Performance Analysis of Six-Phase Induction Motor

Performance Analysis of Six-Phase Induction Motor

Mr. Sumit Mandal1

Electrical Engineering Department JIS college of Engineering Kalyani, India

Abstract This paper presents a mathematical d-q model of six-phase, two pole induction motor in rotating reference frame. The model is simulated in Simulink environment to evaluate its performance under load and no-load conditions. The results show reliable and good performance of the motor.

KeywordsD -q model, six-phase induction motor.

1. INTRODUCTION

   Asynchronous, induction motor is one of the very important and widely used ac motors. Single phase and three- phase both induction motors are popular and widely used because of its simplicity, robustness, good performance. But multiphase (more than three) induction motors are becoming popular and have been being studied from many years because of its several advantages over conventional three-phase induction motors or induction motors having lesser phases. The advantages are better fault tolerance[1][2][3][4], higher efficiency, lower current ripple, less torque pulsation, reliability[5] and facility to split certain amount of power in to multiple phases to reduce the power per-phase. This power splitting enables to use devices of less rating in case of high power applications[6]. Multi-phase motors are used in case of ship propulsion, traction, electric vehicles etc. where high power and reliability is required.

   Simulation of symmetrical induction machinery was done in [7]. Multiphase machines use in electric vehicles was studied in [8]. R. Gregor, F. Barrero, S. Toral and M.J. Durán studied induction motor drive test-rig to obtain superior performance[9]. Anushree Kadaba, Shaohua Suo, Gennadiy. Sizov, Chia-Chou Yeh, Ahmed Sayed-Ahmed, Nabeel A.O. Demerdash designed reversible three-phase to six-phase induction motor[10]. A spectral method of speed ripple analysis for a fault-tolerant six-phase squirrel-cage induction machine was presented in [11]. Matrix converter has been used to drive six-phase induction motor in [12]. Transient analysis of three-phase induction machine using different reference frames has been done in [13]. Rangarajan M. Tallam, Thomas G. Habetler and Ronald G. Harley studied transient model of induction motor with winding faults[14].

   [15] presents experimental investigation of a naval propulsion drive model with the PWM-based attenuation of the acoustic and electromagnetic noise. G.Renukadevi, K.Rajambal developed a generalized model of multiphase induction motor

   laws allowing an explicit control of system stability in closed- loop operation of five-phase induction motor drives. Using flux-linkage model, stability analysis of five phase induction motor has been done in [20]. Y. Maouche, A. Boussaid, M. Boucherma, A. Khezzar studied pulsating torque and harmonic components in rotor current of six-phase induction motor under healthy and faulty conditions.

   In this paper a dynamic model of asymmetrical six-phase, cage type induction motor is developed to study the performance of the motor in detail. The model is simulated in MATLAB/Simulink environment. The study gives a detailed idea about the motor and indicates towards the smooth and promising performance of the motor.

2. MATHEMATICAL MODEL OF THE MOTOR

   A simplified and equivalent diagram of a six phase induction motor is shown in fig.1. To develop this model some assumptions are made and those are as follows: The air gap is uniform and the windings are sinusoidally distributed around the air gap. There is no core loss and magnetic saturation in the core. There is no friction and windage loss in the system.

   Fig.1. Simplified Diagram of Six- Phase Induction Motor

   The voltage equations of the motor are mentioned

   below:

   with symmetrical winding displacement[16]. Use of multiphase machines is proposed in [17]. Control of five

   Vqs1

   = rsiqs1

   + qs1

   + ds1

   (1)

   phase induction motor using space vector modulation, is discussed in [18]. [19] This paper deals with the high performance Backstepping control strategy which is based on

   Vds1 = rsids1 + ds1 – qs1 (2)

   Vqs2 = rsiqs2 + qs2 + ds2 (3)

   Vds2 = rsids2 + ds2 – qs2 (4)

   Vqr = rr iqr + qr + (-r) dr (5)

   Vdr = rr idr + dr – (-r) qr (6)

   (7)

   (8)

   (9)

   idr)(10) (11)

   The flux linkage equations are as follows:

   qs1 = Llsiqs1 + Llm (iqs1 + iqs2) + Lm (iqs1 + iqs2+ iqr) ds1 = Llsids1 + Llm (ids1 + ids2) + Lm (ids1 + ids2+ idr) qs2 = Llsiqs2 + Llm (iqs1 + iqs2) + Lm (iqs1 + iqs2+ iqr) ds2 = Llsids2 + Llm (ids1 + ids2) + Lm (ids1 + ids2+ qr = Llriqr + Lm (iqs1 + iqs2+ iqr)

   = L i + L (i + i + i )

   Fig.3. d-Axis Dynamic Equivalent Circuit Per Phase

3. SIMULATION OF THE MODEL

   Six phase stationary axis voltages are transformed in to dq synchronous axis voltages and dq axis currents are transformed in to stationary axis voltages. The transformation

   (12)

   dr lr dr

   m ds1

   ds2 dr

   equations are as follows:

   The electromagnetic torque can be calculated from the equation below:

   Te = (P/2)(Lm/Lr)[ dr(iqs1 + iqs2) – qr(ids1 + ids2)]

   (13)

   The rotor speed equation is,

   r = (1/Jr) (Te-TL) dt (14)

   The position of d-q axis with respect to – axis can be measured in terms of and it can be calculated by integrating with respect to time.

