Evaluation of Electric Propulsion Systems (Zeraoulia, 2006)
1. Introduction
The need for more power per volume, or mass and reliability has promoted the advancement of higher phase order (
In this chapter, an approach of modelling and analysis of the higher phase order machine will be explored where the stator has a symmetrical winding layout. The machine stator winding is connected to a balanced phase supply and the machine performance characteristics observed during normal operation and under fault conditions, both in loaded and unloaded conditions. The performance under fault is considered to demonstrate the fault tolerance of the machine. Though rating may fall during the loss of 1 or more phases due to fault, unlike the conventional 3phase ones, does not stop the machine from running as long as the condition for the production of rotating magnetic field in the airgap is met.
Furthermore, a six phase squirrel cage induction machine was investigated using the classical field analysis method, the generalised theory method and the finite element method (
2. Mathematical modelling of the six phase squirrel cage induction machine
The arbitrary reference frame theory is used in the dynamic analysis of electrical machines. The highly coupled nature of the machine, especially the inductances within the winding makes it rather challenging to perform the dynamic simulations and analysis on this machine (Ogunjuyigbe A.S.O., 2009), (Krause P.C., Wasynczuk O., et al, 2002). By using this method as applied to the three phase case, a sixphase machine is also transformed to a fourphase machine with their magnetic axis in quadrature. This method is also commonly referred to as the
The matrix transformation of the
Likewise, the rotor matrix transformation between ABC and
Where
In developing the equations which describe the behaviour of the six phase induction machine the following assumptions were made:
The airgap is uniform.
Eddy currents, friction and windage losses and saturation are neglected.
The windings are distributed sinusoidally around the air gap.
The windings are identical.
2.1. Voltage and flux linkage equations
The voltage equation of the six phases (
The flux linkage equations are expressed as current dependent variables (Levi E., 2006):
The mutual inductances between the stator and the rotor are given as:
Where λ is the flux linkage,
2.2. Mechanical equations voltage and flux linkage equations
The mechanical equations for the six phase squirrel cage induction machine comprises of the electromagnetic torque and the speed as expressed in Equations (23) and (24). These equations are derived using the same concept of the three phase case (Ogunjuyigbe A.S.O., 2009), (Krause P.C., Wasynczuk O., et al, 2002).
Where
2.3. Equivalent circuit
The equivalent circuit diagram of figure 2 summarises the voltage and flux linkage equations of the six phase squirrel cage machine in
There is no mutual coupling in the equations (9)(12) and (17)(20) as presented in figure 2(c) where
3. Modelling of sixphase squirrel cage induction machine under fault conditions
The operation of the machine under fault is considered here to demonstrate its fault tolerance ability. This machine consists of a symmetrical six phase supply with a fault at the stator terminal, assuming the phase
3.1. Open circuit fault
With phase
For a balanced six phase, the total phase currents may be expressed as:
From equation (2), assuming
From equation (26), as
The open circuit voltage is also expressed as:
Putting
There is no mutual coupling between the stator and the rotor winding of the
Back substituting equations (29) and (30) into (28) gives the open circuit voltage as:
Where
The open circuit voltage in equation (31) is placed across the open circuit terminal in the simulation.
3.2. Short circuit fault simulations
In this section we consider a short circuit between two phases during a normal operation of the machine. For this instance, the balanced six phase total phase voltages may be expressed as:
With phase
3.3. Classical field analysis
In this section, the classical field analysis is used to determine the magnetic field distribution in the airgap of the machine. With this magnetic field distribution, the performance behaviour of the machine at steady state was determined using the equivalent circuit in figure 2. The corresponding smooth airgap flux density distribution of the stator and the rotor is given in more details by (Appiah E.K. et al, 2013):
The permeance factor
Where
The six phase airgap power can be expressed as:
Where:
The electromechanical power and torque of the machine is expressed as:
Similarly, the input power, output power and the power factor are also expressed as:
Also
As the permeance factor of equation (34) is superimposed on the flux density distribution expressed in equation (33), the effects of slot opening on the flux density distribution is accounted.
