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generator of hybrid electric vehicle
Electric Power Systems Research 75 (2005) 153–160
Design of switched reluctance machine for starter/generator of hybrid electric vehicle Jawad Faiz ∗ , K. Moayed-Zadeh Center of Excellence on Applied Electromagnetic Systems, Department of Electrical and Computer Engineering, Faculty of Engineering, University of Tehran, Tehran 14399, Iran Received 15 June 2004; received in revised form 24 November 2004; accepted 7 February 2005 Available online 13 June 2005
Abstract Simple and robust structure, high power density, high efficiency and fault tolerability of switched reluctance machine (SRM) are good reasons for its selection as starter/generator of hybrid electric vehicles (HEV). Different requirements in generating and motoring modes require special design of SRM. The design is based on pre-defined equations with the objective functions as high torque over low speed and high efficiency over high speed. Experimental results of a typical SRM confirmed the finite element (FE) results, and static analytical model is confirmed by FE computations on the designed motor. Simulation results show that the SRM is capable for starting the vehicle and charging the battery. © 2005 Elsevier B.V. All rights reserved. Keywords: HEV; Starter/generator; SRM; Modeling; FE
1. Introduction Electric vehicles (EV) can be considered as long-term solution for air pollution problem. For short-term solution, hybrid electric vehicle (HEV) is a good choice. HEV utilizes the advantages of fossil fuel vehicles as well as electric vehicles. The electrical machine used in HEV is important from the requirements of the vehicle and its operation. A machine that operates as starter/generator (S/G) should be able to start the vehicle safely. During normal operation, internal combustion engine (ICE) provides the driving force of the vehicle and electrical machine (EM) operates as a generator, providing the required electricity as well as charging the battery. Different types of electrical machines have been studied and among these machines, switched reluctance machine (SRM) is chosen as a proper candidate. The distinguishing features of the SRM system include its ability to operate under fault condition [1], its suitability for operation in harsh environments [2] and its power density to be competitive ∗
Corresponding author. Fax: +98 21 8633029. E-mail address: [email protected] (J. Faiz).
0378-7796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2005.02.004
when compared to other conventional machines [3]. An overview of a similar SRM starter/generator system has been presented in Ref. [4]. So, the SRM can be selected as a convenient approach to meet the system performance requirements and constraints. The simulation results also will show that the starting torque of SRM is high enough for starting HEV. Dual (S/G) operation of SRM requires a design algorithm, which differs with that of individual starter or generator case. High starting torque is important over low speed and during starting period. However, this period is short and high efficiency is not a main issue. High efficiency and good power factor are important factors over high speeds in generating mode. So far all previous researches were concentrated on the overall design procedure of HEV and there is no general method for studying, selecting, designing, modeling and simulating the starting and generating modes SRM. In Ref. [5], only generating mode of the machine has been emphasized and current control of the operation region has been proposed. However, one of the most important factor affecting the current amplitude and waveform is not considered, this factor is the design of the machine in the motoring mode. In Refs. [6] and [7], S/G has been designed
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for the space satellite and gas turbines, but algorithm for torque calculation and required speed are not given. In Ref. [8], without introducing the requirements of S/G application, a starting torque of 140 nm has been suggested which is low for a safe starting of the machine. In Ref. [9], vehicle and its requirements have been studied for an EV, but S/G has not been proposed. In Ref. [10], a FE modeling has been used to predict the steady-state performance of SR motor. Also in Ref. [11], boundary element method has been applied for optimal design of SR motor. However, both methods are computationally time consuming. In optimal design of SRM, an iterative procedure is used, and therefore it is too difficult to employ the above-mentioned methods. Here, FE method is only used to verify the analytical modeling results. The FE results also are compared with the experimental results. The aim of this paper is to introduce a complete algorithm for selecting, modeling and simulating the electrical part of S/G of a HEV. Performance of a typical HEV is obtained and the required torque and speed are determined in order to design the SRM. FE analysis has been carried out to confirm the accuracy of the predicted flux-linkage characteristics, which play a key role in the design process. An algorithm is used to design the SRM; the designed SRM data may be employed as input of an optimization routine for final optimal design.
2. HEV and S/G technology International electrotechnical commission (IEC) defines a hybrid vehicle as a vehicle with two or more energy sources. At least one of these sources must be on board [12]. Fig. 1 describes the concept of HEV. Energy flow is controlled based on the required load and specifications of the vehicle. Basically, there are different combinations of energy flow in HEV, which can be classified as series and parallel. In a series HEV, ICE and EM1 (generator) are located along the same shaft and EM2 (motor), supplied by battery, runs the vehicle. This battery keeps being charged by a generator driven by ICE. The advantage of this combination is that the ICE is separated from force transmission shaft, which makes it possible to design the ICE for a higher efficiency at constant speed. A very good regeneration can be expected in this case. However, two EM and ICE lead to low efficiency and large
Fig. 1. Energy flow paths in HEV.
