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Efficiency Evaluation of Five-Phase Outer-Rotor Fault-Tolerant BLDC Drives under Healthy and Open-Circuit Faulty Conditions.

I. INTRODUCTION

Regarding their high efficiency and compactness, permanent magnet (PM) motors are gaining more interest in the field of electrical and hybrid electrical vehicles. Absence of field windings and rotor currents in PM motors not only reduces the required maintenance, but also increases the motor efficiency and its robustness [1-2].

The efficiency of an electric drive directly depends on the generated losses of its inverter block and electric motor. In the inverter block, the main sources of power loss are related to inverter snubbers and semiconductors. However, in many IGBT based topologies, it is not necessary to implement snubbers, and as a result, power losses can be categorized as IGBT and diode conduction losses, IGBT and diode off-state losses and IGBT switching losses. Among these categories, switching losses are the most important type of losses in the inverter block.

Switching algorithm has also an important impact on the final losses of inverter block. Different modulation strategies are proposed in literature to improve quality of converter outputs. These modulation methods can be categorized in two main groups including space vector modulation (SVM), and carrier based (CB) pulse width modulation (PWM) [3-4]. SVM methods let us to have a better utilization of dc bus. On the other hand, CB methods (equivalent to SVM algorithms) are easier to implement.

The second important source of drive losses is the electrical motor. During the last two decades, many controlling algorithms have been proposed in literature to minimize the motor losses by adapting machine flux to the load. These algorithms can be generally divided in three categories.

In the first category motor power factor [5] or rotor slip frequency [6] is controlled. Control of motor power factor is a practical choice for industrial drives as there is no need to speed or load information, and moreover, its adaptation is relatively fast (1 s). On the other hand, to control the rotor slip, it is required to know both speed and load information.

In the second category, the output power of the drive is kept constant and motor flux is adapted to reduce the input power of the machine [7]. However these methods are usually accompanied by several disadvantages. For example, precise load information is always required in their algorithms, and the adaptation period of these methods is quite long (7 s) [8]. In addition, a continuous disturbance can be observed in generated electrical torque. As a result, this category of efficiency improvement methods is not very popular in industrial applications.

In the third category, efficiency optimization methods are directly based on the loss model of electrical motor. These methods can be easily combined by field oriented controlling (FOC) algorithms which are already based on machine's knowledge [9]. Although efficiency optimization algorithms provide fast and smooth control of stator flux, but they usually require machine parameters and their computational loads is relatively high.

In addition to control algorithm, machine design has also an important effect on the final efficiency of electrical drive. Efficiency maps are usually used to describe the generated losses of an electrical motor with respect to a particular speed/torque. In permanent magnet machines, power losses can be divided into winding (copper) losses and core (iron) losses [10-11].

Comparing to induction machines, core losses in PM motors stand for a larger portion of the total losses. A three-term core-loss model is used in [12-13] to calculate the generated core losses of a PM machine. In [12] [14] the flux density waveforms are estimated in stator tooth and yoke, and some analytical expressions are derived to calculate hysteresis loss and eddy-current loss. However, these approaches are usually used in the design procedure of PM machines where iron losses should be calculated many times while executing the design algorithms.

Finite-element methods (FEM) are used in [13] and [15] to precisely calculate tangential and radial flux densities within the stator core and to calculate hysteresis and eddy current loss of each element. The ratio between winding and core losses is a key factor in determining the maximum efficiency point of an electrical motor. While having a constant-speed application, this point can be considered in the design procedure of electrical motor.

Fault tolerant concept is an important issue in applications where the process cannot be stopped due to additional cost penalties or safety reasons [16]. PM drive faults can be generally categorized as actuator faults, airgap irregularities, rotor magnet faults, and stator winding faults [17]. Among these categories, stator winding open-circuit fault and semiconductor failures are the most common ones [18]. Fault tolerant inverter topologies are considered in many papers. In many studies, an additional leg is implemented in inverter configuration to be replaced with the faulty inverter leg, or to feed the machines neutral point [19].

Compared with standard three-phase systems, five-phase motor drives present better fault tolerant capabilities. These systems are able to maintain operational in the case of one or even two faulty phases [11] [16] [20-21]. Fault tolerant capability can be achieved by means of modifying stator reference currents and inverter topology.

