Winding open‐circuit fault‐tolerant operation of single DC‐link dual‐inverter fed three‐phase open‐end induction motor drive

Correspondence Abanishwar Chakrabarti, Department of Electrical Engineering, NIT Agartala, Tripura, India. Email: abanishwar@yahoo.com Abstract This study presents a winding open-circuit fault-tolerant control scheme for an open-end induction motor drive with common DC bus for dual inverters. The proposed control scheme also permits balanced three-phase operation of the same motor under healthy operation. It can suppress common mode current easily, yet permits maximum DC bus utilisation in both operating modes. It is mathematically established here that during faulttolerant operation, the magnetising current increases by a factor of √3. As a result, the airgap flux during fault-tolerant operation is same as that during balanced three-phase operation. An analytical relation is proposed for maximum torque capability of the machine during fault-tolerant operation, taking into account the limit of winding current to its rated value and increase of magnetising current during such an operation. Extensive mathematical analysis is supported by simulation and experimental results to validate the performance of the proposed scheme during balanced three-phase operation as well as winding opencircuit fault-tolerant operation.


INTRODUCTION
An important and desirable feature of modern highperformance induction motor drive is its fault-tolerant capability [1][2][3][4]. A fault in a motor drive system can be due to a fault in inverter or fault in motor [5][6][7][8][9][10][11][12][13][14][15][16]. Under a winding open-circuit fault in a three-phase standard induction motor, when only two of the motor windings distributed in space by 2π/3 electrical radian are excited in a particular manner, it is possible to develop a steady torque [9][10][11][12]. Hence, it is possible to start and run the machine (at reduced torque) with only two healthy windings and such operation is referred in this study as a fault-tolerant operation. The maximum torque capability of the machine at rated speed during such fault-tolerant operation depends on the winding connection. There are three possible configurations of three-phase induction machine: star, delta and open-end connection. In case of fault-tolerant operation of a star-connected machine, the neutral may be connected to the midpoint of DC bus. In such a case, if DC bus voltage is kept constant and rated current is allowed through the windings, the maximum torque that the machine can produce with two windings energised is 50% of rated value [10]. If a fourth leg is used, and the neu- tral is connected to the fourth leg, then maximum torque during similar fault-tolerant operation increases to 57.7% [10][11]. In delta-connected machine, maximum possible torque during similar fault-tolerant operation is 57.7% [12].
In open-end configuration, the windings are not interconnected, but each winding is supplied at both ends through two separate inverters. In case of failure of semiconductor devices in an open-end induction motor (OEIM) drive, several modified switching techniques have been proposed to drive the machine [13][14][15][16]. In these techniques, balanced three-phase voltage is generated across motor winding by reconfiguring the open-end drive. However, during winding open-circuit fault, applied voltage across the two healthy windings should be phase shifted by π/3 [9][10][11][12] (instead of the usual 2π/3) in order to generate steady state torque during starting and running of the drive. Since switching schemes proposed in [13][14][15][16] generate balanced three-phase voltages (with 2π/3 phase shift), these techniques cannot be used to drive a three-phase OEIM with π/3 phase shift during an open-circuit fault in one of its winding.
In a conventional OEIM drive, the phase difference between the voltages applied across the two ends of a winding is π (180 • ) [17]. Thus, the voltage across the motor winding is twice the voltage generated by each inverter, ensuring maximum DC bus utilisation. Common mode voltage (CMV) produced by both the inverters, being a third harmonic component, are additive when the fundamental voltages are phase shifted by π. When a common DC bus is used for both the inverters, due to this CMV, a third harmonic current flows through the motor winding, which increases loss in the system. To eliminate this third harmonic current, CMV generated by the inverters should be eliminated. Space vector modulation (SVM) technique is extensively used in literature to reduce or eliminate CMV in OEIM drive [18][19][20][21]. Carrier-based pulse width modulation (PWM) techniques are also used to eliminate CMV in different topologies of multilevel inverter [22][23][24]. However, these techniques are used for eliminating CMV in a balanced three-phase induction motor drive. In the event of an open-circuit fault in any one winding, a steady rotating magnetic field can be created by changing the phase shift between the voltages of the healthy phases from 2π/3 to π/3. As a result, during winding opencircuit fault-tolerant operation of OEIM drive, both the inverters do not generate balanced three-phase voltages and existing methods cannot be directly applied to eliminate CMV.
This study proposes a new and yet simple control technique for operation of a three-phase OEIM drive with both its constituent inverters supplied from a single DC bus, during balanced three-phase operation as well as during one phase winding open-circuit fault-tolerant operation. The control scheme permits a smooth transition from balanced three-phase operation into the fault-tolerant operation of the OEIM drive. The proposed switching scheme ensures maximum DC bus utilisation but restricts the flow of third harmonic current in both the modes of operation. Analytical expressions are proposed to estimate the flux and maximum torque in the machine during faulttolerant operation.