3.4. Finite element analysis
In this section, the finite element analysis using a two dimensional Quickfield software package is used to evaluate the performance behaviour of the machine. The magnetic vector potential is employed in the numerical solution to give the magnetic flux density distribution. The magnetic vector potential is expressed as (Pyrhonen T. P., Valeria H., 2008), (Appiah E.K., Jimoh A. A., et al, 2013):
For a two dimensional problem of the vector potential, the Poisson equation is expressed as:
The performance behaviour of the machine at steady state was evaluated by loading the machine in
The torque derivation of the
where
The geometry of the whole machine was developed using the software package. Two boundary conditions were used for this analysis within the entire structure: the Dirichlet’s boundary condition for the outer layer of the machine structure and the homogeneous Neumann boundary condition for the change over from one geometry or medium to another such as from the core to the airgap and vice versa. The automatic meshing of the machine geometry which is generated by the software and spread over the whole cross section is shown in figure 6(a (i)). The field solution is now obtained by running the mesh geometry in the software solver by solving the Maxwell’s equation. The machine winding has been excited with balanced stator currents for noload and full load conditions.
4. Simulation results
In this section, the simulation results for the three methods; the generalised theory of machine, the classical field, and the finite element analysis are presented. The dynamic performance behaviour of the machine was determined using the derived mathematical modelling in
4.1. Magnetic flux density distribution of the classical field
To obtain the airgap flux density distribution the permeance factor distribution, which reflects the effects of the slot openings, is superimposed on the flux density distribution. If saturation is to be accounted for, the
4.2. Magnetic flux density distribution of the FEA
In this section, the automatic meshing of the machine and the magnetic flux lines are shown in figure 6 (a).The colour map of the magnetic flux line shows that most of the portion of the yoke is under high flux density. The effect of slot opening on the magnetic flux density distribution of the airgap is shown in figure 6 (b), for noload and rated load condition. This is achieved by clicking the midairgap of the whole geometry in Quickfield. The magnetic saturation of the materials is taken care of by the magnetization curve.
4.3. Steady state analysis
This section presents the results of the analysis of the machine in steady state for the three methods; the generalised theory of machine, the classical field and the finite element analysis. For test performance under load condition the machine has been loaded to approximately 125% of rated torque. The values obtained for torque, efficiency, input power, output power, power factor and reactive power were respectively plotted against the loading as shown in figures 79. Experimental measurements were also plotted on the same curve for validation of the theoretical work. The machine performance characteristics increase with increasing load. The range of loading of the machine from 0 to 0.2 per unit shows that the three scenarios under study have the same effects until they begin to deviate from each other. However, the case of the reactive power is different in such that it deviates from each other from 0 to 125% of the rated load. It is further observed during the load study that the reactive power at start is high but decreases with loading and vice versa for the active power. The difference in deviation could be so because of the rotor losses when the machine is being loaded. The effect of the reactive power at start gives a very poor power factor to the machine but the performance improves with loading. The experimental results validate the theoretical model and are plotted alongside those of the three methods.
4.4. Dynamic analysis
Steadystate analysis is not always sufficient in determining the behaviour of an electrical machine. The behaviour of the machine under changing conditions is also necessary. The dynamic model will show the exact behaviour of the machine during transient and or dynamic periods. The derived voltage, flux linkage and mechanical equations for the squirrel cage six phase induction machine is implemented in Matlab/ Simulink as follows:
All partial differential variables are converted to integral variables. This concept is similarly applicable to the three phase case (Chee Mun Ong, 1998).
The flux linkage equations are resolved into state variables and current as dependent variables. (Ogunjuyigbe A.S.O., 2009), (Krause P.C., Wasynczuk O., et al, 2002).
The entire equations are then modelled, implemented and simulated within the Matlab/Simulink environment.
