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Saturation Change

A. Baskys, Semiconductor Physics Institute, Lithuania

V. Zlosnikas, Semiconductor Physics Institute, Lithuania

IEMDC2009-10905

Model Predictive Speed Control with Optimal Torque Constraints

Handling of Drive Systems with Elastic Transmission

Marcin T. Cychowski, Cork Institute of Technology, Ireland

Krzysztof Szabat, Wroclaw University of Technology, Poland

IEMDC2009-10996

A Maximum Power Point Tracker Using Positive Feedforward Control

Based on the DC Motor Dynamics and PVM Mathematical Model

Jesus Gonzalez-Llorente, University of Puerto Rico, Puerto Rico

Eduardo I. Ortiz-Rivera, University of Puerto Rico, Puerto Rico

Andres Diaz, University of Puerto Rico, Puerto Rico

IEMDC2009-11082

Enhanced Predictive Current Control Method forthe Asymmetrical Dual–

Three Phase Induction Machine

R. Gregor, Camino de los Descubrimientos s/n, SPAIN

F. Barrero, Camino de los Descubrimientos s/n, SPAIN

S. Toral, Camino de los Descubrimientos s/n, SPAIN

M.R. Arahal, Camino de los Descubrimientos s/n, SPAIN

J. Prieto, Camino de los Descubrimientos s/n, SPAIN

M.J. Durán, University of Málaga, SPAIN

IEMDC2009-11099

A MRAC Parameter Identification Algorithm for Three-Phase Induction

Motors

R. Z. Azzolin, Power Electronic and Control Research Group – GEPOC, Brazil

H. A. Gründling, Federal University of Santa Maria – UFSM, Brazil

IEMDC2009-11140

PMSM Drives Sensorless Position Control with Signal Injection and

Neural Filtering

Angelo Accetta, Universit`a degli studi di Palermo, Italia

Maurizio Cirrincione, Universit`e de Technologie de Belfort–Montb´eliard

(UTBM), France

Marcello Pucci, I.S.S.I.A.–C.N.R., Italy

Gianpaolo Vitale, I.S.S.I.A.–C.N.R., Italy

IEMDC2009-10873

Design of Synchronous Reluctance Motor by Equivalent Magnetic Circuit

Method Considering Zig-Zag Magnetic Flux

of 62Table of Contents

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Enhanced Predictive Current Control Method for

the Asymmetrical Dual–three Phase Induction

Machine

R. Gregor1, F. Barrero1, S. Toral1, M.R. Arahal1, J. Prieto1, M.J. Durán2

1 Department of Electronic Engineering

Camino de los Descubrimientos s/n, 41092 Sevilla - Spain

Phone/Fax number: +34 954481304, e-mail: rgregor@esi.us.es, fbarrero@esi.us.es,

toral@esi.us.es, arahal@esi.us.es, jprieto@esi.us.es

2 Department of Electrical Engineering

University of Málaga

Plaza del Ejido S/N, 29013 Málaga - Spain

Phone/Fax number:+34 952 131091, e-mail: mjduran@uma.es

Abstract—The interest in multiphase drives has re–emerged in

the last decade, being the asymmetrical dual three–phase

induction motor drive one of the most popular options. Predictive

control techniques have been recently implemented in these

multiphase drives. Proposed schemes have demonstrated high

performance at the expenses of high computational cost, unknown

switching frequency and the appearance of large undesirable

stator current harmonic components. In this paper, an enhanced

predictive current control technique (ePCC) with fixed switching

frequency is presented for the asymmetrical dual three–phase ac

drive. Fast torque and current response is achieved, and stator

current harmonic suppression is favored. Experimental results

are provided to examine the benefits of the proposed control

method.

Index Terms—Asymmetrical dual three–phase induction

machine, Predictive Control.