PROPOSED SCHEME FOR OPEN-CIRCUIT FAULT-TOLERANT OPERATION OF OEIM DRIVE
The working of the proposed control scheme is presented in this section separately for balanced three-phase operation as well as for winding open-circuit fault-tolerant operation. The change over from balanced three-phase operation to the winding open-circuit fault-tolerant operation is only through the control logic without any change in hardware. Analytical relation presented in this section validate that the proposed scheme can eliminate common mode voltage in both the above conditions while retaining maximum DC bus utilisation.

2.1
Principle of operation of proposed scheme Figure 1 shows the OEIM drive fed by two voltage source inverters from each end, having a common DC bus, as in conventional scheme. The operation of the power circuit depicted in Figure 1 can be explained by assuming each coil of the OEIM to be supplied from its two terminals by an equivalent one-phase inverter as shown in the simplified diagram of Figure 2. Considering the first phase winding aaʹ, it is supplied from the DC voltage through the two limbs a and aʹ of the equivalent inverter. The voltage across the winding will be a PWM waveform with multiple pulses per half cycle. For each pulse in the positive half cycle of winding voltage, the switch Sa1 turns on along with Saʹ2, creating a winding current flow as shown in Figure 2(a). For creating a zero voltage across the winding in this half cycle, switch Sa1 is kept on while Saʹ2 is to be switched off, such that the inductive energy freewheels through the diode of Saʹ1, effectively short-circuiting the load with current flow as depicted in Figure 2(b). Similarly, for each pulse in the negative half cycle of winding voltage, switch Saʹ1 and Sa2 are turned on together as in Figure 2(c), that creates a reverse current flow through the winding. To achieve a zero voltage across winding in this half cycle, switches Sa2 and Saʹ2 are kept on together as in Figure 2(d), permitting a closed path for the inductive current flow. The switches of each limb are switched in the complimentary mode, that is, if Sa1 is on, Sa2 is off and vice versa such that a finite voltage is maintained at any instant at each inverter pole, which is the midpoint of each limb, for example, point a. The two capacitors shown in Figures 1 and 2 create the hypothetical midpoint of the DC bus for the purpose of defining the pole voltage of the inverter, which is the voltage between midpoints of a limb and DC bus, say between points a and O. Since there is no physical connection to the midpoint of the DC bus, there is no current flow into or out of it, hence the midpoint need not be considered in the physical operation of the inverter. The complete three-phase inverter system can be considered to be operating with three such one-phase inverters, phase shifted from each other by 120 degrees. Because of this, it is common to club the three limbs on each side and call each such cluster as a three-phase inverter, for example, inverters 1 and 2.
Conventional techniques use a phase difference of π [17] between the fundamental voltages generated by the two inverter limbs across a winding to obtain maximum DC bus utilisation and depend on the use of SVM techniques to limit the flow of third harmonic currents through the windings. This study proposes that under balanced three-phase operation, the phase difference between the fundamental voltages generated by the two inverter limbs across a winding be kept at 2π/3 [25]. With such a condition, a phase shift of 3 × 2π/3 = 2π ≡ 0 is created between the third harmonic voltages of the two inverters and hence no third harmonic current flows through individual winding. This gives the flexibility of injecting third harmonic voltage to maximise DC bus utilisation (as explained later) while restricting the flow of the third harmonic current. This method of eliminating the third harmonic current is implemented independently for each phase without the requirement of the inverter generating balanced three-phase voltages. Since this technique is implemented by consideration of the voltage across one winding of the motor only, it is applicable with any arbitrary phase shift between the voltages across the windings of the OEIM. Hence, it permits a smooth transition from the normal balanced threephase operation to the fault-tolerant operation with energisation of only two windings due to open-circuit of one winding of the OEIM. Figure 3 presents the power circuit schematic of the OEIM drive during an open-circuit fault in one of the phase (phase c). During fault-tolerant operation, the two healthy windings (here, phases 'a' and 'b') are energised with voltages that are mutually phase shifted by π/3 through the operative limbs of the inverters. This result in a π/3 phase shifted current in the two healthy windings and hence generates a steady torque during fault-tolerant operation [9][10][11][12] of the OEIM even under the complete loss of one of the motor winding continuity.
Under this condition, by creating a phase shift of 2π/3 between fundamental voltages of the two inverters across each healthy winding of an OEIM drive, third harmonic current through the healthy motor windings can be eliminated also during fault-tolerant operation. Since balanced three-phase voltages do not exist now, it is not possible to apply conventional techniques for elimination of third harmonic current under the above fault-tolerant operation of the OEIM drive [17][18][19][20][21][22][23][24]. However, the proposed control scheme is able to eliminate the third harmonic currents as well as attain maximum DC bus utilisation in this situation.

