Sensorless speed control of a fi ve-phase induction machine under open-phase condition

Recently, multiphase machines have been promoted as competitors to their three-phase counterparts in high-power safety-critical drive applications. Among numerous advantages of multiphase induction machine (IM) drives, self-starting and operation under open phase(s) stand as the most salient features. With open phase(s), optimal current control provides disturbancefree operation given a set of objective functions. Although hysteresis current control was merely employed in the literature as it offers a simple controller structure to control the remaining healthy phases, it is not suitable for high-power applications. In the literature, multiple synchronous reference frame (dq) control can be an alternative; however, it requires back and forth transformations with several calculations and additional sophistication. In this paper, a simple technique employing adaptive proportional resonant (PR) current controllers is presented to control a five-phase IM under open-phase conditions. Results for both volt/hertz (V/f) and field oriented control (FOC) systems are presented. Moreover, sensorless operation under fault condition is also demonstrated by estimating the machine speed using a rotor flux-based model reference adaptive system (MRAS) speed estimator. The proposed controllers are experimentally verified and compared. Although FOC provides better dynamic performance, V/f control offers a simpler control structure and a lower number of PR controllers.


Introduction
In high power and safety-critical applications, multiphase induction motors (IMs) are strong competitors to their three-phase counterparts based on the numerous advantages offered by multiphase systems [1].First, multiphase machines can be designed with a reduced per-phase current correspondingly reduced semiconductor devices' current rating.Second, multiphase systems offer additional degrees of freedom that improve system performance, increase system fault tolerant capability and enhance machine power density using harmonic current injection [1][2][3].Among these vast features, fault tolerant capability is recognised as the most salient feature of multiphase systems.Theoretically, multiphase machines with 'n' phases can continue running with up to 'n − 2' disconnected phases [4].Multiphase machine performance with open circuited phases has been addressed in the literature [4,5] to a large extent, and control strategies to ensure disturbance-free operation with the same pre-fault magneto-motive force have been demonstrated.
Field oriented control is usually employed to control multiphase IMs.Several recent papers [6][7][8][9][10][11] introduce control schemes to ensure motor operation when one or more phases are open-circuited while satisfying specific optimisation criteria [6].Generally, minimum torque ripples, equal phase currents and minimum copper losses are among the most common targeted optimisation functions [6].Most of the proposed controllers are mainly based on rotor field oriented control (FOC) which requires accurate machine parameters to ensure proper orientation.
Another widely used control technique for IMs is the constant volt/hertz (V/f) method [12,13].Despite the fact that vector control gives better dynamic response; yet, scalar control is simpler and still widely used in industrial fields.In the literature, the control of multiphase IM using V/f is addressed for the healthy case [12,13]; however under the open phase case, little work has been conducted [14].In earlier work [14], a simple open-loop V/f controller is provided for open-circuit faults using proportional resonant (PR) controllers to ensure equal line currents and hence minimum torque ripples.Under open phase, the sequence components of stator currents as calculated by the control system may contain a significant negative sequence, that is, at angular frequency −ω s .Additionally, optimal current control requires unbalanced current components in the non-fundamental sequence planes which yield negative sequence components of frequency −ω s in the reference currents.Hence, employing conventional synchronous reference frame proportional-integral (PI) regulators yield non-zero tracking errors.This problem has been tackled in [6], but with adding current regulators in negative sequence (dq) synchronous reference frame which sophisticates the controller structure.On the other hand, PR controllers [15] are advantageous over conventional PI controllers in the synchronous reference frame with their capability to track unbalanced reference currents without sophisticated transformations [14].
Sensorless operation of a three-phase IM is well recognised in the literature [16,17]; however, little work has been conducted for multiphase IMs [18][19][20][21][22] and assuming unbalanced operation.In this paper, two sensorless closed-loop speed controllers based on V/f and FOC to control a five-phase IM under phase open conditions are presented and compared.The earlier work for open-loop V/f control of a five-phase IM presented in [14] is extended to obtain sensorless closed-loop operation.Moreover, a controller based on rotor FOC is presented where PR controllers are employed for each sequence plane to generate the stator voltage components corresponding to these planes.Although this proposed controller is functionally equivalent to that presented in [6], which used synchronous PI controllers, the total number of controllers is now reduced from six PI controllers to three PR controllers.Moreover, the required forward and backward transformations are dispensed.Sensorless operation is provided by estimating the machine speed using an model reference adaptive system (MRAS) observer [18] using the fundamental sequence components of the rotor flux (RF-MRAS).The proposed controllers are experimentally verified using a 1 hp prototype five-phase IM.Both steady-state and dynamic performances are presented.