4.4.1. Simulation of healthy machine
The dynamic and transient simulation of the six phase squirrel cage induction machine is done in the arbitrary reference frame. The Simulink model built using equations (524) is shown in figure 10. Figure 10a shows the complete model of the sixphase machine system, while the power block is represented in Figure 10b. The power supply block converts the machine variables from the balanced
The results in figure 11 show that the speed settles a little below synchronous speed at 314.1 rad/sec for the 50 Hz supply system. It is to be noted that the friction and the windage losses have been neglected in this model and as such the speed is almost equal to the synchronous speed. This effect is shown in the torque versus speed curve, and the speed versus time. From the theoretical simulations, it is observed that the starting current is about 10.8 A as compared to the rated current of 1.8 A. At the steady state settling of the current at noload, the current is not zero but is at 0.8 A. This accounts for the magnetizing current present in the machine at noload. The speed versus time, torque versus speed curve characteristics and the waveforms of the two stator currents, phases
Furthermore, the results of figure 11b show that the speed of the machine settles at rated load to 293.194 rad/sec, corresponding to a slip of 0.07. The simulation was done by applying the rated load of 1 pu at the time of 2.5 seconds, after the settling of the free oscillation at noload. It is observed that the current immediately increased to show the presence of load. The speed versus time, torque versus speed curve characteristics and the waveforms of the two stator currents, phases
4.4.2. Simulation results of faulty machine under open circuit condition
Equation (31) is used to obtain the performance characteristic of the machine under noload and loaded conditions during fault. The Simulink representation of the open circuit voltage (
From the occurrence of fault at 4 seconds, the current in the faulty phase
4.4.3. Simulation results of faulty machine under short circuit condition
The short circuit voltage is achieved by making the supply voltages equal to zero by short circuiting two phases using the signal builder. The Simulink representation of the short circuit voltage model blocks is represented in figure 14. For the theoretical analysis of short circuit, a fault was created at 4 seconds for phases
In this instance currents in both phase
5. Experimental validation
In order to validate the theoretical results with the experimental results, the experimental set up shown in figure 16 is utilised. The experimental results are used to validate the theoretical model. The set up consists of an induction motor which was reconstructed to a six phase machine, data acquisition equipment, torque transducer and computer system for waveform acquisition and a six phase supply. The machine performance at steady state has been plotted alongside the theoretic figures 79.
The dynamic simulations of the stator currents have been observed for the machine performance characteristics during normal operation and under fault conditions, both in loaded and unloaded conditions. These are shown in the figures 17 and 18. Given a fault condition, the current drawn at full load under fault condition is higher than that of the no load. This means that operating the machine for a long period of time under full load fault without derating can damaged the machine winding. The good agreement, shown by the curves, between theoretical and experimental results tends to validate the model.
6. Application possibility in electric vehicles (EV) and hybrid electric vehicles (HEV)
In view of the need to reduce the continued dependency on petroleum as a source of energy for powering cars and the drive to reduce CO_{2} emissions, EV/HEV has received huge research interest. The applications of HEV range from small cars to buses, and even trucks. Researchers are generally working towards developing more efficient drive systems for EV/HEV vehicles. With different vehicle applications and requirements, it is clear that no single electric motor design fits all. As such motors designed for electric vehicle applications have to meet rigorous demands, with space limitations and the driving environment key factors. Reports of achievements has demonstrated that the specific performance characteristic of HPO machines matches the technical demands of HEV and also has the potential to further improve its quality. HPO machines finds application in areas where high power, high torque as well as high reliability is demanded. This is because it has a reduced amplitude and increased frequency of torque oscillation, reducing the rotor harmonic current per phase without increasing the voltage per phase, lowers the dclink current harmonics, high fault tolerance (in the case of loss of one or more phases), reduction of required power rating per inverter leg and increase torque per ampere for the same volume of machine. HPO has been utilised also for integrated stator/alternator in HEV and ordinary vehicles with combustion engines Miller et al (2001) and Miller and Stefanovic (2002). The integrated idea replaced two electrical machines with a single machine and matches the goal of reducing the number of assemblies to have lighter vehicles.