weight of vehicle. In a parallel HEV, ICE and EM operate in parallel, and vehicle is driven by ICE with the assistance of EM. Also EM provides electrical power to vehicle and charges the battery as a generator. Advantage of this combination is a smaller ICE and a better performance due to the existence of two drives. However, ICE is not always optimal over the operation region and the control of the system operation is complicated. Now what are the sizes of the required ICE and EM? The first option for the designer is that the vehicle is EMdominated or ICE-dominated. The answer to this question determines the approximate size of EM and ICE. For this purpose, a degree of hybridization (DOH) is defined [13]. DOH is between 0 and 1, which relates to the maximum power of two energy sources. For a HEV, DOH is as follows: DOH = 1 −
|Pmax,EM − Pmax,ICE | Pmax,EM + Pmax,ICE
(1)
For a conventional vehicle powered by an ICE or an EV, DOH is equal to zero. In the present work, HEV with small DOH is emphasized. The vehicle operation is ICEdominated. Therefore, the S/G responsibility of EM is to start the vehicle up to a particular speed. In addition, EM charges the battery of the vehicle in generating mode. Performance characteristic of such machine is shown in Fig. 2. This machine operates with a constant torque up to the base speed. Then the ICE provides driving force. Following a particular speed, EM is controlled in generating mode and charges the battery up to the maximum speed with constant power. But starting torque, base speed, maximum speed and other details are determined by design strategy of HEV. At this end, it is necessary to know the vehicle load applied to the drive. Generally, this load can be divided into the three components [9,14]: FRL = Fgxt + Froll + FAD
(2)
The first component is due to the required force on the slope surface and it is equal to: Fgxt = mg sin β
(3)
where m is the mass of vehicle, g the gravity acceleration and β is the angle of the slope surface with horizontal level. The
Fig. 2. Performance characteristic of S/G.
J. Faiz, K. Moayed-Zadeh / Electric Power Systems Research 75 (2005) 153–160
second component is due to the friction of the tire with the road calculated as follows: Froll = Sgn[vxt ]mg(C0 + C1 v2xt )
(4)
where vxt is the speed of the vehicle, C0 the dimensionless resistance factor of the road (between 0.004 and 0.02) and C1 is much smaller than C0 . The third component is due to the air aerodynamic force evaluated as follows: FAD = Sgn[vst ]{0.5ρCD AF (vxt + v0 )2 }
(5)
where ρ is the air density (1.22 kg/m2 ), CD the aerodynamic factor (between 0.2 and 0.4), AF the equivalent area of the vehicle front and v0 is the speed of the wind in the front of the vehicle. The applied force on the vehicle can be calculated as follows: FTR − FRL = Km m
dvxt dt
(6)
In this design, it is assumed that the vehicle moves on horizontal direction and aerodynamic force is also small and negligible. It is also assumed that the vehicle speed reaches 100 km/h in 20 s. Starter runs the vehicle up to 25 km/h in 4.75 s. This speed is approximately equivalent to 250 rpm with radius of wheel equal to 25 cm. The mass of the vehicle is taken to be 800 kg. By these assumptions, the required force is found equal to 1271 N, which requires a starting torque of 317 nm. Hence, 300 nm is the minimum required torque for the safe starting of the machine. It is noted that the voltage level has been increased from 12 V in the traditional vehicle to 42 V in response to the increasing electricity demand of the HEV [5]. In the next section, design of EM is carried out for this voltage level.
a three-phase machine is required. Higher phase number will increase the number of switches. Design algorithms and their various aspects are general problems in SRM. The proposed design is devoted to a specific application and primary design algorithm is only defined the starting point of the optimal design procedure. So far primary design algorithms, such as Refs. [15] and [16], have been introduced that can be employed to obtain the initial design. But a trial and error technique then used to lead this initial design to the optimal design. The design procedure in Ref. [16] has been followed in the present work and flowchart of the design procedure has been shown in Fig. 3. First, the stack length and stator outer diameter are determined based on the required torque (300 nm), speed (250 rpm) and constraints of the dimensions of the machine. Parameters, such as ratio of rotor diameter and stator diameter, pole arc, yoke thickness, height of rotor and stator teeth are determined using two optimization strategies: (1) higher starting torque over low speed and (2) higher efficiency over high speed. Objective function is a combination of starting torque and efficiency in generating mode, this function must be maximized. Starting torque is calculated in low speed such as 30 rpm and generator efficiency is computed in high speed, such as 1200 rpm. Hence, a combine function of these
3. Electromagnetic design of SRM SRM has efficient performance and simple structure, at the same time it is robust and has a reasonable cost compared with the PM machines. Good controllability of SRM by computer, improvement of its control by new power electronic devices over high frequency, high current and low cost, improvement on the knowledge of SRM technology, small and compact design, high speed capability due to the absence of the winding and PM on the rotor, high ratio of torque per volume and torque per weight, capability of working in harsh environments, fault tolerability are some of the advantages of SRM. Different configurations have been proposed and 12/8 SRM has been chosen. A 12/8 SRM is the repetition of a 6/4 SRM, and it has all advantages of 6/4 SRM, in addition the higher number of teeth leads to a shorter end-winding and smaller unaligned inductance. This reduces the copper losses. Simultaneous excitation of four poles shortens the magnetic flux path, which leads to lower core losses. However, higher frequency increases the core losses at the same speed. Also SRM must be able to start at any position of the vehicle, thus
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Fig. 3. Flowchart of design procedure.
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Table 1 Dimensions and specifications of the designed 12/8 SRM
order to include the end-winding effect:
Unaligned inductance (mH) Input voltage (V) Rotor pole arc (degrees) Stator pole arc (degrees) Radius up to rotor pole surface (cm) Stator outer radius (cm) Shaft radius (cm) Air-gap length (mm) Stack length (cm) Rotor core thickness (cm) Stator yoke thickness (cm) Winding turns no./pole
Lend =
0.52 42 16 15 11.56 16.51 4.16 0.5 17.3 3.22 2.12 23
two, F, can be considered as follows: F = ATstart + BηGene
(7)
Depending on the importance of each of these sections, coefficients A and B can be determined. Following determination of the required mmf in the stator poles and taking into account the low level of voltage and high current, attempt is made to achieve the same mmf with lower number of turns and higher current. This leads to thicker wire with low number of turns. The design results have been summarized in Table 1. A three-phase 12/8 SR machine is introduced in such a way that resultant two series opposite poles with pole pair in 90◦ mechanical displacements, is connected in parallel and forms a phase of the machine. Therefore, topology of the drive of the machine is similar to other three-phase machines. From control aspect, different strategies can be applied.