Optimal current control
In multiphase systems, disturbance-free operation can be provided with some phases open by controlling the currents of the remaining healthy phases to ensure certain optimisation criterion [6].For a five-phase machine with one phase open, the remaining healthy phases are usually controlled to ensure equal stator phase currents, minimum machine torque ripples and maximum torque production by nullifying the fundamental negative sequence [23].
For a five-phase system, the sequence currents can be obtained from the phase values using the transformation shown in (1) [6] where i sab = i sa1 i sb1 i sa3 i sb3 i s0 The transformation matrix, [T ], is defined by ( 2) where γ = 2π/5.For a star-connected five-phase machine with line 'a' assumed open, the remaining healthy phase currents that maintain same rated fundamental magneto-motive force (MMF) and nullify the fundamental negative sequence component are given in per-unit as [5] Substituting in (1) by these optimum current in (3), the corresponding sequence current components in per-unit are as in (4) This results in the identities shown in (5) Controlling the αβ current components of the third sequence plane to fulfil the conditions given by (5) yields equal stator phase currents in the remaining healthy phases, maximum output torque and minimum torque ripples.Nevertheless, a corresponding increase in the machine copper loss by ∼53% is expected.Practically, the machine should be deloaded to avoid excessive copper loss [5].
As a first glance, four current controllers are needed to control the four current components, which is the case for the available literature.However, for star connection with phase 'a' open and based on the inverse transformation given by (1), one can write Hence, the first identity in ( 5) is always achieved, which reduces the system degrees of freedom and, hence, the required controllers to only three.Therefore, the second identity in ( 5) can be properly achieved by applying proper voltage component v sβ3 , whereas the other voltage component v sα3 is redundant (can be simply set to zero).Reducing the total number of current controllers to three represents one of the main contributions of this paper when compared with available controllers in the literature.

Proposed controllers
In this section, two speed controllers are proposed based on V/f control and FOC to control the speed of a five-phase IM under onephase open with MRAS speed estimation.PR controllers are employed to control the current components of the third sequence plane in accordance with the current components of the fundamental sequence plane to fulfil the relations given by (5).

V/f control
The complete system block diagram for the proposed V/f controller is shown in Fig. 1.In this controller, the fundamental stator voltage is decided as in conventional V/f control.The speed error is used to calculate the required slip frequency through a PI controller which is then added to the estimated rotor speed to determine the required synchronous speed.The measured currents are decomposed to their sequence components.The fundamental sequence is used to calculate the optimum reference of third sequence current component i * sb3 , using (5), that ensures equal stator currents under phase open.Consequently, the third sequence stator voltage component v sβ3 that ensures equal remaining phase currents is obtained using a PR controller from the error in i * sb3 , whereas v sα3 is set to zero since i * sa3 is already achieved as shown in (6).Both fundamental voltage and current components are used to estimate the machine speed using a conventional MRAS observer.

Field oriented control
The complete system block diagram for the proposed FOC is shown in Fig. 2. In this controller, the fundamental flux and torqueproducing current components i * ds1 and i * qs1 , respectively, are obtained as in conventional indirect rotor field orientation [3], then they are transformed to their stator frame current components i * as1 and i * bs1 using the machine estimated speed and the calculated machine slip.Based on (5), the corresponding third sequence β current component i * bs3 that ensures equal stator currents under phase open is determined, whereas i * as3 is naturally achieved as previously shown in (6).These reference current components are compared with their actual sequence current components and three PR controllers, two for the first sequence plane and one for the third sequence plane, are then used to obtain the corresponding first and third sequence voltage components.Both fundamental voltage and current components are used to estimate the machine speed using a conventional MRAS observer as will be shown in the next section.