In [18] [22-23] stator reference currents are optimized to improve the generated output torque of five-phase PM machines and at the same time to limit the stator ohmic losses of each winding to its 1 pu. Although the calculation methods of these studies are quite different, but the resultant values of reference currents are in common.

In this study the efficiency of a fault-tolerant five-phase BLDC drive is evaluated for healthy and different faulty conditions. Open-circuit fault is considered for one, two-adjacent and two-nonadjacent stator phases, and in each case, optimized reference current values of [18] [23] are used to drive the faulty machine. Copper loss and switching loss are calculated by analytical simulations in MATLAB, and stator core losses are computed by FEM simulations in Flux. Different speed values are considered in the efficiency evaluation of five-phase drive. Automotive applications are kept in mind and experimental tests are conducted on an outer-rotor in-wheel type of five-phase BLDC machine with a two-layer winding configuration.

The remaining parts of the paper are organized as follows. In section II, general structure of selected BLDC machine is explained, its electrical model is derived, and its optimized current references under different faulty conditions are introduced. Section III is dedicated to theoretical calculation of different loss sources in BLDC drive and their simulations. Experimental evaluation of developed theories is presented in section IV, and finally, the conclusions extracted from this study are summarized in section V.

II. BLDC MACHINE STRUCTURE AND DRIVE LOSSES

A general structure of BLDC machines with an outer-rotor topology and a two-layer stator winding is considered in this paper. In this section, BLDC machine model is extracted on the assumption of having a symmetric five-phase winding configuration, and P poles. Let us start with the general equation of machine's electrical dynamics:

[[V.sub.s]] = [r.sub.s] [[I.sub.s]] +d/dt [[[LAMBDA].sub.s] (1)

where [V.sub.s] is voltage matrix of stator winding terminals, [r.sub.s] and [I.sub.s] are resistance and current respectively. [LAMBDA]s is the magnetic flux linkage of stator windings which is generated by stator currents and rotor magnets.

[[LAMBDA].sub.s] = [L.sub.ss] [I.sub.s] +[[LAMBDA].sub.PM] (22)

where [L.sub.ss] represents stator inductance matrix.

The magnetic flux of rotor magnets in a BLDC machine airgap can be estimated by its first and third harmonic components:

[mathematical expression not reproducible] (3)

where [[lambda].sub.pm1] and [[lambda].sub.pm3] are first and third harmonic component of rotor magnetic flux, and [theta] = wt is rotor electrical angle. Electrical parameters of stator windings can be transferred into synchronous rotating frames which under normal (healthy) conditions result in a simpler and more conceptual control in a DC environment. Considering first and third harmonics, the transformation equation is written in (4) at the beginning of the next page. using this transformation, stator voltages and currents will be transferred into [d.sub.1] - [q.sub.1] and [d.sub.3] - [q.sub.3] planes which respectively rotate at synchronous speed, and its third multiple.

[mathematical expression not reproducible] (4)

Multiplication of (1) by T results in the related electrical equations of BLDC machine in two reference frames. These equations can be summarized as:

[V.sub.sd1] = [r.sub.s][i.sub.ds1] - [omega][[lambda].sub.qs1] + d[[lambda].sub.ds1]/dt (5)

[V.sub.sd1] = [r.sub.s][i.sub.ds1] + [omega][[lambda].sub.qs1] + d[[lambda].sub.ds1]/dt (6)

[V.sub.sd3] = [r.sub.s][i.sub.ds3] - 3[omega][[lambda].sub.qs3] + d[[lambda].sub.ds3]/dt (7)

[V.sub.sd3] = [r.sub.s][i.sub.qs3] + 3[omega][[lambda].sub.qs3] + d[[lambda].sub.ds3]/dt (8)

where [r.sub.s] is the stator resistance, and [omega] is the electrical rotational velocity. These equations will be used in vector control of BLDC motor. Generated electrical torque will be calculated as:

[T.sub.e] = 5/2 P/2[[lambda].sub.m1][i.sub.qs1] + 3[lambda].sub.m3][i.sub.qs3]] (9)

Several studies have focused on optimization of amplitude and phase angle of current references under faulty conditions. In almost all of these studies, rated RMS value of phase copper losses is considered as a limit in the optimization process to avoid thermal stress (hot spots) within the stator core. Moreover, it is tried to increase the output power, while limiting the generated torque ripples. Optimization procedure of stator reference currents under different conditions is beyond the scope of this paper. Table I presents the desired reference current values which are globally optimized by genetic algorithm in [23] and analytically computed in [24] for a five-phase BLDC machine.