I. INTRODUCTION

he analysis and application of multiphase machines goes

back to the late 1920’s [1]. However, the development and

research in this area has been scarce until the beginning of the

21st century. The interest in multiphase drives has re–emerged

in the last decade showing the advantages provided by the

additional phases [2]–[3], being recently proposed for

applications where some specific advantages can be better

exploited (lower torque pulsations, less DC link current

harmonics, higher overall system reliability, better power

distribution per phase). A niche of applications for their

industrial use includes electrical and hybrid vehicles [4]–[5],

ship propulsion [6] or wind power systems [7]. Among these

multiphase drives, asymmetrical dual three–phase ac machines,

with two sets of three–phase stator windings spatially shifted

by 30 electrical degrees and isolated neutral points, are

between the most promising and widely discussed options [8]–

The most frequent control structure for asymmetrical dual

three–phase drives is a cascaded scheme with an inner loop for

current control and an outer loop for flux and speed control.

The well–know field oriented control (FOC) techniques have

been successfully applied to asymmetrical dual three–phase

machines, dealing with problems associated with machine and

converter asymmetries [10]–[11]. Controllers are usually of PI

type while current control is achieved by means of PWM or

SVPWM schemes [12]–[14]. The current control is usually

based on the multidimensional extension of conventional

three–phase current controllers, coping with unbalanced

currents, machine asymmetries and large harmonic currents.

These peculiarities have drawn the attention in developing

effective control strategies at the expense of degrading the

generalization of the control method.

The predictive control (PC) technique, recently proposed for

the asymmetrical dual three–phase ac drive [15]–[16],

overcomes the difficulties in the generalization of the current

control method. Fast current and torque responses are also

guaranteed. The predictive control technique determines and

applies during a sampling period the optimal set of VSI

switching states based on a model of the real system, which it

is used to predict its future evolution and therefore it is called

“predictive model”. The prediction is carried out for each

possible VSI switching vector to determine which one

minimizes a defined cost function. An important drawback of

the application of predictive control in the multiphase drives is

the variable switching frequency, depending on the load

parameters characteristics. Power converters that operate at a

fixed switching frequency have desirable electrical noise

behavior, allowing the use of simple filters and blanking

techniques to suppress this electrical noise. Enhanced versions

of predictive control techniques have been presented for the

asymmetrical dual three–phase ac drive [17]–[18]. The

proposed ideas use the linear combination of active and null

vectors during a computation period, resulting in some kind of

modulated predictive current control method. This work goes

beyond previous work, taking into account a new control

scheme that considers the use of predictive and modulation

schemes for the current control of the asymmetrical dual three–

phase ac machine. The performance of the proposed control

technique ePCC is studied for quasi–balanced drive operation.

Lower ripple in the stator current response is achieved, while

fast dynamic behaviour is maintained. Comparison tests

against conventional PI-PWM techniques and previous PC

techniques are presented.

The paper is organized as follows. First, the asymmetrical

dual three–phase induction motor drive is described in Section

II. Section III details different predictive current control

techniques for the asymmetrical dual three–phase induction

machine, and presents the general principles of the proposed

predictive current control method. Then, section IV compares

the results obtained using ePCC with a standard PWM strategy

and other predictive current control methods. Finally, the

conclusions are given in the last section.

II. THE ASYMMETRICAL DUAL THREE–PHASE AC DRIVE

The system under study consists of an asymmetrical dual

three–phase AC machine supplied by a six–phase VSI and a

DC link, considering a normal squirrel cage induction motor

with isolated neutral points. A detailed scheme of the drive is

provided in Fig. 1.

This six–phase machine is a continuous system which can be

described by a set of differential equations. Machine modelling

follows two different paths: the double d–q winding approach

and the vector space decomposition (VSD) approach.