DC bus utilisation and CMV elimination
Let the instantaneous fundamental voltage (v 1a ) generated by 'a' phase of inverter 1 with respect to DC bus midpoint be: where V p is the peak value and ω is the angular frequency of fundamental voltage generated by an inverter. According to the proposed scheme, instantaneous fundamental voltage generated by 'a' phase of inverter 2 with respect to midpoint of DC bus (v 1a ′ ) is phase shifted by 2π/3 from v 1a and hence expressed as: The instantaneous fundamental voltage across winding a-a ′ (v 1aa ′ ) is thus given by In the proposed carrier-based scheme, 15.5% of third harmonic voltage is added to the modulating fundamental waveform. The instantaneous third harmonic voltage generated by 'a' phase of inverter 1 (v 3a ) and inverter 2 (v 3a ′ ) are thus given by: From Equation (4) it can be observed that the instantaneous third harmonic voltages produced by the two inverters are same in magnitude and in phase. Thus, no resultant third harmonic voltage will exist across the winding nor any third harmonic current will flow through the winding. On the other hand, the injection of third harmonic increases the fundamental voltage by 15.5% [26], resulting in the instantaneous fundamental voltage across the motor winding to be: This is same in magnitude as conventional open-end drive with a phase difference of π across a winding [27]. Thus, the fundamental voltage across the motor winding during fault-tolerant operation remains same as in conventional balanced three-phase operation. Hence, it can also be inferred that maximum DC bus utilisation is achieved in the proposed technique. Now, consider an open-circuit fault in any one of the windings of the machine; say in phase c-c′. For producing a uniformly rotating flux in this condition, current in other two phases should have a mutual phase shift of π/3 [9][10][11][12]. This is obtained by creating a phase shift of π/3 between fundamental voltage of 'b' and 'a' phases of inverter 1. The instantaneous fundamental voltage of 'b' phase of inverter 1(v 1b )is now given by: As per the proposed scheme, fundamental voltage produced by 'b' phase of inverter 2 (v 1b ′ ) is also phase shifted from fundamental voltage produced by 'b' phase of inverter 1 by 2π/3, and can be expressed as: Thus, instantaneous fundamental voltage across winding b-b′ (v 1b ′ ) after adding 15.5% of third harmonics is given by: From Equations (5) and (8), it can be seen thatv 1bb ′ lags v 1aa ′ by π/3, which is the requisite condition for fault-tolerant operation. Similar to the explanation given for winding a-a′, it can be proved that, third harmonic injection in winding b-b′ will increase the DC bus utilisation by 15.5%, but no third harmonic current will flow through the motor winding.
Conventional PWM schemes can simultaneously maximise DC bus utilisation and eliminate third harmonic current for a balanced three-phase system where the output voltages are phase shifted by 2π/3. Conventional algorithms for OEIM drives are based on the assumption that both the inverters will generate balanced three-phase voltages. Hence, conventional schemes cannot generate π/3 phase shifted two-phase voltage while simultaneously eliminating common mode voltage. The latter is an essential criterion for optimal performance of open-end induction motor drive during fault-tolerant operation From Equations (4), (5) and (8), it can be seen that the proposed scheme can maximise DC bus utilisation, eliminate third harmonic current and can generate two-phase voltage with π/3 phase shift. Hence, it is suitable for optimal performance of open-end induction motor drive during winding open-circuit fault-tolerant operation.