III. LOSS SIMULATION

Simulations are conducted to evaluate the stator core (iron) losses, stator winding (copper) losses, and inverter switching losses. Each of these aspects will be explained in the following subsections.

A. Stator Core (Iron) Losses

Iron losses can play an important role in generated thermal stresses of stator core. However, as stator core losses are a function of used material, winding configuration and machine design, it is not possible to generally optimize the reference values of stator phase currents for all types of five-phase BLDC machines under faulty conditions. In this paper, optimized values of stator currents are used to evaluate both copper and iron losses of an outer-rotor five-phase BLDC machine.

Stator core losses [W.sub.t] can be divided into three categories of hysteresis losses [W.sub.h], eddy current losses [W.sub.e], and anomalous (or excess) losses [W.sub.e] [10][25]:

[W.sub.t] = [W.sub.h]+[W.sub.e]+[W.sub.f] (10)

Hysteresis losses of the stator core can be calculated as:

[W.sub.h] = [k.sub.h][B.sub.max.sup.2]f (11)

where [k.sub.h] is the experimental coefficient of magnetic losses due to hysteresis [Ws[T.sup.2][m.sup.3]], [B.sup.max] is the peak value of magnetic flux density [T], and f represents the electrical frequency [Hz] [10] [26]. In addition, the losses related with induced eddy currents can be computed as:

[W.sub.e] = [[pi].sub.2][sigma][d.sup.2]/6 [B.sub.max.sup.2][f.sup.2] (12)

where [sigma] is the electrical conductivity of implemented ferromagnetic material [S/m], and d is lamination thickness [m]. Moreover, anomalous power losses can be calculated as:

[W.sub.a] = 8.67[k.sub.e] [([B.sub.max]f).sup.1.5] (13)

where [k.sub.e] is the experimental coefficient of anomalous (excess) losses [W[([Ts.sup.-1]).sup.-1.5][m.sup.-]]. Assuming the stacking factor of [K.sub.f] for steel laminations, equation (10) can be written as:

[mathematical expression not reproducible] (14)

In this equation [sigma], d and [k.sub.f] are known values. Moreover, [k.sub.h] and [k.sub.e] can be provided by lamination's manufacturer. As a result, equation (14) can be used to compute stator iron losses [10][25].

To compute stator iron losses, FEM simulations are conducted in two dimensions by Flux-Cedrat[R] software. Simulation sampling frequency is set on 4.9 kHz, and the total numbers of simulated points are set to 2048. Stator winding configuration is similar to Fig. 1 but with 26 pole-pairs. Stator winding configuration, core laminations, and applied 2D mesh plot of the simulations are presented in Fig. 1.

Non-oriented electrical steel M235-35A laminations are considered in the simulation which corresponds to the implemented material in the real test bench. Specific losses of soft ferromagnetic materials include hysteresis losses, eddy losses and excess losses. Figure 2 shows the specific losses of M235-35A steel as a function of magnetic polarization. This information is provided by manufacturer at [f.sub.e] = 100 Hz and [f.sub.e] = 200 Hz. By applying interpolation, specific losses of these laminations can be computed for the rated frequency of five-phase BLDC machine in the test bench ([f.sub.e] = 173 Hz). Figure 2 presents the specific losses of M235-35A steel as a function of peak value of magnetic flux density. As a result, by extracting the information of two separate points in Fig. 2, it is possible to compute the experimental coefficients of [k.sub.h] and [k.sub.e] at rated frequency of 173 Hz. Physical properties of simulated laminations are summarized in Table II.

The derived coefficients are used in FEM simulations to calculate stator core losses while the machine is rotating at its rated speed. Table III presents the simulated values of stator core losses for five-phase BLDC machine under healthy and different faulty conditions. As it can be seen from Table III, in the case of missing one phase, [P.sub.loss-iron] is less than its value in normal conditions. In fact, if reference currents were not modified and stator windings were physically separated, then iron losses due to stator currents should be reduced to 80% its rated value. However, [P.sub.loss-iron] is reduced to 84% of its value under normal conditions.