According to the first approach [19], the machine can be

represented with two pairs of d–q–o windings corresponding to

the two three–phase stator windings. From this point of view,

the analytical model of the asymmetrical dual three–phase

induction machines is an extension of the conventional three–

phase induction machine model. The d–q–o reference frame

transformation decomposes the original three–dimensional

vector space into the direct sum of a d–q subspace and a zero

sequence subspace which is orthogonal to d–q, decoupling the

components that produce rotating m.m.f. and the components

of zero sequence. According to the second approach [12],

VSD, the machine can be represented with three stator–rotor

pairs of windings in orthogonal subspaces. One stator–rotor

pair engages with electromechanical energy conversion (α–β

subspace in what follows), while the others do not. The first

stator–rotor pair represents the fundamental supply component

plus supply harmonics of the order 12n±1 (n=1,2,3,…). The

second stator–rotor pair represents supply harmonics of the

Fig. 1. A general scheme of an asymmetrical dual three–phase AC drive.

order 6n±1 (x–y subspace with n=1,3,5,…), while the zero

sequence harmonic components can exist only if there is a

single neutral point and they then belong to the third pair.

Although it can be modelled using the double d–q approach

as an extension of the d–q approach of three–phase machines,

the most popular option is the use of the vector space

decomposition (VSD) approach because it explains the

physical phenomena in the machine better. According to the

VSD approach, the machine can be modelled, using an

amplitude invariant criterion in the transformation, as follows:

⋅⋅

⋅−⋅−

⋅⋅

βriαriβsiαsi

=βsuαs

⋅⋅

where p is the time derivative operator, ωr the rotor angular

speed, and Rs, Ls=Lls+Lm, Rr, Lr=Llr+Lm and Lm the electrical

parameters of the machine. From the motor model, the

following conclusions should be emphasized here:

1) The electromechanical energy conversion variables are

mapped in the (α,β) subspace, meanwhile the non-

electromechanical energy conversion variables can be

found in the other subspaces.

2) The current components in the (x,y) subspace do not

contribute to the airgap flux, and are limited only by the

stator resistance and stator leakage inductance, which is

usually small. These currents will only produce losses and

consequently should be controlled to be as small as

possible.

It can be noted that α–β equations are similar to those of a

three–phase machine so the control of the asymmetrical dual

three–phase machine can be greatly simplified. The x–y

equations do not link the rotor side and consequently do not

influence the machine dynamics but are just an important

source of Joule losses in the machine.

The VSI has a discrete nature and has a total number of

26=64 different switching states defined by six switching

functions corresponding to the six inverter legs [Sa, Sb, Sc, Sd,

Se, Sf], where Si∈0,1. The different switching states and the

voltage of the DC link (VDC) define the phase voltages which

can in turn be mapped to the α–β–x–y space according to the

VSD approach. Consequently, the 64 different on/off

combinations of the six VSI legs lead to 64 space vectors in the

α–β and x–y subspaces. Figure 2 shows the active vectors in

the α–β and x–y subspaces, where each vector switching state

is identified using the switching function by two octal numbers

corresponding to the binary numbers [SaSbSc] and [SdSeSf],

respectively. For the sake of conciseness, the 64 VSI switching

vectors will be usually referred as voltage vectors, or just

vectors, in what follows. It must be noted that the 64

possibilities imply only 49 different vectors in the α–β–x–y

space. Nevertheless, redundant vectors should be considered as

different vectors because they have a different impact on the

switching frequency even though they generate identical torque

and losses in the six–phase machine.

III. PC TECHNIQUE IN THE ASYMMETRICAL DUAL THREE–PHASE

AC DRIVE

Current control in VSI drives is one of the most important

and classical subjects in power electronics, and has been

extensively studied during the last decades. Nonlinear methods

like hysteresis control and, more recently, linear methods like

proportional–integral controllers using PWM techniques have

been frequently used. With the development of modern

microprocessors, increasing attention has been paid to other

control techniques in power electronics and drives, like the

predictive current control method [20]. Figure 3 shows a block

diagram of the conventional PC technique, also called Model

Based Predictive Control or MBPC, applied to the

asymmetrical dual three–phase AC drive, where isolated

neutral points are assumed. A detailed block diagram of the

control technique is provided, including a pseudo code of the

control algorithm.