ANALYSIS OF PROPOSED SCHEME
Let the fundamental voltage applied to the machine windings during an open-circuit fault in winding c-c′ be represented by v aa′ leading v bb′ by π/3 as follows: V m is the peak of the winding voltage and ω is the angular frequency of the stator voltage. Since the voltage applied to the two healthy phases are mutually phase shifted by π/3, currents in these windings will also be phase shifted by π/3. Let the instantaneous magnetising components of the currents in 'a' phase (i m_aa ′ ) and 'b' phase (i m_bb ′ ) of the machine during fault-tolerant operation be where (I m_2 ) is the peak of the magnetising current. Assuming that axis of 'b' phase winding is leading axis of 'a' phase winding by 2π/3 electrical radian in space, net MMF produced by these two currents at an angular position θ (F 2ϕ ) with respect to 'a' phase axis is given by where N represents the number of turns on the stator coil. This implies that if two windings of a three-phase OEIM are excited using a two-phase voltage with a mutual phase shift of π/3, a uniformly rotating magnetic field is created. Decomposing the unbalanced three-phase voltages in Equation (9) into positive, negative, and zero sequence components using the standard operator 'a', the following results are obtained: From Equation (12), it can be seen that the negative sequence component of voltage during fault-tolerant operation is zero, which is consistent with earlier published studies [28]. The zero sequence components, although present, do not produce any resultant flux in space [29]. Hence, the flux in the machine will be only due to positive sequence component of voltage.

Inductance of the machine during fault-tolerant operation
The equivalent circuit of a balanced three-phase machine is obtained by transforming inductance of the machine to an arbitrary reference frame using the following transformation matrix (K θ ) [30]: where θ is the angle between the stator 'a' phase coil axis and direct axis (d-axis) of arbitrary reference frame. In this transformation matrix, it is assumed that the three-phase voltages and three-phase currents are phase shifted by 2π/3. To obtain the transformed inductance of the machine during fault-tolerant operation similar transformation needs to be applied; however, in case of fault-tolerant operation the voltages are in two healthy phases and hence the current are phase shifted by π/3. Thus, the transformation matrix given in Equation (14) cannot be directly applied to the machine during fault-tolerant operation.
In case of fault-tolerant operation, a steady torque is produced if two healthy phases displaced in space by 2π/3 are supplied with current displaced in time by π/3 [9][10][11][12]. If the direction of current is considered to be reversed in the coil, the axis of the coil also effectively reverses. Hence, this is equivalent to a set of two coils displaced by (π -2π/3) = π/3 in space with the currents displaced by (π -π/3) = 2π/3 in time. This gives the flexibility of using Equation (14) in case of fault-tolerant operation with the assumption that the 'b' phase coil is shifted from 'a' phase coil in space by π/3 and 'c' phase coil is open circuited. Hence, 'c' phase coil do not contribute to the flux linkage which is equivalent of assuming that the inductance of that coil to be zero. Thus, self-inductance matrix of stator in a stationary reference frame (L 0 s_2 ) neglecting the leakage reactance is given by: Self-inductance of stator in an arbitrary reference frame (L s s_2 ) neglecting the leakage reactance is given by: Using similar analysis on a healthy three-phase machine, the transformed self-inductance matrix neglecting the leakage reactance in arbitrary reference frame (L s s_3 ) is given by [30]: Since leakage inductance is assumed to be negligible, the diagonal element of matrix in Equations (16) and (17) represents the magnetising reactance in the equivalent circuit of an induction motor [30]. Comparing the diagonal elements of Equations (16) and (17), it can be inferred that: where (L m_3ϕ ) is the magnetising inductance of the machine during balanced three-phase operation and (L m_2ϕ ) is the magnetising reactance of the same machine during fault-tolerant operation. Since magnetising current is a ratio of applied voltage to magnetising reactance, it can be concluded from Equations (13) and (18) that the magnetising current in case of fault-tolerant operation (L m_2ϕ ) is larger than the magnetising current in case of balanced three-phase operation (L m_2ϕ ) by a factor of √3. This can be mathematically expressed as: Substituting the value of l m_2ϕ from Equations (19) to (11), or Since the reluctance of the air-gap has remained same, it can be concluded that if the same magnitude of voltage is applied across a winding, flux in the machine during fault-tolerant operation will remain same as in balanced three-phase operation.