This higher value of losses is due to double-layer configuration of stator winding which leads to iron loss in all regions of stator core. Moreover, although the RMS value of stator phase currents is still 1 pu, but the peak value of optimized reference currents has increased by 10% in two of the remaining stator phases which increases the saturation level of implemented laminations. In addition, rotor magnetic field does not depend on stator winding currents and generates a constant value of iron losses in the stator.

In the case of missing two adjacent faulty phases, [P.sub.loss-iron] is 76% of its value under normal conditions. Again, in the case of separated windings and no modification in stator reference currents, the expected value of [P.sub.loss-iron] due to stator currents should be 60% its rated value.

However, to generate a ripple-free torque, the stator phase currents should be adapted. In fact, in this case the peak value of stator phase currents are [I.sub.C-peak] =0.68 pu, [I.sub.D-peak] = 1.24 pu, and [I.sub.E-peak] = 0.68 pu. High value of [I.sub.D-peak], double-layer configuration of stator windings, and constant value of rotor magnetic field are the main reasons of higher core losses in the case of missing two adjacent phases.

In the case of missing two non-adjacent phases, the physical situation of the remaining healthy phases are quite symmetric, and peak values of stator reference currents are [I.sub.B-peak] [approximately equal to] 0.88 pu, [I.sub.D-peak] [approximately equal to] 1.12 pu, and [I.sub.E-peak] [approximately equal to] 1.12 pu. Under this operational condition, [P.sub.loss-iron] is 72% of its value while operating under normal conditions. Comparing to the case of having two adjacent missing phases, stator current peak values are more moderated. However, again peak values of stator reference currents are more than 1 pu in two of the remaining phases. As it can be seen in this case [P.sub.loss-iron] is 4% less than its value in the case of missing two adjacent faulty phases which is firstly due to a reduction in maximum peak value of stator current in the remaining healthy phases, and secondly, more uniform distribution of remaining phase windings.

B. Stator Winding (Copper) Losses

Stator copper losses in the remaining healthy phases can be simply calculated as:

p(t) = v(t)i (t) = r[i.sup.2] (t) (15)

Using the reference values of [22] and by knowing that [r.sub.s] = 0.1[OMEGA], pu values of generated copper loss in stator windings are summarized in Fig. 3 for each condition.

RMS value of stator phase currents is the main limiting factor in the optimization procedure of stator reference currents while missing one or two stator phases. In the case of missing one stator phase, copper losses are 1 pu in the remaining healthy phases, and total amount of stator copper losses is 80% of its value under normal operation.

While missing two adjacent stator phases, stator copper losses are less in the two non-adjacent remaining phases. The main reason of this fact is torque ripple constraints in the optimization procedure of stator reference currents. In other words, to generate a ripple-free torque in the case of missing two-adjacent phases, it is not possible to use the entire copper capacity of the remaining three healthy windings. The entire copper losses under this condition is 37% its value under normal operation.

C. Inverter Losses

As it was mentioned previously, off-state losses are not considered in this study. To calculate the conduction losses, IGBT and diode models are considered as voltage sources with a resistor in series. The average value of conduction losses during the modulation period T can be computed as:

[mathematical expression not reproducible] (16)

where [V.sub.Fo], [i.sub.F] and [R.sub.on] are respectively threshold voltage, forward current and dynamic resistance of semiconductors. The main reason of switching losses is non-ideal characteristics of IGBTs during turn-on and turn-off moments (switching instants). As a result, switching losses are directly dependent on inverter switching frequency and modulation period. Average value of switching losses in one modulation period can be calculated as [24]:

[mathematical expression not reproducible] (17)

where n is the number of transitions in each switching period, [E.sub.on], [E.sub.off] and [E.sub.rec] are turn-on, turn-off and reverse recovery losses of IGBT switch, and T is the fundamental period of drive component. To simulate the inverter losses, it is required to formulate dynamic and static characteristics of implemented IGBTs and diodes. These characteristics include turn-on and turn-off energy and voltage drop of each semiconductor.