PR controller
When compared with PI controllers in synchronous reference frame (dq control), the PR controller can effectively achieve zero tracking error for unbalanced reference currents without sophisticated transformations, using reduced calculations and without the need for the transformation angle [6].To achieve zero tracking error at a variable fundamental frequency, its resonant poles in (7) must be adaptively tuned to the fundamental frequency of the tracked signal [15].Figs. 1 and 2 show adaptive PR controller implemented (in V/f and FOC, respectively) to track the stator reference currents as For digital implementation on the digital signal processor (DSP), the PR controllers given in ( 7) are discretised at 5 kHz using a zero-order hold method [14].
The controller gains K p , K i1 and K i3 , shown in Table 1, can be found as in [15].The current control loop is required to be much faster than the speed control loop.The bandwidth of the current control loop (third sequence frame) is in the order of several hundreds of rad/s and it is set according to the machine time constant (L/r), whereas the speed loop bandwidth is in the order of tens of rad/s (depending on the inertia/friction time constant of the drive system).
4 Speed estimation using MRAS observer MRAS schemes have been extensively employed for speed estimation in various control applications.Depending on the output states that form the error function, various MRAS observers have been introduced in the literature, where the most common are those based on RF-MRAS [24] and back EMF (BEMF-MRAS) [25].
The design of an MRAS estimator for speed estimation of IM drives requires the definition of two models having similar outputs.One model, termed the reference model, should be independent of the rotor speed, whereas the other, the adaptive model, is speed dependent on it.An adaptive mechanism, based on a PI controller, is employed to generate the value of the estimated speed in such a way as to minimise the error between the reference and estimated outputs [26].A block diagram showing the MRAS speed estimator is given in Fig. 3. Since the fundamental sequence is the torque-producing sequence plane, this sequence plane can be effectively used to estimate the machine speed even under onephase open.In the RF-MRAS scheme, the reference model represents the stator equation (voltage model) of the fundamental sequence plane and can be given by ( 8) and ( 9) [24,26] where s = 1 − L 2 m1 /L s1 L r1 is the leakage factor.The adaptive model represents the rotor equation (current model) and can be given by ( 10) and ( 11) The estimated speed is then given by ( 12) where the MRAS PI control parameters K po and K io are equal to (500, 10 000), respectively.

Experimental setup
A five-phase stator was built to fit an existing squirrel cage rotor of a three-phase machine to obtain the same power rating.The stator comprises a 4-pole five-phase single layer winding occupying 40 slots.The machine was fed from a custom made five-phase inverter operating at a 5 kHz switching frequency and fed from a 350 V DC-link.An eZdsp TM DSP kit hosting a Texas Instrument floating point DSP (F28335) is used to provide the pulse width modulation (PWM) signals.The DSP is sending real-time measurement and control signals (voltages, currents and speed) on controller area network (CAN)-bus.The host personal computer is connected to the CAN-bus via CANcaseXL in order to display DSP signals and log them for post-analysis.Four Hall-effect transducers are used to measure the motor currents.The IM is coupled to a PM DC-generator of the same power rating which acts as a mechanical load.The IM output power can be estimated from the generator output after adding the estimated mechanical and generator copper losses.Fig. 4 shows the actual laboratory setup.The detailed ratings of the prototype machine are given in Table 2.The machine parameters for the fundamental sequence plane are given in Table 3 and estimated using conventional no-load, locked rotor and DC tests.Under V/f control, the V/f constant is calculated based on rated peak voltage and frequency.With FOC, the rated direct current component is selected based on the machine magnetising current, which is calculated by dividing the V/f constant by the fundamental magnetising inductance, L m1 .

Experimental results
In this section, the prototype machine is tested using different controllers and under healthy as well as open phase cases.First, the machine characteristic curves are plotted with the machine reference speed set to the rated synchronous speed, 1500 rpm.Next, the machine dynamic response and current waveforms are shown for both controllers.
To estimate the losses efficiency and torque, the following procedure is carried out.First, the system is run by powering the DC machine (in motoring mode) up to the rated speed then measuring its current to estimate the copper losses, hence mechanical losses can be found as the difference between the DC input power and the copper losses of the DC machine (running as a motor).Then, the five-phase machine is controlled in closed loop to run at the rated speed and the load connected to the DC-generator is varied.Generator copper losses are estimated from the current and armature   resistance.The five-phase machine input power and the generator output power are measured.The five-phase machine output power is found from subtracting the generator losses and mechanical losses from the input power to the five-phase machine.Torque is found from the computed output power five-phase machine and the shaft speed.

Steady-state characteristic curves
In this section, the machine steady-state characteristic curves under healthy as well as open-phase cases are compared for both controllers with machine reference speed set to 1500 rpm.Figs.5a and b show the root-mean-square (RMS) stator phase current against torque characteristic under V/f control and FOC, respectively, whereas the machine efficiencies against output power are depicted in Figs.5c and d.Figs.5e and f show the relation between the output power and the machine total loss for V/f control and FOC, respectively.The latter characteristic curves can be used to find the maximum output load under open-phase condition to avoid excessive machine losses.It is clear that for the same load torque, the phase current magnitude for the open-phase case is increased by an approximate factor of 1.38 compared with healthy case, as depicted by (4).As given by Figs.5e and f, the rated machine losses are ∼250 W for both cases which correspond to an output power of 750 W, 1 hp.Hence, for the same total losses, the maximum machine load under open phase is limited to 592 W, 0.79 pu.
For sake of comparison between the two controllers, both healthy and open-phase cases are plotted in Figs. 6 and 7, respectively.It is shown that for the healthy case the FOC offers slightly higher efficiency than V/f control especially for low mechanical loads.Under open phase, FOC also offers lower stator current, lower copper loss and, hence, higher efficiency.