Torque capability during fault-tolerant operation
Let the rated winding current in two healthy phases of OEIM during open-circuit fault in one of the phases be Isin(ωt−φ) and Isin(ωt−φ-π/3) where I is the peak of rated current of motor winding and φ is the angle between the applied voltage and current in the motor winding. Component of these currents along two mutually perpendicular axes (α and β) are calculated as: These two sinusoidal quantities along two mutually perpendicular axes represent a circle of radius (√3/2)I and is the current space vector (CSV). This CSV is resolved along two perpendicular axes, one along stator flux, being denoted as direct axis or d-axis, and another in quadrature, being denoted as quadrature axis or (q-axis) as shown in Figure 4. The corresponding components of CSV are denoted as i d_2ϕ and i q_2ϕ . When the same mathematical analysis is applied to a threephase balanced system, the magnitude of CSV is found to be (3/2)I. During balanced three-phase operation at rated voltage and rated current, let i d_3ϕ and i q_3ϕ be the direct and quadrature axes components of CSV. Since flux in both the operations is the same, the d-axis component of current (flux producing component of CSV) will also be same. Hence, it can be expressed as: Let the ratio of flux producing component of current (i d_3ϕ ) to the magnitude of CSV during three-phase balanced operation at rated voltage and rated load be k. Thus, i d_3ϕ and i d_2ϕ can be expressed in terms of peak of rated current of motor (I) as follows: Since i d_3ϕ and i q_3ϕ are perpendicular components of CSV, it follows that: In case of fault-tolerant operation, CSV is reduced by a factor of √3. However, the flux in the machine and hence the direct axis component of current has remained same. Hence, referring to Figure 4, the quadrature axis component of current during fault-tolerant operation is Since stator flux orientation is used, λ qs will be zero and hence electromagnetic torque produced by the machine (T e ) is expressed as [30]: It has been established in previous subsection that flux in the machine during fault-tolerant operation will be same as in case of balanced three-phase operation. Thus, during fault-tolerant operation, a reduction in the torque capability of the machine will be only due to a reduction in quadrature component of CSV. Hence, from Equations (24) and (25), it may be concluded that if rated voltage is applied across motor windings with rated current allowed through them, then the relation between the torques produced by the machine during balanced three-phase operation (T 3ϕ ) and winding open-circuit fault-tolerant operation (T 2ϕ ) is given by: It may be noted that in order to obtain rated torque from the machine under open-circuit fault-tolerant operation, the quadrature component of CSV during fault-tolerant operation (i q_2ϕ_r ) should be equal to quadrature component of CSV during balanced three-phase operation: Thus, magnitude of CSV required to produce rated torque in fault-tolerant operation (I 2ϕ_r ) is given using Equations (28) and (29) as: From Equation (21), it can be established that to generate a CSV of magnitude (3/2)I during fault-tolerant operation, the individual phase current should be √3 times of rated current. Hence, to produce rated torque during fault-tolerant operation, the magnitude of individual phase current should be √3 times of rated current. Since the power loss will now be high in the machine, such operation is possible only for a short time, depending on overload capacity of the machine under given cooling condition.

PROPOSED CONTROL SCHEME
The schematic diagram for implementation of the proposed control scheme is depicted in Figure 5. The 'motor speed controller' generates three-phase balanced sinusoidal signals as references for each of the phases of inverter 1. The magnitude, frequency and phase of these signals are controlled by the speed controller which can be a V/f control or a field-oriented control. These sinusoidal signals are sent to two separate blocks for further processing, depending on normal operation or faulttolerant operation as depicted in Figure 5. Letv * 1a ,v * 1b and v * 1c be the three-phase reference signals generated from motor control algorithm as depicted in Figure 5 and where V r is the peak of the reference signal. Under normal operation, each of the sinusoidal reference signals generated from the motor control algorithm is modulated with 15.5% third harmonic to increase the DC bus utilisation by 15.5% [26]. Since the sine waves are mutually displaced by 2π/3, the addition of the same third harmonic (0.155V r sin3ωt) creates three symmetrical wave-shapes with a dip around the peak of each output.
This modulated waveform is compared with a triangular carrier to generate the gate pulses for IGBTs of inverter 1. According to the proposed control scheme, the sinusoidal reference signals for inverter 2 is obtained by phase shifting the reference signals for inverter 1 by 2π/3. The modulation scheme described for inverter 1 is applied on the phase shifted reference signals to generate the IGBT gate pulses for inverter 2. During balanced three-phase operation, the 'select' signal, which is a multibit digital data generated from the fault detection block, activates 'balanced three-phase operation' and simultaneously deactivates 'fault-tolerant operation' (see Figure 5).
When an open-circuit fault in any one phase is detected through monitoring of motor winding currents by a separate circuit (fault detection block), the information about which phase has developed the fault is sent out in the form of a multibit digital data. The 'select' signal now deactivates the balanced threephase operation and activates the gate pulses corresponding to the healthy phases only. For fault-tolerant operation, the voltage across two healthy windings (say x where xϵ{a,b,c} & y where yϵ{a,b,c}, which are selected by the 'phase selection logic') must be mutually phase shifted by π/3. To achieve this, the existing three sinusoidal signal referencesv * 1a ,v * 1b and v * 1c for inverter 1 are manipulated to yield the resulting two π/3 phase shifted voltages as shown in Figure 5.
As an example, if the fault has occurred in phase 'c', then phases 'a' and 'b' are healthy. The post-fault reference signal for phase 'a' (v * 1a f ) and phase 'b' (v * 1b f ) are obtained as follows: v The post-fault reference signal for the surviving two healthy phases of inverter 1 as obtained above has a mutual phase shift of π/3. It can be observed that the post-fault reference signal for phase 'a' (v * 1a f ) lags the pre-fault reference signal for phase 'a' (v * 1a ) by π/6. Similarly, the post-fault reference signal for phase 'b' (v * 1b f ) leads the pre-fault reference signal for phase 'b' (v * 1b ) by π/6. This phase relation between the pre-fault and