4. Modeling of SRM Following are the reasons for non-linear behavior of SRMs: 1. non-linear B/H characteristic of ferromagnetic materials; 2. dependency of flux-linkage upon rotor position and stator winding current; 3. applying electrical input from one point. Generally, four models have been proposed for SRM. They are graphical models based on FEM, models for special software’s, models based on equivalent magnetic circuit and computational mathematic models and analytical models. The FEM based model produces very precise results, but it is normally used for confirmation of the final design. Second models are normally used for prediction of the dynamic performance and they are suitable to study the performance of a designed machine. The third model is used for approximate design. However, among these models, the fourth, or the analytical model has reasonable accuracy and quickly lead to the results. Hence, it can be used in iterative design procedure. In this paper, an analytical model with proper modifications is used [17,18]. The following empirical equation is used in
Lu ls Lstk 4
(8)
where Lu is the unaligned inductance, Lstk the stack length and ls is the distance between two poles of the stator. In the design of electrical machines, it is a common practice to use some empirical equations. It is in this area that the experience in SRM design must be applied. Of course, most of the many formulas given in the paper are derived from basic electrical and magnetic relations. Derivation and exploration of the various formulas and empirically determined factors will challenge the serious SRM designer seeking the ultimate in economic balance between performance and cost. For this purpose, a comprehensive program has been developed which consists of designing, modeling and simulating SRM using MATLAB. The developed program using MATLAB is too long and detailed has not been included in this paper. In the first section of program, the initial data such as starting torque, base speed and dimensional constraints are taken from the user and initial dimensions are derived using equations in [16]. Then, static analytical modeling is carried out and the necessary database is generated. For prediction of SRM dynamics, first the stator pole flux waveform is obtained. Then flux waveforms in all parts of the machine can be calculated. But, for calculation of the stator pole flux and current, voltage equation and static flux-linkage characteristic are used. Based on the energy conversion, co-energy is the integral of the flux-linkage versus current and torque is calculated from derivative of co-energy versus rotor angle. For efficiency computation, the losses must be first computed. Core losses are calculated using a very quick analytical technique. Then output power is evaluated from torque and speed. This general trend is repeated up to optimal final design and satisfying the designer. Loss modeling, based on Ref. [19], is developed for losses calculation. To obtain the core losses, flux waveforms in different parts of the machine including rotor and stator pole, rotor core and stator yoke are determined. For example, flux waveform in a part of rotor body of the designed machine in the starting mode analytically calculated and has been shown in Fig. 4. The copper losses are also obtained based on the dynamic current. Finally, windage, friction and stray losses are included in a way similar to induction motors. Since the analytical modeling technique is new, it is necessary to confirm the accuracy of the technique. A most convenient tool, which can be used for comparison is modeling by FEM. Although FEM is too slow, in the sametime it is precise and widely used to finalize the design. However, before applying the available FE software’s, it is worth to compare the FE results with the static flux-linkage test results. The static test magnetization data for an 8/6 SRM was available and the static modeling results of a typical 8/6 SRM has been confirmed by that of the FEM results as shown in Fig. 5. Then, the analytical modeling of the designed 12/8 SRM and FE analysis has been compared. The error in static
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157
Fig. 4. Flux waveform (in Wb) in a part of the rotor body.
modeling is due to its analytical nature and quick static modeling which is necessary for the design. This error is small (less than 10%) at high currents. This machine operates in starting mode for a very short time, and frequently operates over high speed and generating mode. In this case, the current is low and error of static modeling using FE method and also experimental is small. Fig. 6 shows the meshed cross-section and flux paths of the machine at the unaligned position. The number of nodes and elements of the employed mesh are 28,433 and 14,176, respectively. Fig. 7 exhibits the FEM and analytical results. Generating mode is the dual of the motoring mode and current is the symmetrical mirror of the motoring current with respect to the aligned position [20,21], Fig. 8 shows this.
5. Performance and simulation results Performances of SR machine in both starting and alternating mode are studied. Fig. 9 shows the analytically calculated current, phase torque of the machine and also its total torque in the starting mode at 50 rpm. It can be realized that the machine is able to develop the starting torque. Since the starting period is short, high current in this mode of operation
Fig. 5. Flux-linkage characteristics for a typical 8/6 SRM: (—) measured, (- - -) FEM.
Fig. 6. (a) Meshed cross-section and (b) flux paths in the designed 12/8 SRM.
does not cause high temperature rise. The current and torque in Fig. 9 show large variations. Here, the proposed SRM have been designed to obtain high starting torque over low speed and high efficiency over high speeds. The variations of the current and torque are intrinsic in SRM and many control
Fig. 7. Flux-linkage for the designed 12/8 SRM: (—) analytical method, (- - -) FEM.