The major types of electric motors adopted for EV/HEV includes DC motor, Induction motor, permanent magnet motor and Switched reluctance motor. A general review of the state of the art in EV/HEV shows that cage induction motors and the permannet magnet motors are highly dominant, whereas, study on the use of DC motors are going down.
6.1. Comparative study
6.1.1. Dc motor
DC motors have established presence in electric propulsion because their torquespeed characteristics suit traction requirement well and their speed controls are simple, Wildi (2004). However, dc motor drives have large assemblage, low efficiency, low reliability and continuous need of maintenance, mainly due to the presence of the mechanical commutator (brush).
Contrary to this, the continuous development of rugged solidstate power semiconductors has made it increasingly practicable to introduce AC induction and synchronous motor drives that are mature to replace dc motor drive in EV/HEV /traction applications.
The motors without commutator are attractive, as high reliability and maintenancefree operation are prime considerations for electric propulsion. Nevertheless, with regard to the cost of the inverter, ac drives are used generally just for higher power. At low power ratings, the dc motor is still more than an alternative (Zeraoulia, 2006).

DC 
IM 
PM 
SRM 


DC  IM  PM  SRM  
Power Density  2.5  3.5  5  3.5 
Efficiency  2.5  3.5  5  3.5 
Controllability  5  5  5  3 
Reliability  3  5  4  5 
Technology Maturity  5  5  4  4 
Cost  4  5  3  4 





ΣTotal  22  27  25  23 
6.1.2. Induction motor
Cage induction motors has wide acceptance as a potential candidate for the electric propulsion of EV/HEVs based on their reliability, ruggedness, low maintenance, low cost, and the ability to operate in a hostile environment. They are particularly well suited for the rigors of industrial and traction drive environments. Today, induction motor drive, Chris (2007) is the most mature technology among various commutatorless motor drives.
The introduction of, as well as the level of development in the HPO machines has further strengthened the position of Induction machine for electric propulsion in EV/HEV, particularly because of the possibility of high power, high torque and high torque per ampere for same volume of machine.
Zeraoulia (2006) carried out an evaluation of electric propulsion systems based on the main characteristics EV/HEV’s propulsion, table 6.1. It was consensually established that induction motor is the most adapted for the propulsion of urban HEV’s. This report is prethe recent developments in the design and control of HPO machines.
7. Conclusions
A study of
The results obtained showed that in both healthy and unhealthy cases the machine is able to produce the starting torque. However, it has been observed that the torque produced by the healthy machine is greater in magnitude and produces fewer oscillations than the machine with faults at the stator phases. The significant observation is that the machine settles down to a new steady state with the fault, thus confirming fault tolerance, albeit the performance of the signal variables is compromised.
The steady state performance of real power, reactive power, power factor, electromagnetic torque, the stator currents and efficiency have been shown. In the steady state results, the performance characteristics obtained from the simulations were compared with the experimental results, while the dynamic ones were similarly compared. While good agreements were generally observed the generalized theory gave closer result to the experiment than the classical field and the finite element methods.
References
 1.
Appiah E.K., Mboungui G., Jimoh A.A., Munda J.L. & Ogunjuyigbe A.S.O. 2013. Symmetrical Analysis of a SixPhase Induction Machine under Fault Conditions. Paper presented at the World Acadeny of Science Engineering and Technology , Brazil.  2.
Appiah E.K., Jimoh A.A., Mboungui G.&Munda J.L. “Effects of slot opening on the performance of a six phase squirrel cage induction machine using Finite Element and Field Analysis”, Paper Accepted and presented at the IEEE Africon Conference in Mauritius, September 2013.  3.
Apsley J. & Williamson S. 2006. Analysis of Multiphase Induction Machines with Winding Faults. IEEE Transactions On Industry Applications, 42(2).  4.