PERFORMANCE EVALUATION
A 230 V, 1.5 kW, three-phase, four-pole, open-end induction machine is selected for the performance study. The machine is supplied from 2 three-phase, two-level voltage source inverters (VSI) operating from a common DC bus. Equivalent circuit parameters of the machine during balanced three-phase operation, given in Table 1, are same in both simulation and experimental study. As proposed in this study, a phase shift of 2π/3 is introduced between the reference signals of two inverters and 15.5% of third harmonic is added to the modulating wave to obtain DC bus utilisation of 70.7% at a modulation index (defined as the ratio of peak of reference signal to peak of carrier wave) of 1.

Results
The model of the proposed open-end induction motor drive is developed in MATLAB/Simulink [30]. The simulation schematic of the proposed system is presented in Figure 6. The it is in the latter, then which phase winding is affected. Accordingly, it selects the references for the two inverters and enables gate pulses to the appropriate IGBTs. Figure 7 shows the simulation result of reference voltage, pole voltage (voltage between midpoint of a limb and midpoint of DC bus, say between a & O in Figure 1) generated by one of the phase of inverter 1, voltage across motor winding and current through it. Figure 8 shows the spectrum of pole voltage, line voltage and motor current of odd harmonics only, up to 25th order.

Simulation of balanced three-phase operation
From the spectrum analysis it can be seen that the pole voltage contains 15.5% of third harmonic. However, the voltage across the motor winding has negligible third harmonic component. Hence, the third harmonic content in the motor current is small. Weighted total harmonic distortion (WTHD) of voltage across motor winding calculated up to 25th order is 0.36% and total harmonic distortion (THD) of motor current calculated up to twice the carrier frequency is 2.23%. The magnitude of  fundamental AC voltage obtained from spectrum analysis is 230 V. Hence, the DC bus utilisation appears to be 65.7% at 0.95 modulation index. However, considering switch voltage drops, dead time and the present operation at 0.95 modulation index, it can be predicted that the maximum DC bus utilisation is about 70% at modulation index 1.0, which is maximum for an openend drive in linear modulation region [27]. Figure 9 shows the CMV generated by inverters 1 and 2 along with CMV across motor winding. It can be observed that instantaneous value of CMV is same for both the inverters, resulting in CMV cancellation across the motor winding.

Simulation of winding open-circuit fault-tolerant operation
An open-circuit fault is simulated in one of the winding ('c' phase) of three-phase OEIM. The other two healthy phases of the machine are supplied with equal magnitude of fundamental voltage with a mutual phase shift of π/3. Figure 10 shows the reference voltages for the two inverters and the current through the motor winding. Harmonic spectrum of motor current shows that negligible amount of third harmonic current flows through the machine winding, validating the elimination of third harmonic current during fault-tolerant operation. Figure 11(a) shows the two winding voltages during faulttolerant operation of the proposed PWM scheme with π/3 phase shift between them, along with the two winding currents. The harmonic spectrum of current and voltage are given in