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the torque it must be noted that ICE has ripple and certainly modifications are required in order to reduce the effects of the ripple of the dive system on the transmission system. Due to low speed in starting mode, the returned voltage is small, therefore, maximum current is limited and machine operates in chopping mode. However, in generating mode, due to high speed, the returned voltage is also large and current does not approach the maximum value and machine operates in a single-pulse mode. The equivalent power factor for SRM is as follows [9]: PF = Fig. 8. Comparison of motoring and generating modes of SRM.
techniques have been introduced to minimize the ripples [22]. This has been considered as a control problem and has not been taken into account in the proposed design procedure. Fig. 10 exhibits the analytically calculated phase current and total current of SRM in generating mode at 1000 rpm. During this long period, the output current of the machine can easily charge the battery. As a generator the SR machine produces high ripple content in the generated current as shown in Fig. 10. This current is only the output in the terminal of the machine. There is a control system between the terminals of machine and battery that can control the torque ripple and also battery charging current characteristic. For instance, a coil can be used to reduce the ripple. Regarding the ripple of
Tavg ω Vdc Irms
(9)
where Tavg is the developed average torque of the machine, ω the speed, Vdc the dc bus voltage and Irms is the rms current. The equivalent power factor in starting and generating modes has been analytically calculated and has shown in Fig. 11a. The figure indicates that the equivalent power factor is good and this indicates a suitable use of this machine. Efficiency of the machine has been analytically calculated and shown in Fig. 11b, which tends to unity over high speed. This machine operates in the starting mode of vehicle over low speeds which lasts a short time, it operates frequently in the generating mode and high speeds where its efficiency and power factor are fair. In addition, power factor and efficiency over the low speeds are sacrificed for high starting torque. Also torque/speed and power/speed characteristics of the machine
Fig. 9. (a) Phase current, (b) phase torque and (c) total torque versus time at 1000 rpm.
J. Faiz, K. Moayed-Zadeh / Electric Power Systems Research 75 (2005) 153–160
159
Fig. 11. (a) Equivalent power factor and (b) efficiency of the designed machine. Fig. 10. (a) Phase current and (b) total current of SRM in generating mode at 1000 rpm.
have been shown in Fig. 12, indicating the expected performance. As Fig. 12 shows, the starting torque of SRM is very fair and capable to start the vehicle. Therefore, it is clear that it is a convenient candidate for HEV. The designed SRM has not been yet built, but an optimal design has been obtained using the Genetic algorithm. The motor designed by the above-mentioned routine and used as input of the optimal design process. Table 2 has compared the initial design and the final design. It is noted that the flux-linkage/current/rotor angular position characteristics are a main key for SRM design and comparison of the analytically Table 2 Optimum design results with conventional procedure and genetic algorithm Parameter name
Conventional procedure
Genetic algorithm
DC bus voltage (V) Rotor diameter (cm) Stator diameter (cm) Stack length (cm) Air gap length (cm) Rotor yoke width (cm) Rotor slot depth (cm) Rotor pole arc (◦ ) Stator pole arc (◦ ) Winding turn (turn) Unaligned inductance (mH)
42 23.116 33.023 17.337 0.05 3.217 4.182 16 15 23 230.52
42 21.753 29.357 17.337 0.05 3.036 4.115 15.7 15.3 23 224.87
Fig. 12. (a) Torque/speed and (b) power/speed characteristics of the designed SRM.
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obtained flux-linkage characteristics with the corresponding characteristics shows a good agreement and it is expected that the built machine satisfy the necessary requirements.
6. Conclusions Choice of HEV structure based on the size of EM and ICE was studied and starter/generator has been introduced as a suitable choice for HEV. After successful starting of the vehicle, EM is used to charge the battery over higher speed. Due to high capability of SRM, it has been employed as starter/generator of HEV. In the dual design of starter/ generator, the design algorithm is somehow different with the traditional design algorithm. In addition to the static modeling, the loss modeling has also been included. The study shows that the static modeling results have a good agreement with FEM and experimental results. Simulation results indicated that besides developing the required torque during the starting period of the machine, the machine operates as a generator with good efficiency and equivalent power factor and it is able to charge the battery.
7. Acknowledgements The authors appreciate the help of Dr. Radun from Kentucky University for the static modeling part of the paper. This project was financially supported by University of Tehran.
References [1] C.M. Stephens, Fault detection and management system for fault tolerant switched reluctance drives, in: Conference Record IEEE Industry Applications Society Annual Meeting, September 1989, pp. 574–578. [2] E. Richter, Switched reluctance machines for high performance operations in a harsh environment. A review paper, in: International Conference on Electrical Machines (ICEM), Boston, MA, 1990. [3] E. Richter, et al., The integral starter/generator development progress, in: Proceedings of SAE Aerospace Atlantic’92, Dayton, OH, 1992. [4] S.R. MacMinn, W.D. Jones, A very high speed switched reluctance starter/generator aircraft engine applications, in: Proceedings of NAECON’89, OH, May 1989. [5] B. Fahimi, A switched reluctance machine based starter/generator for more electric cars, in: International Electric Machines and Drives Conference, IEMDC, 2001, pp. 1544–1550.
