG wire

Fig. 7. Comparison of Static Torque Profiles: 2A, 4A, 6A

T ABLE I

C OMPARISON OF S TATIC T ORQUE P ROFILES

P ARAMETER OF C OMPARISON SRM 8/6 SRM 8/14 D IFFERENCE

(%)

Peak Torque 2 A 5,83 6,83 17,15 Average Torque 2 A

3,50

4,29 22,57

Peak Torque 4 A 21,92 24,80 13,14 Average Torque 4 A 12,53 14,14 12,85 Peak Torque 6 A 42,76 45,63 6,71 Average Torque 6 A 23,40 24,60 5,13 Analysis of static torque profiles can provide indication of the torque ripple in dynamic states [12]. For the four

phases SRMs the conduction angle needs to be at least 90° electrical. From the intersection of the individual phase's static torque profiles the turn-on and turn-off angles are chosen: θon = 45° and θoff = 135° electrical for SRM 8/6; θon = 36,5° and θoff = 126,5° electrical for SRM 8/14. Fig. 8 and

Fig. 9 shows output torques of SRM 8/6 and SRM 8/14 for

90° conduction with defined θon and θoff . Torque ripple T r is calculated as: max()min()

100 %i i r avg

T T T T ?=

?, (6) where are: max(T i ) and min(T i ) – maximum and minimum values of instantaneous torque, T avg – average torque.

Calculated values of torque ripple for SRM 8/6 and SRM

8/14 and their differences are presented in Table II. It can be

observed that SRM 8/14 has up to 21,69 % higher torque

ripple. The difference rising toward higher currents since high torque production involves more saturation at these currents for SRM 8/14.

Fig. 8. Evaluation of Torque Ripple for SRM 8/6

Fig. 9. Evaluation of Torque Ripple for SRM 8/14

T ABLE II

C OMPARISON OF T ORQUE R IPPLE

P HASE

C URRENT (A)

Tr (%)SRM 8/6 Tr (%) SRM 8/14 D IFFERENCE (%)

46,91 55,81 18,97 4 45,54 54,91 20,57 6

41,87

50,95 21,69

Since winding phase resistance for SRM 8/14 is 12,36 %

lower than that of the SRM 8/6, this new configuration offers improvements in copper losses. Also, due to relatively thicker conductor, SRM 8/14 offers better continuous current rating. Copper losses per phase calculated for phase current

6 A, for both SRM 8/6 and SRM 8/14, are 131 W and 114,8 W, respectively.

Implementation of the SRM 8/14 in traction drives requires further analysis especially regarding overload capacity and constant-power operating range. The results shown in the Table I allow assessing that the SRM 8/14 will have a limited peak torque due to saturation. Therefore, peak

overload capability of the SRM 8/14 is comparable to that of

the SRM 8/6 but the overload duration for SRM 8/14 can be

higher due to lower copper losses. SRM 8/14 has lower base

speed than SRM 8/6 due to increased number of winding turns. Relatively high number of rotor poles of the SRM

8/14 reduces the room for phase advancing with respect to the SRM 8/6. Future work is planned to explore torque-speed characteristics of SRM 8/14.

Rotor Position (Electrical Degree)

T o r q u e (N e w t o n M e t e r )

Rotor Position (Electrical Degree)T o r q u e (N e w t o n M e t e r )

V. C ONCLUSIONS

In this paper static characteristics of the four-phases conventional SRM 8/6 and novel configuration SRM 8/14 are presented. Inherent advantages of the SRM 8/14 over SRM 8/6 are additional winding space and higher number of rotor poles. Also, SRM 8/14 has lower production cost than that of the SRM 8/6. Static characteristics analysis shows that SRM 8/14 with higher number of winding turns and thicker conductors for windings has better torque density and lower copper losses than conventional SRM 8/6 but also has a higher static torque ripple due to saturation. The new configuration enjoys all other advantages of the SRMs, such as simple construction, mechanical robustness and reliability. SRM 8/14 can improve usability of the SRMs for high-performance HEV's propulsion systems but further investigation is needed in order to obtain optimal machine’s design for this application. Several issues need to be addressed: core losses, constant-power operating range, peak overload capability, and acoustic noise.

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VII. B IOGRAPHIES

Senad Smaka was born on 1969 in Sarajevo, Bosnia and Herzegovina. He graduated from the Faculty of Electrical Engineering at University of Sarajevo in 1996. From 2000 he works as teaching assistant on Department of Power Engineering of Faculty of Electrical Engineering in Sarajevo. He received M.S. degree in electrical engineering from the Faculty of Electrical Engineering and Computing at University of Zagreb in 2004. He is currently working toward the Ph.D. degree in electrical engineering. His research interests include HEVs, modeling and numerical analysis of electrical machines and drives. He is member of IEEE.

?emsudin Ma?i? graduated from University of Sarajevo 1974, received M.S. degree from University of Zagreb 1982 and Ph.D. degree from University of Sarajevo 1992. After completing his graduate studies, he became an Assistant in Department of Power Engineering at the Faculty of Electrical Engineering, University of Sarajevo. Since 1982 he is Research Fellow at the Institute for Automatic and Computer Science and at the Electrical Power Institute by Energoinvest Company, Sarajevo. His research interests are in the areas of electric machines and drives, especially numerical analysis of magnetic fields, mathematical models and measuring characteristics of electric machines and electrical drives in traffic systems. He is now Full Professor, Head of Department of Electrical Machines and Drives. Dr Ma?i? is senior member of IEEE. Currently, he is the Chairman of the A1 Study Committee of Cigré section of Bosnia and Herzegovina.

Mirsad ?osovi?was born on 1984 in Travnik, Bosnia and Herzegovina. He graduated at Faculty of Electrical Engineering at University of Sarajevo in 2009. He works on Department of Power Engineering of Faculty of Electrical Engineering in Sarajevo. His research interests are computer modeling and analysis of electrical machines and drives, generation, transmission and distribution (network components, analysis, operation and control, optimization, planning).

Iris Salihbegovi?was born on 1984 in Sarajevo, Bosnia and Herzegovina. She graduated at Faculty of Electrical Engineering at University of Sarajevo in 2009. From July 2009 she works in Public enterprise Elektroprivreda BiH d.d. Sarajevo, in Generation Department. Her research interests are computer modeling and analysis of electrical machines and drives.