Simulation of transition between balanced three-phase operation and fault-tolerant operation
An OEIM drive is energised from a balanced three-phase source. The load on the motor shaft is adjusted such that the motor draws 57.7% of its rated current at steady state. At t = 1.3 s an open-circuit fault is created in phase 'c' by removing gate pulses from phase 'c' of both the inverters simultaneously. At  Figure 5.
The reference voltage signal derived from the proposed control scheme is shown in Figure 12(a). It can be observed from the simulation result that the post fault reference signal for phase 'a' lags the pre-fault reference signal by π/6 whereas postfault reference for phase 'b' leads the pre-fault reference signal by π/6. The two post-fault references also maintain a relative phase shift of π/3. Figure 12(b) shows the per-unit winding currents. Since the load is maintained constant, the current during post-fault operation is about √3 time higher.
The simulated speed variation during the transition is shown in Figure 12(c). It can be observed that there is no significant variation in the speed during the transition from balanced threephase operation to fault-tolerant operation. From the simulation result, it can be concluded that the proposed scheme can provide a disturbance-free smooth transition from balanced threephase operation to fault-tolerant operation.

Experimental results for balanced three-phase operation
The OEIM drive is set up in the laboratory and tested for its performance under the proposed scheme. Both the inverters of the OEIM drive are supplied from a common DC bus of 350 V (see Figure 1) and is operated at a modulation index of 0.95. To maximise DC bus utilisation the reference signals are modulated  Figure 13 shows pole voltage of one inverter and its harmonic spectrum up to the 25th order. From the spectrum, it can be seen that fundamental rms voltage produced by one of the inverter is 131.6 V with a peak of 186.1 V. Magnitude of third harmonic component is 21.6 V which is approximately 15.5% of fundamental with negligible other harmonics. Figure 14 shows the voltage across one winding and its harmonic spectrum up to the 25th order. From the spectrum, it can be seen that fundamental rms voltage produced is 228.5 V with a peak of 323.2 V. Magnitude of third harmonic and other harmonic components are negligible. The experimental value of DC voltage utilisation appears to be 65.3% at 0.95 modulation index. However, considering switch voltage drops, dead time and the present operation at 0.95 modulation index, it can be estimated that the maximum DC bus utilisation at modulation index 1.0 will be about 70%. WTHD of voltage across motor winding calculated up to the 25th order is found to be 0.32%. Figure 15 shows the PWM voltage waveform developed across the motor winding.
Load on the motor shaft is adjusted such that rated current flows through the motor winding. Figure 16(a) shows the three-phase currents flowing through the motor windings when the motor operates at rated voltage and rated current. Current Experimental current through motor during balanced threephase operation of proposed scheme (a) winding current waveform from digital oscilloscope, (b) winding current waveform acquired in real time platform and its transformed values along mutually orthogonal axis, (c) spectrum of motor winding current up to the 25th order through the motor winding is also sensed by a current sensor (LA 55-P) and is acquired in real time using dSPACE 1104. Figure 16(b) shows the three-phase motor currents acquired in realtime platform and its transformed values along mutually perpendicular axis (I alpha and I beta ). The spectrum of current up to the 25th order is presented in Figure 16(c). The rms value of fundamental component of current is found to be 3.52 A and harmonics up to the 25th order is found to be negligible. Experimental value of THD calculated up to twice the switching frequency is found to be 1.85%. Figure 17 shows the experimental CMV produced by inverters 1 and 2. Although each of the inverter produces CMV, the instantaneous value of CMV produced by both the inverters is same. Hence, as predicted, CMV across the motor winding is experimentally found to be negligible.

Experimental results for open-circuit fault-tolerant operation
Open-circuit fault is emulated in one of the phase of OEIM and other two phases are supplied with rated fundamental voltages with π/3 mutual phase shift. Figure 18 shows the voltage waveforms across the motor windings and the currents through them.
The load on the shaft is adjusted so that rated current flows through the motor winding. Figure 19(a) shows the motor