[6] S.R. MacMinn, W.D. Jones, A very high speed switched reluctance generator for aircraft engine application, in: Proceedings of NAECON’89, Dayton, OH, May 1989. [7] C.A. Ferreira, S.R. Jones, W.S. Heglund, W.D. Jones, Detailed design of a 30 kW switched reluctance starter/generator system for a gas turbine engine application, IEEE Trans. Ind. Appl. 31 (No. 3) (May/June 1995) 553–561. [8] A. de Vries, Y. Bonnassieux, M. Gabsi, E. Hoang, F. d’Oliveira, C. Plasse, A switched reluctance machine for a car starter-alternator system, in: IEEE International Electric Machines and Drives Conference, IEMDC, 2001, pp. 323–328. [9] I. Husain, M.S. Islam, Design, modeling and simulation of electric vehicle system, in: SAE Technical Paper Series, International Congress and Exposition, Detroit, Michigan, March 1999. [10] M. Moallem, C. Ong, Predicting the steady-state performance of a switched reluctance machine, IEEE Trans. Ind. Appl. 27 (No. 6) (November–December 1999) 1087–1097. [11] Y. Tang, J.A. Kline, Modeling and design optimization of switched reluctance machine by boundary element analysis and simulation, IEEE Trans. Energy Convers. 11 (No. 4) (December 1996) 673– 680. [12] D. Hermance, Sh. Sasaki, Hybrid electric vehicle take to the streets, IEEE Spectr. 35 (11) (November 1998) 48–52. [13] B.M. Baumann, G. Washington, B.C. Glenn, G. Rizzoni, Mechatronic design and control of hybrid electric vehicles, IEEE/ASME Trans. Mechatron. 5 (No. 1) (March 2000) 58–72. [14] M. Ehsani, K.M. Rahman, H.A. Tolyat, Propulsion system design of electric and hybrid vehicle, IEEE Trans. Ind. Electron. 44 (No. 1) (February 1997) 19–27. [15] M.N. Anwar, I. Husain, A.V. Radun, A comprehensive design methodology for switched reluctance machines, IEEE Trans. Ind. Appl. 37 (No. 6) (November–December 2001) 1684– 1692. [16] T.J.E. Miller, Switched Reluctance Motors and Their control, Magna Physics Publishing and Clarendon Press, 1993. [17] A. Radun, Analytical calculation of the switched reluctance motors unaligned inductance, IEEE Trans. Magnet. 35 (No. 6) (November 1999) 4473–7781. [18] A. Radun, Analytically computing the flux linked by a switched reluctance motor phase when the stator and rotor poles overlap, IEEE Trans. Magnet. 36 (No. 4) (July 2000) 1996–2003. [19] J. Reinert, R. Inderka, R.W. de Donker, A Novel Method for the Prediction of Losses in Switched Reluctance Machines, 7th European Conference on Power Electronics and Applications, ETEP’97, pp. 3.608–3.612. [20] A. Radun. Generating with the Switched Reluctance Motor, 9th Annual Conference on Applied Power Electronics Conference and Exposition, APEC’94, 1994, vol. 1, pp. 41–47. [21] D.A. Torrey, Switched reluctance generators and their control, IEEE Trans. Ind. Electron. 49 (No. 1) (February 2002) 3–14. [22] J. Faiz, Gh. Soltani-Khosroshahi, Torque ripple minimization in switched reluctance motor by optimal commutation strategy using a novel reference torque, J. Electr. Power Comp. Syst. 30 (No. 7) (July 2002) 769–782.
Design of switched reluctance machine for starter/generator of hybrid electric vehicle Jawad Faiz ∗ , K. Moayed-Zadeh Center of Excellence on Applied Electromagnetic Systems, Department of Electrical and Computer Engineering, Faculty of Engineering, University of Tehran, Tehran 14399, Iran Received 15 June 2004; received in revised form 24 November 2004; accepted 7 February 2005 Available online 13 June 2005
Abstract Simple and robust structure, high power density, high efficiency and fault tolerability of switched reluctance machine (SRM) are good reasons for its selection as starter/generator of hybrid electric vehicles (HEV). Different requirements in generating and motoring modes require special design of SRM. The design is based on pre-defined equations with the objective functions as high torque over low speed and high efficiency over high speed. Experimental results of a typical SRM confirmed the finite element (FE) results, and static analytical model is confirmed by FE computations on the designed motor. Simulation results show that the SRM is capable for starting the vehicle and charging the battery. © 2005 Elsevier B.V. All rights reserved. Keywords: HEV; Starter/generator; SRM; Modeling; FE
1. Introduction Electric vehicles (EV) can be considered as long-term solution for air pollution problem. For short-term solution, hybrid electric vehicle (HEV) is a good choice. HEV utilizes the advantages of fossil fuel vehicles as well as electric vehicles. The electrical machine used in HEV is important from the requirements of the vehicle and its operation. A machine that operates as starter/generator (S/G) should be able to start the vehicle safely. During normal operation, internal combustion engine (ICE) provides the driving force of the vehicle and electrical machine (EM) operates as a generator, providing the required electricity as well as charging the battery. Different types of electrical machines have been studied and among these machines, switched reluctance machine (SRM) is chosen as a proper candidate. The distinguishing features of the SRM system include its ability to operate under fault condition [1], its suitability for operation in harsh environments [2] and its power density to be competitive ∗
Corresponding author. Fax: +98 21 8633029. E-mail address: [email protected] (J. Faiz).
0378-7796/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2005.02.004
when compared to other conventional machines [3]. An overview of a similar SRM starter/generator system has been presented in Ref. [4]. So, the SRM can be selected as a convenient approach to meet the system performance requirements and constraints. The simulation results also will show that the starting torque of SRM is high enough for starting HEV. Dual (S/G) operation of SRM requires a design algorithm, which differs with that of individual starter or generator case. High starting torque is important over low speed and during starting period. However, this period is short and high efficiency is not a main issue. High efficiency and good power factor are important factors over high speeds in generating mode. So far all previous researches were concentrated on the overall design procedure of HEV and there is no general method for studying, selecting, designing, modeling and simulating the starting and generating modes SRM. In Ref. [5], only generating mode of the machine has been emphasized and current control of the operation region has been proposed. However, one of the most important factor affecting the current amplitude and waveform is not considered, this factor is the design of the machine in the motoring mode. In Refs. [6] and [7], S/G has been designed
154
J. Faiz, K. Moayed-Zadeh / Electric Power Systems Research 75 (2005) 153–160
for the space satellite and gas turbines, but algorithm for torque calculation and required speed are not given. In Ref. [8], without introducing the requirements of S/G application, a starting torque of 140 nm has been suggested which is low for a safe starting of the machine. In Ref. [9], vehicle and its requirements have been studied for an EV, but S/G has not been proposed. In Ref. [10], a FE modeling has been used to predict the steady-state performance of SR motor. Also in Ref. [11], boundary element method has been applied for optimal design of SR motor. However, both methods are computationally time consuming. In optimal design of SRM, an iterative procedure is used, and therefore it is too difficult to employ the above-mentioned methods. Here, FE method is only used to verify the analytical modeling results. The FE results also are compared with the experimental results. The aim of this paper is to introduce a complete algorithm for selecting, modeling and simulating the electrical part of S/G of a HEV. Performance of a typical HEV is obtained and the required torque and speed are determined in order to design the SRM. FE analysis has been carried out to confirm the accuracy of the predicted flux-linkage characteristics, which play a key role in the design process. An algorithm is used to design the SRM; the designed SRM data may be employed as input of an optimization routine for final optimal design.
