Production of Circular Stator Current Trajectory in Multi-Phase Induction Drive Under Open Phase Fault Condition

In this paper multi-phase induction drive with a frequency converter is researched under open phase fault condition. Control strategy of stator voltage phase shift is proposed for dealing with over-currents during steady state. Symmetry of stator current trajectory is achieved. Experiments with six-phase induction motor without a neutral wire under one open phase condition were carried out.

Open phase fault is the most common fault that increases peak values of currents in the rest of the phases significantly.Under these conditions trajectory of rotating magnetic field becomes elliptical.
It is important to find appropriate methods to obtain circular currents trajectories in six-phase motors for single-phase fault.Therefore, a control strategy of stator voltage phase shift is proposed for dealing with over-currents during steady state.

II. STATOR OPEN-PHASE FAULT
Induction motor torque depends on the generated stator magnetic flux.Ideally, the magnetic flux trajectory is circular.
A six-phase squirrel-cage induction motor with isolated neutral point is investigated.Measuring the magnetic flux directly is complicated, therefore stator phase currents are measured and the trajectory of magnetic flux is calculated instead.Current trajectory in stationary frame is calculated by the following expressions:     Where: isdis d component of stator current of stationary frame; isqis q component of stator current of stationary frame; isA … isFare instantaneous stator phase currents.
Stator current trajectory in healthy mode is circular as all instantaneous currents have the same peak values and are shifted 60 electrical degrees.Upon loss of a phase, adjacent phases share the load on the missing phase and current peak values increase significantly.As this is not a three-phase machine, it does not stop and continues producing torque.Stator current trajectory shows a current drop in the direction of the lost phase and increment in orthogonal direction.While the mean power consumption stays the same, stator current trajectory and, therefore, the flux trajectory becomes elliptical (Fig. 1) in faulty mode.
Effective stator phase current values in healthy mode are equal and in faulty mode (Fig. 2) they are all different in an induction motor with an isolated neutral point.The effective value in the greatest phase current is 40 % greater in faulty mode (correspondingly 92,4 mA and 129 mA).Adjusting the angles of voltage phases generated by inverter is proposed as a method for control of current trajectory in stator phase fault mode.This way meeting the minimum copper loss criterion is expected.
-0.7-0.6-0.5-0.4-0.Based on trajectories presented in Fig. 3, it is obvious that a more circular stator current trajectory could be achieved using the proposed method.Although there is a 60° angle between stator current vectors, a 10° voltage angle shift of two phases is two phases is too great.Voltage phase adjustments in both cases had a negative effect on instantaneous currents: peak values increased significantly in most phases.Note that shift in current phase angles does not match voltage angles.Current phase angle shifts in A and E phases are 40-50° instead of 10°.This effect would not be present in an induction machine with a grounded neutral point.

IV. REDISTRIBUTION OF STATOR CURRENTS
By running multiple experiments with various stator voltage angle shifts, a near circular current trajectory was achieved (Fig. 5).The most important conclusion to be made is that optimal (circular) trajectory can be achieved with numerous phase shifts and does not have a sole solution.Analysis of instantaneous stator phase currents is in order.In Fig. 6 and Fig. 7 instantaneous stator phase currents are presented for both angle shifts.Both cases show worse results compared to unadjusted open-phase fault mode as peak values are significantly greater in some phases (Fig. 2): 62% and 81% correspondingly compared to 40% of unadjusted faulty mode.This would cause a significant strain on all of the system as it might result in further damage.
Note that greatest currents flow in different phases (Fig. 6 and Fig. 7).This means our method allows any distribution of power to all phases.The optimal redistribution would uniform currents of all the stator phases.This way minimum copper loss criterion would also be met.
The best result was achieved by changing 4 phase angles (Fig. 8).Note that the minimum stator voltage angle shift increment is 1°.The achieved effective value in the greatest phase current is 31 % greater in adjusted faulty mode while in the unadjusted mode it is 40 % (Fig. 8).The stator current trajectory is slightly more elliptical compared to results presented in Fig. 5.This is considered to be the best result as the over-all quality was increased.
Mathematical model of an asymmetric induction machine is not accurate enough to reproduce experimental results.Stator phase voltage angles are adjusted by 10% to achieve near circular current trajectories.This degree of accuracy could not be guaranteed.

V. CONCLUSION
A compensation method for stator open-phase fault is presented.It allows control of stator current amplitudes by adjustment of stator voltage phase angles without reducing voltage amplitudes.This way maximum potential is drawn from the power source and no investments or changes to the hardware are required.
Using proposed method circular stator trajectory can be achieved.Experiments show that slight adjustments to voltage phase angles (up to 10% of spatial displacement of adjacent stator windings) has great impact on the trajectory in an induction motor with isolated neutral point.Currently mathematical models are not accurate enough to calculate optimal stator voltage phase angles with required accuracy.Individual stator phase currents can also be controlled.One of the currents increases 40% during open-phase fault compared to healthy mode which may cause damage to the machine.With a minimal stator phase angle shift increment of one degree the greatest current was reduced to 31%.In theory, equal effective stator current values of all phases may be achieved with optimal stator voltage phase angles and, therefore, the greatest current value could go down to 20%.In all modes, including the healthy mode, power consumption is almost the same.

MFig. 1 .
Fig.1.Stator current trajectory in healthy mode and under open phase F fault condition without adjustments

Fig. 2 .
Fig.2.Steady state currents under open phase F fault condition without adjustments III.CONTROL OF STATOR CURRENTS BY ADJUSTING STATOR VOLTAGE ANGLES

Fig. 4 .
Fig.4.Steady state currents under open phase F fault condition with additional phase A shift of -10° and phase E shift of +10°

Fig. 5 .
Fig.5.Stator current trajectory under open phase F fault condition with adjustments: additional phase A shift of -9° and phase E shift of +0°; and additional phase A shift of -0° and phase E shift of +9°

Fig. 6 .-Fig. 7 .
Fig.6.Steady state currents under open phase F fault condition with additional phase A shift of -9°

Fig. 8 .
Fig.8.Steady state currents under open phase F fault condition with additional phase A shift of -6°, phase B shift of -1°, phase D shift of +4° and phase E shift of +6°

Fig. 9 .
Fig.9.Stator current trajectory under open phase F fault condition with additional phase A shift of -6°, phase B shift of -1°, phase D shift of +4° and phase E shift of +6°