5.3
Performance comparison between balanced three-phase and fault-tolerant operation

Simulation study
CSV is obtained as a plot of i α versus i β in per unit (peak of i α during balanced three-phase operation at rated load is treated as base) where i α and i β is obtained from Equation (21). Figure 20(a) shows a comparison between CSV during balanced three-phase operation and fault-tolerant operation, when rated current is allowed through motor windings. It can be concluded from the simulation study that if the phase current of the machine is kept same during balanced three-phase operation and fault-tolerant operation, the magnitude of CSV in case of fault-tolerant operation is smaller than the magnitude of CSV in balanced three-phase by a factor of √3.
Standard flux estimation technique is used to obtain the space vector of stator flux linkage in per unit (peak stator flux linkage along α axis during balanced three-phase operation at rated voltage and frequency used as base) [30]. Figure 20(b) shows that the stator flux linkage remains same in balanced threephase and fault-tolerant operation, confirming the result in (20). Figure 20(c) shows a comparison of electromagnetic torque (presented in per unit value where rated torque of the machine is taken as base) produced by the machine during balanced threephase operation and fault-tolerant operation, when only rated current is allowed through the motor winding. From the graph, it can be seen that during fault-tolerant operation, if rated current is allowed to flow through the winding and rated flux is maintained across the air gap, then torque produced by the machine is approximately 52% of rated value.

Experimental study
The OEIM under test is loaded both under balanced threephase operation and under fault-tolerant condition such that rated current flows through the motor windings. The motor winding currents are acquired and transformed into i α and i β in real time using dSPACE1104. CSV is obtained as a plot of i α versus i β in per unit. Figure 21(a) shows a comparison of CSV during balanced three-phase operation and fault-tolerant operation. From Figure 21(a), it can be inferred that for same value of phase current, during fault-tolerant operation, the magnitude of CSV is reduced by a factor of √3. From the parameters of the motor in Table 1 and real-time measurement of motor voltage and current, stator flux linkage and electromagnetic torque are estimated in real time. Figure 21(b) shows the space vector of stator flux linkage in per unit during three-phase balanced operation and fault-tolerant operation. Figure 21(b) experimentally validates that flux in the machine is maintained at rated value during fault-tolerant operation as  Figure 21(c) shows a comparison of estimated electromagnetic torque developed by the machine during balanced threephase operation and proposed fault-tolerant scheme. From the experimental result, it can be concluded that electromagnetic torque developed by the machine (with parameters given in Table 1) during fault tolerant operation is approximately 50% of rated value.
From the equivalent circuit parameters of the machine given in Table 1, the magnetising current is estimated approximately at 30% of the rated current. From Equation (23), it can be inferred that the value of k for the machine under test is 0.3. Substituting k = 0.3 in Equation (27), it is estimated that value of torque during fault-tolerant operation is 51.71% of rated torque. The experimental value of torque is slightly lower than the analytical result because of mechanical losses and saturation in the core [9]. The experimental setup is presented in Figure 22.

Comparison of proposed scheme with existing fault-tolerant schemes
Existing fault-tolerant schemes for OEIM drives describes algorithms for operation of the drive during inverter device failure [13][14][15][16]. During such fault-tolerant schemes, redundant switching arrangements are used to generate balanced three-phase voltage across motor windings.
However, during winding fault-tolerant operation of OEIM drive, the voltages applied across the two healthy phases should be mutually phase shifted by π/3 in order to generate steady state torque during starting and running of the drive. Existing PWM schemes cannot generate the π/3 phase shifted voltage and simultaneously eliminate third harmonic current, which creates additional problems. Hence, existing schemes are not suitable for sustained faul-tolerant operation of OEIM drive. Figure 23(a) shows the simulated waveforms of the two winding voltages with π/3 phase shift between them, along with the two winding currents, during fault-tolerant operation of a conventional PWM scheme. Note the distortion in the current waveform. The harmonic spectrum are given in Figure 23(b) which shows the presence of a large magnitude of third harmonic in both the voltage and current.  The proposed scheme, however, can generate π/3 phase shifted two phase voltage and simultaneously eliminate third harmonic current without sacrificing DC bus utilisation. The simulated waveforms of the two winding voltages and currents have been presented in Figure 11(a) during fault-tolerant operation of the proposed PWM scheme with π/3 phase shift between them. Note the smooth current waveform, confirmed by negligible presence of third harmonic in the harmonic spectrum of voltage and current of Figure 11 The experimental waveforms of the OEIM drive under faulttolerant operation for the conventional scheme is depicted in Figure 24 while similar waveforms for the proposed scheme have been presented in Figure 18. In both the cases, the experimental voltage and current waveforms are found to be in good agreement with the simulated waveforms, respectively, showing the distortion of current in conventional and no distortion in the proposed scheme. Table 2 presents a comparison of the harmonics obtained in both the experimental methods. Table 2 confirms that while the third harmonic significantly exists in the conventional scheme, it is effectively reduced to negligible value in the proposed technique.

CONCLUSION
A