Dynamic response
In this section, the machine dynamic response is compared for both controllers with MRAS speed estimation and with one-phase open.It is assumed that a step reference speed of 750 rpm is applied at 2 s with the machine mechanically unloaded and then it is increased to 1500 rpm at 7 s.Then the machine is loaded with its full-load torque of 4.7 Nm.The actual and estimated speeds are shown in Fig. 8.It is clear that FOC results in better dynamic response.It is also shown that both controllers yield a steady-state speed error which increases with the reference speed and reduces with mechanical loading.For FOC the steady-state speed error is lower.The corresponding αβ current components for fundamental and third sequence planes are also shown in Fig. 8.The relation between them is shown to follow (5), with improved dynamic response using FOC.
Fig. 9 shows the no-load and full-load currents with the reference speed set to 1500 rpm.It is evident that the proposed controller ensures equal remaining healthy phase currents under different loading cases.The wave distortion is mainly because of the effect of saturation and machine non-linearities and asymmetries.Unlike FOC, the V/f controller experiences some deviation in current magnitude for the remaining healthy phases as well as higher wave distortion which are mainly because of machine asymmetry and saturation effects [27].To investigate this point, the αβ current and voltage components for each period are shown in Figs. 10 and 11 for V/f control and FOC, respectively.The FOC shows more sinusoidal current components as both planes are completely controlled using three PR controllers.However for V/f control, the reference value of the third sequence plane is decided based on the measured fundamental αβ current components.In V/f control, the fundamental αβ voltage components, v sαβ1 , are perfectly balanced as these components are derived from a sinusoidal generator, whereas the corresponding αβ current components, i sαβ1 , experience some degree of unbalance because the prototype machine has notable unbalance and winding asymmetry.On the other hand in FOC, the fundamental voltage components, v sαβ1 , are unbalanced as they are derived from two PR controllers to ensure balanced i sαβ1 irrespective of  winding asymmetry.It can be shown also that the voltage and current components of the third sequence plane with V/f control experience notable distortion because of the induced third harmonic caused by magnetic saturation [27].On the other hand, FOC corresponds to a more sinusoidal waveform in both sequence planes.
The main advantage of V/f control over FOC control is that it does not require accurate parameter determination.On the other hand, FOC is highly affected by accurate machine parameter determination, which is still challenging for multiphase machines [28].

Conclusions
In this paper, two simple sensorless fault tolerant control schemes based on conventional V/f control and FOC control of a five-phase IM are presented.In the literature, FOC is usually employed with relatively sophisticated controllers that require several transformations to maintain certain optimisation objectives.On the contrary, the proposed control schemes allow for disturbance-free operation in cases of open-circuit faults using only one and three PR controllers for the V/f control and FOC.The PR controllers are used to control the third sequence current component in accordance with the fundamental sequence current to maintain equal current magnitude in the remaining healthy phases, which in turn maximises torque production, minimises torque ripples and improves overall efficiency.Sensorless operation is provided by estimating the machine speed using a RF-based MRAS speed observer based on fundamental sequence voltage and current components.The comparison between V/f control and FOC based on experimental investigation reflects the following conclusions: † Both controllers can effectively maintain equal remaining phase currents under one-phase open.Deviations mainly occur because of winding asymmetry and saturation effects.† Although FOC provides better dynamics as well as steady-state performance, V/f control requires less current controllers and has a simpler overall controller structure.† The main disadvantage of FOC is that the performance of FOC is highly affected by accurate machine parameter determination, which is still challenging for multiphase machines.On the other hand, V/f control does not require accurate machine parameters.† Sensorless operation of the multiphase machine under fault can be simply provided using a conventional technique used for the three-phase case by using the fundamental voltage and current components.

Fig. 1 Fig. 2
Fig. 1 Block diagram of the proposed V/f sensorless speed controller

Fig. 5 Fig. 6
Fig. 5 Machine characteristics under healthy and open-phase cases a, b RMS current against torque characteristic c, d Total losses against output power characteristic e, f Efficiency against output power characteristic

Fig. 7 Fig. 8
Fig. 7 Machine characteristics with one-phase open a RMS current against torque characteristic b Efficiency against output power characteristic

Fig. 9
Fig. 9 Machine phase currents at different cases a, b V/f sensorless speed control c, d FOC sensorless speed control vertical axis scale (2.0 A/division), horizontal axis scale (5 ms/division) fault case with V/f control at no load a Fault case with V/f control at no load b Fault case with V/f control at full load c Fault case with FOC control at no load d Fault case with FOC control at full load

Fig. 10
Fig. 10 Experimental CAN results for V/f sensorless speed control

Table 1
Current control parameter

Table 3
Prototype five-phase IM parameters This is an open access article published by the IET under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)