These characteristics are formulated by using datasheet information of inverter semiconductors and MATLAB Curve Fitting toolbox. Table IV presents the derived polynomial functions of FP15R06W1E3 IGBT model and their reverse diodes.

Moreover, Fig. 4 illustrates the simulated losses of inverter block. Five-phase BLDC drive is simulated and inverter losses are computed (in watts) for steady states and under healthy and each faulty condition. In the case of healthy conditions, total amount of conduction and switching losses in each leg is 0.83% of the rated power. In this case, conduction losses and switching losses are equal for all inverter legs.

While missing one stator phase, both switching and conduction losses increase in the remaining inverter legs. Under this condition, [I.sub.B-peak]= 1.12 pu, [I.sub.C-peak]=1.00 pu, [I.sub.D-peak]= 1.00 pu, and [I.sub.E-peak]=1.12 pu. As a result, it is expected that the losses increase more in phases B and E. comparing to the healthy case, conduction loss increment of phase B and E is 0.10% rated power. Moreover, switching loss increment is 0.10% rated power. The increment of both conduction and switching losses for the remaining two phases is 0.028% rated power.

In the case of missing two adjacent phases, both conduction and switching losses increase in the remaining three phases. Comparing to normal (healthy) operation, the increment of conduction losses in phases C, D and E are respectively 0.35%, 0.90% and 0.36% of the rated power. The increment of switching losses for phases C, D and E are 0.32%, 0.72% and 0.32% rated power, respectively. As it can be seen from Fig. 5, inverter losses are higher in leg D of the inverter which is due to higher peak value of stator currents in its corresponding phase.

On the other hand, while missing two non-adjacent phases, stator phase currents are more symmetric. As a result, comparing to the case of missing two adjacent faulty phases, the switching losses are less in this case. Comparing to normal operation, the conduction loss in phases B, D and E have an increment of 0.13%, 0.19% and 0.21% of the rated power. Moreover, switching loss increment in each one of these cases is 0.14%, 0.17% and 0.19% of the rated power.

IV. EXPERIMENTAL EVALUATION

To evaluate the theoretical investigations, experimental tests are conducted on a commercial type of five-phase BLDC hub motor. Figure 5 presents the general configuration of the test bench. The stator incorporates a double-layer fractional-slot winding accompanied by an outer-rotor. Due to its high number of pole pairs, the magnets are simply installed on rotor inner surface. Machine's parameters are summarized in Table V.

Motor phase terminals are fed by a five-phase inverter with a 48V dc-bus and 5 kHz of switching frequency. In addition, stator current controlling algorithm is realized by DS1005 dSpace board, and mechanical speed is controlled (fixed) by the load system. under each operational condition, real and reference values of stator phase currents are compared, and the resultant current errors are used in controllers to calculate the required reference voltages of each phase. under faulty conditions, stator phase currents are directly controlled in phase reference coordination. Proportional-resonant (PR) controllers are used to calculate the reference values of phase terminal voltages [27].

An incremental encoder and 5 Hall Effect sensors are used to close the position and current loops. Load system is a commercial three-phase PMSM which is driven independently by a three-phase AC drive (famous as SINAMICS S120). A real-time controller (known as cRio) is used as an interference between host computer and three-phase inverter. Constructed five-phase inverter and the mechanical link between load and five-phase BLDC motor are also shown in Fig. 5. In addition, stator currents under healthy and each faulty condition are summarized in Fig. 6. The computational power of implemented dSpace and its IO port speed are limited. As a result, 5 kHz is the maximum achievable switching frequency. It is worth noting that due to relatively low value of motor speed, air friction losses and ball bearing losses are negligible. As a result, these sources of losses are not considered in simulation evaluations.

In each case, input and output power of BLDC drive are measured under steady state to evaluate the efficiency of BLDC drive. Input power is directly calculated by measuring the output current of dc power supply and multiplying it by dc bus voltage. On the other hand, to compute the output power of five-phase BLDC drive, mechanical torque is measured in healthy and different faulty conditions. Table VI summarizes the measured values of input and output power for each case.

While operating under normal conditions, the measured efficiency value of the entire drive is 88.4% which is close to its simulated value (87.9%). regarding simulation results, while working with a healthy machine the main part of BLDC drive losses are related to iron core (0.06 pu), and after that, inverter unit losses (0.04 pu) and stator windings copper losses (0.03 pu).