2. HEV and S/G technology International electrotechnical commission (IEC) defines a hybrid vehicle as a vehicle with two or more energy sources. At least one of these sources must be on board [12]. Fig. 1 describes the concept of HEV. Energy flow is controlled based on the required load and specifications of the vehicle. Basically, there are different combinations of energy flow in HEV, which can be classified as series and parallel. In a series HEV, ICE and EM1 (generator) are located along the same shaft and EM2 (motor), supplied by battery, runs the vehicle. This battery keeps being charged by a generator driven by ICE. The advantage of this combination is that the ICE is separated from force transmission shaft, which makes it possible to design the ICE for a higher efficiency at constant speed. A very good regeneration can be expected in this case. However, two EM and ICE lead to low efficiency and large
Fig. 1. Energy flow paths in HEV.
weight of vehicle. In a parallel HEV, ICE and EM operate in parallel, and vehicle is driven by ICE with the assistance of EM. Also EM provides electrical power to vehicle and charges the battery as a generator. Advantage of this combination is a smaller ICE and a better performance due to the existence of two drives. However, ICE is not always optimal over the operation region and the control of the system operation is complicated. Now what are the sizes of the required ICE and EM? The first option for the designer is that the vehicle is EMdominated or ICE-dominated. The answer to this question determines the approximate size of EM and ICE. For this purpose, a degree of hybridization (DOH) is defined [13]. DOH is between 0 and 1, which relates to the maximum power of two energy sources. For a HEV, DOH is as follows: DOH = 1 −
|Pmax,EM − Pmax,ICE | Pmax,EM + Pmax,ICE
(1)
For a conventional vehicle powered by an ICE or an EV, DOH is equal to zero. In the present work, HEV with small DOH is emphasized. The vehicle operation is ICEdominated. Therefore, the S/G responsibility of EM is to start the vehicle up to a particular speed. In addition, EM charges the battery of the vehicle in generating mode. Performance characteristic of such machine is shown in Fig. 2. This machine operates with a constant torque up to the base speed. Then the ICE provides driving force. Following a particular speed, EM is controlled in generating mode and charges the battery up to the maximum speed with constant power. But starting torque, base speed, maximum speed and other details are determined by design strategy of HEV. At this end, it is necessary to know the vehicle load applied to the drive. Generally, this load can be divided into the three components [9,14]: FRL = Fgxt + Froll + FAD
(2)
The first component is due to the required force on the slope surface and it is equal to: Fgxt = mg sin β
(3)
where m is the mass of vehicle, g the gravity acceleration and β is the angle of the slope surface with horizontal level. The
Fig. 2. Performance characteristic of S/G.
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second component is due to the friction of the tire with the road calculated as follows: Froll = Sgn[vxt ]mg(C0 + C1 v2xt )
(4)
where vxt is the speed of the vehicle, C0 the dimensionless resistance factor of the road (between 0.004 and 0.02) and C1 is much smaller than C0 . The third component is due to the air aerodynamic force evaluated as follows: FAD = Sgn[vst ]{0.5ρCD AF (vxt + v0 )2 }
(5)
where ρ is the air density (1.22 kg/m2 ), CD the aerodynamic factor (between 0.2 and 0.4), AF the equivalent area of the vehicle front and v0 is the speed of the wind in the front of the vehicle. The applied force on the vehicle can be calculated as follows: FTR − FRL = Km m
dvxt dt
(6)
In this design, it is assumed that the vehicle moves on horizontal direction and aerodynamic force is also small and negligible. It is also assumed that the vehicle speed reaches 100 km/h in 20 s. Starter runs the vehicle up to 25 km/h in 4.75 s. This speed is approximately equivalent to 250 rpm with radius of wheel equal to 25 cm. The mass of the vehicle is taken to be 800 kg. By these assumptions, the required force is found equal to 1271 N, which requires a starting torque of 317 nm. Hence, 300 nm is the minimum required torque for the safe starting of the machine. It is noted that the voltage level has been increased from 12 V in the traditional vehicle to 42 V in response to the increasing electricity demand of the HEV [5]. In the next section, design of EM is carried out for this voltage level.