Aroquiadassou G., MpandaMbawe A., Betin F. & Capolino G. A. 2009. Six Phase Induction Machine Drive Model for FaultTolerant Operation. Paper presented at the IEEE Transactions . Retrieved  5.
Bianchi N. 2005. Electrical Machine Analysis using Finite Elements . CRC Press, Taylor and Francis Group.  6.
Boldea I. & Tutelea L. 2010. Steady State, Transients, and Design with Matlab . CRC Press, Taylor & Francis Group.  7.
Ghuru B. S. & Hiziroglu H. R. 2005. Electromagnetic Field Theory Fundamentals . Cambridge University Press.  8.
Jimoh A. A. 1986. Stray load losses in Induction Machine. Doctor of Philosophy, McMaster University, McMaster University.  9.
Jimoh A. A., JacVenter P. & Appiah E.K. (2012). Modelling and Analysis of Squirrel Cage Induction Motor with leading Power factor Injection . Chapter in a book "Induction Motors  Modelling and Control", Edited by Prof. Rui Esteves Araújo, ISBN 9789535108436, Published by Intech: November 14, 2012 under CC BY 3.0 license, in subject Energy Engineering, Chapter 4, pp. 99126.  10.
Krause P. C. & Thomas C.H. 1965. Simulation of Symmetrical Induction Machinery. Paper presented at the IEEE Transactions on Power Apparatus and Systems .  11.
Krause P. C., Wasynczuk O. & Sudhoff S.D. 2002. Analysis of Electrical Machinery and Drive Systems. In: University, P. (Ed.). Analysis of Electrical Machinery and Drive Systems . IEEE Power Engineering Society  12.
Levi E. 2006. Recent Developments in High Performance VariableSpeed Multiphase Induction Motor Drives. Belgrade, SASA, Serbia: Sixth International Symposium Nikola Tesla.  13.
Lipo T. A. 47907. A dq model for Six Phase Induction Machines [Electronic Version].  14.
Ogunjuyigbe A.S.O. 2009. Improved Synchronous Reluctance Machine With Dual Stator Windings And Capacitance Injection. Doctor of Technology, A thesis submitted to the Department of Electrical Engineering, Tshwane University of Technology.  15.
Pyrhonen T. P. & Val´Eria H. 2008. Design Of Rotating Machines . First Ed. United Kingdom: John Willey and Sons Limited.  16.
Singh G.K. & Pant V. 2000. Analysis of a Multiphase Induction Machine Under Fault Condition in a PhaseRedundant A.C. Drive System [Electronic Version]. 577590.  17.
YongLe A., Kamper M. J. & Le Roux A. D. 2007. Novel Direct Flux and Direct Torque Control of SixPhase Induction Machine With Special Phase Current Waveforms. Paper presented at the IIEEE Transactions on Industry Applications .  18.
Chris;, M. 2007. FieldOriented Control of Induction Motor Drives with Direct Rotor Current Estimation for Application in Electric and Hybrid Vehicles Journal of ASIA electric vehicles, 5(2):4.  19.
Wildi T. 2004. Electrical Machines, Drives, and Power Systems . Sixth Edition ed.: Pearson Prentice Hall.  20.
Miller, J.M., Stefanovic, V., Ostovic, V. and Kelly, J., (2001), Design considerations for an automotive integrated startergenerator with polephase modulation, Proc. IEEE Ind. Appl. Soc. Annual Meeting IAS, Chicago, Illinois, CDROM Paper 56_06.  21.
Miller, J.M. and Stefanovic, V., (2002), Prognosis for integrated starter alternator systems in automotive applications, Proc. Power Electronics and Motion Control Conf. PEMC, Cavtat, Croatia, CDROM Paper T5001.  22.
M. Zeraoulia, IEEE, M.E.H. Benbouzid and D. Diallo (2006) Electric Motor Drive Selection Issues for HEV Propulsion Systems: A Comparative Study, 1756 IEEE Transactions On Vehicular Technology, Vol. 55, No. 6, November 2006.