Comparing to normal operation, the measured value of drive efficiency is less in the case of missing one stator phase (84%). In this case, the maximum value of output power is reduced to 0.73 pu [23], and as the RMS value of stator currents in the remaining healthy phases is kept on 1 pu, stator copper losses are 80% their rated value. Stator current peak values are higher than 1 pu in two of the remaining phases which results in higher amplitudes of conduction and switching losses in their correspondent inverter legs. Regarding the simulations, in this case the main part of BLDC drive losses are again generated by stator iron core (0.05 pu), and after that, inverter unit losses (0.04 pu) and stator copper losses (0.028 pu) are the most important reasons of efficiency reduction in the drive.

In the case of missing two adjacent phases, measured drive efficiency decreases down to 66% which is highly noticeable comparing to its value under normal conditions (88%). The main reason of this efficiency reduction is related to optimized values of stator reference currents under this condition [22-23]. In fact to limit the generated ripples in the case of missing two adjacent phases, fundamental component of stator currents should be less than 0.7 pu in two non-adjacent healthy phases, and high amplitudes of third harmonic components are required. Moreover, theoretical value of ripple-free output power is reduced to 0.27 pu. In this case, the main parts of BLDC drive losses are related to the inverter losses (0.0548 pu) which is due to high peak value of stator currents. After inverter losses, stator core losses (0.04 pu) is the biggest source of power losses in BLDC drive. In addition, as it is not possible to use the entire copper capacity of the remaining healthy phases, stator copper losses are reduced to 0.013 pu in this case.

In the case of missing two non-adjacent stator phases, the measured value of BLDC drive efficiency is 83% which is close to its simulated value (84.7%). Comparing to the case of two adjacent faulty phases, there is a noticeable increment in final value of drive efficiency. The main reason of higher efficiency is more symmetric situation of the remaining healthy phases which allows having a better utilization of stator copper capacity to generate more ripple-free output power. The maximum achievable output power in this case is limited to 0.55 pu which is due to keeping the RMS value of stator reference current

under 1 pu. Regarding simulations, in this case, the main source of BLDC drive losses are related to stator core iron (0.04 pu), and after that inverter block losses (0.03 pu) and stator copper losses (0.02 pu) are the most important reasons of efficiency reduction.

V. CONCLUSION

In this paper, the efficiency of a fault tolerant five-phase PM drive is evaluated. Considered machine is a five-phase outer-rotor BLDC motor with a double-layer winding configuration. Open-circuit fault is considered in one, two adjacent and two non-adjacent stator phases. In each case, RMS value of stator reference currents is the main limiting constraint of generated ripple-free torque. Stator core losses are calculated by means of simulations in Flux-Cedrat[R] environment. It is shown that iron losses are the most important part of BLDC drive losses under normal operation and while missing one phase and two non-adjacent phases. In addition, inverter unit losses and stator winding (copper) losses are simulated in MATLAB environment. In the case of having two adjacent faulty phases, inverter losses are the most important reason of BLDC drive losses. Regarding simulations, the final efficiency of BLDC drive is 87%, 86%, 70% and 84% respectively in the case of working with a healthy machine, a machine with one missing phase, a machine with two adjacent missing phases, and a machine with two non-adjacent missing phases. In addition, experimental tests are conducted to verify the simulation results. Measured value of BLDC drive efficiency is 89%, 84%, 66% and 83% respectively in the case of working with a healthy machine, and while missing one phase, two adjacent phases and two non-adjacent phases.

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[27] R. C'ardenas, C. Juri, R. Pena, P. Wheeler, J. Clare, "The application of resonant controllers to four-leg matrix converters feeding unbalanced or nonlinear loads," IEEE Trans. Power Electron., vol. 27, no. 3, pp. 1120 - 1129, March 2012.