a three-phase machine is required. Higher phase number will increase the number of switches. Design algorithms and their various aspects are general problems in SRM. The proposed design is devoted to a specific application and primary design algorithm is only defined the starting point of the optimal design procedure. So far primary design algorithms, such as Refs. [15] and [16], have been introduced that can be employed to obtain the initial design. But a trial and error technique then used to lead this initial design to the optimal design. The design procedure in Ref. [16] has been followed in the present work and flowchart of the design procedure has been shown in Fig. 3. First, the stack length and stator outer diameter are determined based on the required torque (300 nm), speed (250 rpm) and constraints of the dimensions of the machine. Parameters, such as ratio of rotor diameter and stator diameter, pole arc, yoke thickness, height of rotor and stator teeth are determined using two optimization strategies: (1) higher starting torque over low speed and (2) higher efficiency over high speed. Objective function is a combination of starting torque and efficiency in generating mode, this function must be maximized. Starting torque is calculated in low speed such as 30 rpm and generator efficiency is computed in high speed, such as 1200 rpm. Hence, a combine function of these
3. Electromagnetic design of SRM SRM has efficient performance and simple structure, at the same time it is robust and has a reasonable cost compared with the PM machines. Good controllability of SRM by computer, improvement of its control by new power electronic devices over high frequency, high current and low cost, improvement on the knowledge of SRM technology, small and compact design, high speed capability due to the absence of the winding and PM on the rotor, high ratio of torque per volume and torque per weight, capability of working in harsh environments, fault tolerability are some of the advantages of SRM. Different configurations have been proposed and 12/8 SRM has been chosen. A 12/8 SRM is the repetition of a 6/4 SRM, and it has all advantages of 6/4 SRM, in addition the higher number of teeth leads to a shorter end-winding and smaller unaligned inductance. This reduces the copper losses. Simultaneous excitation of four poles shortens the magnetic flux path, which leads to lower core losses. However, higher frequency increases the core losses at the same speed. Also SRM must be able to start at any position of the vehicle, thus
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Fig. 3. Flowchart of design procedure.
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Table 1 Dimensions and specifications of the designed 12/8 SRM
order to include the end-winding effect:
Unaligned inductance (mH) Input voltage (V) Rotor pole arc (degrees) Stator pole arc (degrees) Radius up to rotor pole surface (cm) Stator outer radius (cm) Shaft radius (cm) Air-gap length (mm) Stack length (cm) Rotor core thickness (cm) Stator yoke thickness (cm) Winding turns no./pole
Lend =
0.52 42 16 15 11.56 16.51 4.16 0.5 17.3 3.22 2.12 23
two, F, can be considered as follows: F = ATstart + BηGene
(7)
Depending on the importance of each of these sections, coefficients A and B can be determined. Following determination of the required mmf in the stator poles and taking into account the low level of voltage and high current, attempt is made to achieve the same mmf with lower number of turns and higher current. This leads to thicker wire with low number of turns. The design results have been summarized in Table 1. A three-phase 12/8 SR machine is introduced in such a way that resultant two series opposite poles with pole pair in 90◦ mechanical displacements, is connected in parallel and forms a phase of the machine. Therefore, topology of the drive of the machine is similar to other three-phase machines. From control aspect, different strategies can be applied.
4. Modeling of SRM Following are the reasons for non-linear behavior of SRMs: 1. non-linear B/H characteristic of ferromagnetic materials; 2. dependency of flux-linkage upon rotor position and stator winding current; 3. applying electrical input from one point. Generally, four models have been proposed for SRM. They are graphical models based on FEM, models for special software’s, models based on equivalent magnetic circuit and computational mathematic models and analytical models. The FEM based model produces very precise results, but it is normally used for confirmation of the final design. Second models are normally used for prediction of the dynamic performance and they are suitable to study the performance of a designed machine. The third model is used for approximate design. However, among these models, the fourth, or the analytical model has reasonable accuracy and quickly lead to the results. Hence, it can be used in iterative design procedure. In this paper, an analytical model with proper modifications is used [17,18]. The following empirical equation is used in
Lu ls Lstk 4
(8)
where Lu is the unaligned inductance, Lstk the stack length and ls is the distance between two poles of the stator. In the design of electrical machines, it is a common practice to use some empirical equations. It is in this area that the experience in SRM design must be applied. Of course, most of the many formulas given in the paper are derived from basic electrical and magnetic relations. Derivation and exploration of the various formulas and empirically determined factors will challenge the serious SRM designer seeking the ultimate in economic balance between performance and cost. For this purpose, a comprehensive program has been developed which consists of designing, modeling and simulating SRM using MATLAB. The developed program using MATLAB is too long and detailed has not been included in this paper. In the first section of program, the initial data such as starting torque, base speed and dimensional constraints are taken from the user and initial dimensions are derived using equations in [16]. Then, static analytical modeling is carried out and the necessary database is generated. For prediction of SRM dynamics, first the stator pole flux waveform is obtained. Then flux waveforms in all parts of the machine can be calculated. But, for calculation of the stator pole flux and current, voltage equation and static flux-linkage characteristic are used. Based on the energy conversion, co-energy is the integral of the flux-linkage versus current and torque is calculated from derivative of co-energy versus rotor angle. For efficiency computation, the losses must be first computed. Core losses are calculated using a very quick analytical technique. Then output power is evaluated from torque and speed. This general trend is repeated up to optimal final design and satisfying the designer. Loss modeling, based on Ref. [19], is developed for losses calculation. To obtain the core losses, flux waveforms in different parts of the machine including rotor and stator pole, rotor core and stator yoke are determined. For example, flux waveform in a part of rotor body of the designed machine in the starting mode analytically calculated and has been shown in Fig. 4. The copper losses are also obtained based on the dynamic current. Finally, windage, friction and stray losses are included in a way similar to induction motors. Since the analytical modeling technique is new, it is necessary to confirm the accuracy of the technique. A most convenient tool, which can be used for comparison is modeling by FEM. Although FEM is too slow, in the sametime it is precise and widely used to finalize the design. However, before applying the available FE software’s, it is worth to compare the FE results with the static flux-linkage test results. The static test magnetization data for an 8/6 SRM was available and the static modeling results of a typical 8/6 SRM has been confirmed by that of the FEM results as shown in Fig. 5. Then, the analytical modeling of the designed 12/8 SRM and FE analysis has been compared. The error in static
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157
Fig. 4. Flux waveform (in Wb) in a part of the rotor body.
modeling is due to its analytical nature and quick static modeling which is necessary for the design. This error is small (less than 10%) at high currents. This machine operates in starting mode for a very short time, and frequently operates over high speed and generating mode. In this case, the current is low and error of static modeling using FE method and also experimental is small. Fig. 6 shows the meshed cross-section and flux paths of the machine at the unaligned position. The number of nodes and elements of the employed mesh are 28,433 and 14,176, respectively. Fig. 7 exhibits the FEM and analytical results. Generating mode is the dual of the motoring mode and current is the symmetrical mirror of the motoring current with respect to the aligned position [20,21], Fig. 8 shows this.
