Simulation Based Analytical Investigation of Multi-phase Induction Machine in Motoring and Generating Mode

Multi-phase variable speed machines are now-a-days considered advantageous as compared to three phase counterpart for various applications either operating in motoring mode or generating mode. The modeling and analysis of a multi-phase (six-phase) machine when operating in motoring and generating mode have been presented in this paper. In motoring mode the model is simulated to evaluate its performance under load and no-load conditions which includes current, torque and speed characteristics. During generating mode of operation the simulations were carried out and evaluations were made on the basis of the machine behavior which includes voltage and current behavior during noload period and when subjected to load. Simulation results are provided to confirm the ability of these models to represent during no load as well as during load period and the result were found to be satisfactory.


II. MULTI-PHASE MACHINES
Machines having phases more than three in comparison with conventional machine are termed as a high phase order machine or multi-phase machines. Multi-phase machines have certain advantages when compared with its three phase counterpart such as ability to start and run when one or two stator phases are short or open, lesser current in phase, increment in power [3].Basically a multi-phase induction machine can have two different types of configurations namely split phase electrical machines and dual stator electrical machines.
In a conventional three phase machine ,the conductors are distributed in slots symmetrically for each phase group and the conductors belonging to each phase group are series whereas in a multiphase induction machine we subdivide each phase group of a usual three phase machine into equal subgroups by disconnecting the series connection of the conductors. More number of three phase groups can be obtained from the same machine. In this way multiphase machine such as six phases, nine phases, twelve phases, fifteen phases and eighteen phases can be produced from a three phase machine by subdividing the phase groups into two, three, four subgroups respectively.

III. SIX-PHASE INDUCTION MOTOR MODELING
The machine considered for analysis has a stator which consists of six-phases consisting of two sets are (with phase shift between phases of 120º) separated by an angle α. This angle can take values such as 0º, 30º and 60 º. In this study, the rotor is considered equivalent to a three-phase winding [3,4,5,6]. There is no core loss and magnetic saturation in the core. There is no friction and windage loss in the system.
A induction machine operating in six phase mode has two stator winding sets namely 123 and xyz, whose axes are separated by α [7][8][9][10][11][12]. The three-phase set are distributed and the axes are displaced 120° apart from each other. The rotor windings ar, br, cr a s s h o w n i n F i g u r e 2 is distributed in sinusoidal manner and has separation of 120°.
The electromagnetic torque expression is given by

IV. SIX-PHASE INDUCTION GENERATOR MODELING
The equations for the self excited induction generator operating in six phase mode, describes the behavior of a multi-phase machine, it is assumed that the neutral of both the stator winding sets are separate so that if a fault occurs in one set of the stator windings it does not propagate to the other set. The following voltage equations are written for a multi-phase induction machine as shown in equivalent circuit of the machine in Fig.2.
For the development of model of the six-phase machine operating in generating mode the following differential equations are derived from the equivalent circuit of the machine. In the equivalent circuit applying KVL equations we get the following voltage equations. = +ɷ Where ɷ is the reference frame speed, ɷ is the rotor speed. In this analysis the rotor quantities are referred to stator. The flux linkage expressions in terms of currents obtained from the equivalent circuit. Solving this equations (17-22) for obtaining current equations Substituting the values of the currents obtained in the equation (38) to (43) in the voltage equations (26) to (31) the following expressions are obtained.
(53) The torque can be computed as a function of q and d axes stator and rotor currents The rotor equation is expressed as Where is moment of inertia, is is the number of poles, is the shaft torque. ( 5 6 ) The magnetizing inductance is not a constant but a function which depends on the instantaneous value of magnetizing current given by =function ( ). During simulation, in each step, the magnetizing inductance is updated as a function of the magnetizing current .

= ( 5 7 )
The magnetizing inductance is calculated from the magnetizing characteristics fourth order polynomial for the test machine . The 4th order polynomial is arrived at, by applying curve fit technique to the relationship between and ,obtained by performing synchronous speed test on the test induction machine.
are constants values The torque balance equation is expressed as the derivative of the speed ɷ ( 5 9 )

(C)Shunt Capacitor for excitation
The excitation system of the six-phase machine introduces the following state equations which uses dq components of the stator voltages as state variables in the equivalent circuit.

V. SIMULATION AND RESULTS (A)Six-phase induction machine operating in motoring mode
The model of the six-phase induction machine operating in motoring mode to be analyzed was simulated with two different sources, first with a direct ac start up and secondly as an inverter fed machine. The simulation was carried out in MATLAB/Simulink environment. The complete simulink models of the machine being fed with two different sources are shown in Fig.3 & 4 respectively.

1)No load condition
To analyze the performance behaviour of the six-phase induction machine operating in motoring mode the simulation model of the above mentioned two models were implemented.The current, speed and torque characteristics of the machine during no-load when operated by direct AC supply is shown in Fig.5. Fig.6 shows the torque, current and the speed characteristics of the machine during no-load when operated by a sixphase inverter connected at the input side of the machine.

(B)Six-phase induction machine operating in generating mode
Simulation model of an induction generator operating in six-phase mode is implemented using MATLAB/Simulink environment as shown in Fig.8.The simulations were carried out when the SEIG operating in multi-phase mode is subjected to no-load condition, when the machine is subjected to resistive-inductive load respectively.

1)Voltage and current characteristics of multi-phase induction machine operating in generating mode during no-load condition
The simulated analytical voltage characteristics during no-load are shown in the above Fig.9.The value of the capacitance connected for excitation is 90µF at rated speed of 1500rpm. The voltage across the terminals and current rise from small voltages and amperes until steady state is attained. The machine attains its steady state values at 240 volts approximately during no-load period 2)Voltage and current characteristics of multi-phase induction machine operating in generating mode when resistively loaded Voltage and current waveform of six phase self-excited induction generator when connected to a resistive load of 200Ω is shown in the Fig.10 & 11 respectively. The resistive load is applied to the machine as a time instant of 0.3 seconds.A decrease in voltage is seen in the self-excited induction generator operating in six phase mode which is nearly to 200 volts which reduces the current across the capacitor,which reduces voltage across self-excited induction generator operating in six phase mode.  The load test is conducted with balanced resistive-inductive load consisting 200Ω resistance and inductance 500mH. The load is applied at a time instant of 0.5seconds.The voltage and current waveforms are shown in Fig.12 & 13 respectively. The results show that the terminal voltage and current attain their new steady-state operation with reduction of output voltage.

VI. CONCLUSION
The simulation model of a multi-phase induction machine operating in motoring and generating have been implemented in this paper for analyzing the performance of the machine.When induction machine is operating in motoring mode the result shows high performance, lesser current per phase, torque generated is smooth and the ripples generated are negligible. As the phase currents are not high and efficiency is good this motor is suitable for higher power applications. In the analysis it is observed that when the six-phase machine when operating as a generator gives higher reliability as compared with its three phase counterpart and can feed two separate loads connected across two winding sets which has the advantage that if a fault occurs in one set it will not affect the other set, hence it remains in healthy condition.