Ramin Salehi ARASHLOO, Mehdi SALEHIFAR, Harold SAAVEDRA, Jose Luis ROMERAL MARTINEZ

Electronic Engineering Department, Politechnical University of Catalunya - Barcelonatech

ramin.salehi@mcia.upc.edu

Digital Object Identifier 10.4316/AECE.2014.02023
TABLE I. OPTIMIZED STATOR PHASE CURRENTS OF FIVE-PHASE BLDC MACHINE
UNDER DIFFERENT FAULTY CONDITIONS [22-23]

        Currents          A    B       C      D        E

                          one faulty phase

     [I.sub.1] (pu)       0   0.99    0.99    1       0.98
[[theta][degrees].sub.1]  -  51     137     232     -41
     [I.sub.3] (pu)       0   0.17    0.08    0.09    0.19
[[theta][degrees].sub.3]  -  23      52     186     -19

                          two adjacent faulty phases

     [I.sub.1] (pu)       0   0       0.59    0.95    0.67
[[theta][degrees].sub.1]  -   -      82     218       1
     [I.sub.3] (pu)       0   0       0.12    0.29    0.16
[[theta][degrees].sub.3]  -   -      44     102      41

                          two nonadjacent faulty phases

     [I.sub.1] (pu)       0   0.99    0       0.98    0.99
[[theta][degrees].sub.1]  -  77       -     197     -42
     [I.sub.3] (pu)       0   0.16    0       0.19    0.17
[[theta][degrees].sub.3]  -  15       -      55     -21

TABLE II. PHYSICAL PROPERTIES OF STEEL LAMINATIONS

             Parameter                               Value

  Electrical Conductivity, [sigma]       1.695.[10.sup.6] [Sm.sup.-1]
           Density, [rho]             7850[kgm.sup.-3]
            Thickness, d                 0.35.[10.sup.-3] m
 Hysteresis coefficient, [k.sup.h]     [67.38100WsT.sup.-2][m.sup.-3]
Excess losses coefficient, [k.sup.e]     0.95211W
                                      [([Ts.sup.-1]).sup.-1.5][m.sup.-3]
     Stacking factor, [k.sup.f]          0.96

TABLE III. STATOR IRON LOSSES OF FIVE-PHASE BLDC MACHINE AT ITS RATED
SPEED

        Motor Condition          Stator core (iron) losses (pu)

       Normal (Healthy)                       0.06
       One missing phase                      0.0504
  Two adjacent missing phases                 0.0456
Two non-adjacent missing phases               0.0432

TABLE IV. ESTIMATED DATA FOR FP15R06W1E3

                                       Estimated characteristic
                                               Transistor

          Voltage drop             0.1056x[i.sup.0.4602] + 0.3161
 Turn on Energy: [E.sub.on](mJ)    0.0001723x[i.sup.2] -0.02001xi+7.423
Turn off Energy: [E.sub.off](mJ)   0.0936xi + 3.2687
                                                  Diode
          Voltage drop             0.6781x[i.sup.0.2387] -0.2912
Turn off Energy: [E.sub.off](mJ)  63xexp(-0.001732xi)-
                                  58.3xexp(-0.0029xi)

TABLE V. ELECTRICAL (MEASURED) PARAMETERS OF FIVE-PHASE BLDC MACHINE

          Parameter                 value

     Number of Pole Pairs        26
      Stator Resistance           0.1 [OMEGA]
Stator Inductance  [L.sub.aa]]  408 uH
                   [L.sub.ab]]   15 uH
                                 18 uH
        Nominal Torque            8 Nm
        Nominal Power           350 Watt
    Nominal Phase Current         5 Amp (rms)
    Nominal Phase Voltage        16 V (rms)
     DC-bus Rated Voltage        48 V
        Nominal Speed           400 rpm
    Permanent Magnet Flux         0.0178 Wb

TABLE VI. MEASURED VALUES OF BLDC DRIVE INPUT AND OUTPUT POWERS AND ITS
EFFICIENCY

Condition   [P.sub.in-elec].  [P.sub.out-mech].  [P.sub.loss-tot].  Eff.
                  (pu)              (pu)               (pu)

Normal (H)        1.13              1                  0.13         0.88
   1F             0.86              0.73               0.13         0.84
   2AF            0.39              0.26               0.13         0.66
   2NAF           0.66              0.55               0.11         0.83
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Author:Arashloo, Ramin Salehi; Salehifar, Mehdi; Saavedra, Harold; Martinez, Jose Luis Romeral
Publication:Advances in Electrical and Computer Engineering
Date:May 1, 2014
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