   = dt (15)

   ABC and XYZ to (stationary axis) conversion;

   Vs1 1 -1/2 -1/2 Van

   = 2/3 Vbn

   Vs1 0 3/2 -3/2 Vcn

   Vs2		3/2	-3/2	0	Vxn
   	= 2/3				Vyn
   Vs2		1/2	1/2	-1	Vzn

   Now, to dq conversion; V =V .Cos + V Sin

   qs1

   s1

   s1

   Fig.2. q-Axis Dynamic Equivalent Circuit Per Phase

   Table1.

   Vds1=Vs1.Cos – Vs1 Sin Vqs2=Vs2.Cos + Vs2 Sin Vds2=Vs2.Cos – Vs2 Sin

   dq to conversion;

   is1 = iqs1.Cos – ids1 Sin is1 = ids1.Cos + iqs1 Sin is2 = iqs2.Cos – ids2 Sin is2 = ids2.Cos + iqs2 Sin

   to ABC and XYZ conversion;

   ia 1 0 is1 ib = 2/3 -1/2 3/2

   ic -1/2 -3/2 is1

   ix 3/2 1/2 is2 iy = 2/3 -3/2 1/2

   iz 0 -1 is2

   Motor Parameters	Lls (H)	Llm (H)	Lm (H)	Llr (H)	Rs ()	Rr ()	Van (V)	(rad/sec)	Jr (Kg.m2)	P	Rated Power (KW)
   	0.0132	0.011	1	0.0132	1.9	2.1	230	314	0.02	2	3

   Fig.4. Simulink Model Of The Motor

4. SIMULATION RESULTS

   Fig.5. Electromagnetic Torque

   Transient period lasts up to 0.305 sec. Motor gains steady state at 0.64 sec. During transient period high torque and speed oscillations are noticed. Steady state no-load torque is zero Nm. Constant rated load of 10 Nm is applied to the motor at 3 sec. steady state electromagnetic torque at load condition is 10Nm.

   Fig.6. Rotor speed

   No load speed is 314.15 rad/sec. Rotor speed at load condition is 299.46 rad/sec.

   Fig.7. Phase curren

   Input phase current at no-load and rated load are 0.5 A and

   3.5 A respectively

   Fig.8. Input Power

   At no-load motor consumes 1.475 watt real power as loss. At rated load input electrical power is 3211 watt. At no-load input reactive power is 496 VAR. At rated load input reactive power is 1148 VAR

   Fig.9. Output mechanical power

   At no load and rated load mechanical output of motor are 0 watt and 3000 watt respectively. During transient period high oscillations are observed in output power. At rated load motors efficiency is 93.4%.

   Fig.10. Harmonic analysis of phase current

   0.00% THD observed in harmonic analysis of phase current

5. CONCLUSION

   The result indicates towards high performance, good efficiency, less current per phase. Torque generation is smooth. Torque and speed ripples are negligible at steady state. As phase currents are not high and efficiency is good, it is suitable for high power applications. With respect to three- phase motor devices of less rating can be used per phase for certain amount of power

   The result indicates towards high performance, good efficiency, less current per phase. Torque generation is smooth. Torque and speed ripples are negligible at steady state. As phase currents are not high and efficiency is good, it

   is suitable for high power applications. With respect to three- phase motor devices of less rating can be used per phase for certain amount of power.

6. APPENDIX

Vqs1, Vqs2 = q axis stator voltages

Vds1, Vds2 = d axis stator voltages

Vqr, Vdr = d-q axis rotor voltages Va, Vb, Vc, Vx, Vy, Vz = Six-phase input voltages ia, ib, ic, ix, iy, iz = Six-phase input currents Lls = Stator leakage inductance

Llm = Stator mutual leakage inductance

Lm = Air gap inductance

Llr = Rotor leakage inductance

Lr = Rotor self-inductance

qs1, qs2 = q axis stator flux linkages

ds1, ds2 = d axis stator flux linkages

qr, dr = d-q axis rotor flux linkages

iqs1, iqs2 = q axis stator currents

ids1, ids2 = d axis stator currents

iqr, idr = d-q axis rotor currents

, r = speed of reference frame and rotor speed respectively

Te = Electromagnetic torque

TL = Load torque

P = Number of poles

= d/dt

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