5. Performance and simulation results Performances of SR machine in both starting and alternating mode are studied. Fig. 9 shows the analytically calculated current, phase torque of the machine and also its total torque in the starting mode at 50 rpm. It can be realized that the machine is able to develop the starting torque. Since the starting period is short, high current in this mode of operation
Fig. 5. Flux-linkage characteristics for a typical 8/6 SRM: (—) measured, (- - -) FEM.
Fig. 6. (a) Meshed cross-section and (b) flux paths in the designed 12/8 SRM.
does not cause high temperature rise. The current and torque in Fig. 9 show large variations. Here, the proposed SRM have been designed to obtain high starting torque over low speed and high efficiency over high speeds. The variations of the current and torque are intrinsic in SRM and many control
Fig. 7. Flux-linkage for the designed 12/8 SRM: (—) analytical method, (- - -) FEM.
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the torque it must be noted that ICE has ripple and certainly modifications are required in order to reduce the effects of the ripple of the dive system on the transmission system. Due to low speed in starting mode, the returned voltage is small, therefore, maximum current is limited and machine operates in chopping mode. However, in generating mode, due to high speed, the returned voltage is also large and current does not approach the maximum value and machine operates in a single-pulse mode. The equivalent power factor for SRM is as follows [9]: PF = Fig. 8. Comparison of motoring and generating modes of SRM.
techniques have been introduced to minimize the ripples [22]. This has been considered as a control problem and has not been taken into account in the proposed design procedure. Fig. 10 exhibits the analytically calculated phase current and total current of SRM in generating mode at 1000 rpm. During this long period, the output current of the machine can easily charge the battery. As a generator the SR machine produces high ripple content in the generated current as shown in Fig. 10. This current is only the output in the terminal of the machine. There is a control system between the terminals of machine and battery that can control the torque ripple and also battery charging current characteristic. For instance, a coil can be used to reduce the ripple. Regarding the ripple of
Tavg ω Vdc Irms
(9)
where Tavg is the developed average torque of the machine, ω the speed, Vdc the dc bus voltage and Irms is the rms current. The equivalent power factor in starting and generating modes has been analytically calculated and has shown in Fig. 11a. The figure indicates that the equivalent power factor is good and this indicates a suitable use of this machine. Efficiency of the machine has been analytically calculated and shown in Fig. 11b, which tends to unity over high speed. This machine operates in the starting mode of vehicle over low speeds which lasts a short time, it operates frequently in the generating mode and high speeds where its efficiency and power factor are fair. In addition, power factor and efficiency over the low speeds are sacrificed for high starting torque. Also torque/speed and power/speed characteristics of the machine
Fig. 9. (a) Phase current, (b) phase torque and (c) total torque versus time at 1000 rpm.
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159
Fig. 11. (a) Equivalent power factor and (b) efficiency of the designed machine. Fig. 10. (a) Phase current and (b) total current of SRM in generating mode at 1000 rpm.
have been shown in Fig. 12, indicating the expected performance. As Fig. 12 shows, the starting torque of SRM is very fair and capable to start the vehicle. Therefore, it is clear that it is a convenient candidate for HEV. The designed SRM has not been yet built, but an optimal design has been obtained using the Genetic algorithm. The motor designed by the above-mentioned routine and used as input of the optimal design process. Table 2 has compared the initial design and the final design. It is noted that the flux-linkage/current/rotor angular position characteristics are a main key for SRM design and comparison of the analytically Table 2 Optimum design results with conventional procedure and genetic algorithm Parameter name
Conventional procedure
Genetic algorithm
DC bus voltage (V) Rotor diameter (cm) Stator diameter (cm) Stack length (cm) Air gap length (cm) Rotor yoke width (cm) Rotor slot depth (cm) Rotor pole arc (◦ ) Stator pole arc (◦ ) Winding turn (turn) Unaligned inductance (mH)
42 23.116 33.023 17.337 0.05 3.217 4.182 16 15 23 230.52
42 21.753 29.357 17.337 0.05 3.036 4.115 15.7 15.3 23 224.87
Fig. 12. (a) Torque/speed and (b) power/speed characteristics of the designed SRM.
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obtained flux-linkage characteristics with the corresponding characteristics shows a good agreement and it is expected that the built machine satisfy the necessary requirements.
6. Conclusions Choice of HEV structure based on the size of EM and ICE was studied and starter/generator has been introduced as a suitable choice for HEV. After successful starting of the vehicle, EM is used to charge the battery over higher speed. Due to high capability of SRM, it has been employed as starter/generator of HEV. In the dual design of starter/ generator, the design algorithm is somehow different with the traditional design algorithm. In addition to the static modeling, the loss modeling has also been included. The study shows that the static modeling results have a good agreement with FEM and experimental results. Simulation results indicated that besides developing the required torque during the starting period of the machine, the machine operates as a generator with good efficiency and equivalent power factor and it is able to charge the battery.
7. Acknowledgements The authors appreciate the help of Dr. Radun from Kentucky University for the static modeling part of the paper. This project was financially supported by University of Tehran.
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