The MBPC technique selects control actions solving an

optimization problem at each sampling period. A model of the

real system is used to predict its output. This prediction is

carried out for each possible output, or switching vector, of the

6–phase inverter to determine which one minimizes a defined

cost function, and therefore the model of the real system, also

Fig. 2. Voltage vectors applied in the α–β and x–y subspaces using a 6–phase

VSI. Notice that the same VSI switching state produces different voltage

vector in α–β and x–y subspaces.

called predictive model, must be used considering all possible

voltage vectors in the 6–phase inverter. Different cost

functions (named J) can be used, to express different control

criteria. The absolute current error for the next sampling instant

is normally used for computational simplicity. In this case, the

cost function is defined as ssîiJ −=

*, where

si is the stator

reference current and sî is the predicted stator current which is

computationally obtained using the predictive model.

However, other cost functions can be established [15]–[16],

including square or integral current errors, or flux and torque

errors. The cost function can also include additional terms to

minimize the switching stress or the DC link voltage balancing.

Different aspects must be studied in detail to implement the

MBPC algorithm in the asymmetrical dual three–phase AC

drive. These aspects are related to the considered switching

voltage vectors and the predictive model of the electrical

machine.

Fig. 3. MBPC method. The sequencer issues voltage vectors one at a time,

while the minimizer chooses the one that provides the lower value of J.

The number of voltage vectors to evaluate the predictive

model can be further reduced if sinusoidal output voltage is

considered. This assumption is commonly used if quasi–

balanced operation of the drive is assumed. In this way, the

optimizer can be implemented using only 13 possible stator

voltage vectors (12 active corresponding to the largest vectors

in the α–β subspace and the smallest ones in the x–y subspace

plus a zero vector). The MBPC with sinusoidal output voltage

considering 13 switching vectors requires less computing time

and favors the real–time implementation. Notice that x–y stator

current components should be taken into account in the cost

function to obtain a good dynamic performance, if quasi–

balanced operation of the drive is not assumed.

The machine equations (1)–(2) can be written in state space

taking stator currents in α–β–x–y subspaces as state variables.

The machine model must be discretised in order to be of use as

a predictive model. A forward Euler method with a sampling

time Tm can be used, producing equations in the needed digital

control form, with predicted variables depending just on past

values and not on present values of variables:

βsiαs

)k(X =

( ) ( ) )k(C)k(UB)k(X)k(A=1+kX ++⋅ (4)

where Si is the switching state of the i–leg of the VSI, and the

details can be found in [21]; matrix A depends on the electrical

parameters of the machine and on the sampling time, matrix B

also involves the VSI model relating switching states with

voltages, and matrix C arises from unmeasured variables such

as rotor current:

λ⋅−

λ⋅−λ⋅⋅ω−

λ⋅⋅ωλ⋅−

00RL)k(

00L)k(R

TI)k(A

−−

⋅⋅⋅=

211000

121000

112000

000211

000121

000112

VT))k(U(B

[ ]))1k(U(B)1k(X)1k(A)1k(X)k(X)k(C −+−−−−−= (7)

being I the 4×4 identity matrix, Bt the transpose matrix of B,

ci=cos(i π /6), si=sin(i π /6), )LLL/(L 2

mrsr2 −⋅=λ ,

)LLL/(L 2

mrsm3 −⋅=λ , and ls5 L/1=λ .

Figure 4 shows the evolution in the α–β subspace of the state

vector for each possible switching state of the inverter. Point

i(k) represents the α–β projection of the measured state, while

point i*(k+1) is the α–β projection of the desired state. 49

directions of the state vector evolution could be obtained,

corresponding to the 49 different voltage vectors. However,

only 13 directions of the state vector evolutions have been

considered, corresponding to the 12 outer voltage vectors in the

α–β subspace plus the null voltage vector. It has to be noted

that the reference is not achievable using the MBPC method

because only one among the possible switching states is

applied during the whole sampling period. In the depicted

example, the state vector evolves in the optimal control

direction for each computation iteration; the î4-4 point.

A. PC methods with achievable current reference

Improved versions of the predictive current controller have

been proposed for the asymmetrical dual three–phase induction

motor drive [17], [18]. The ideas use the linear combination of

active vectors plus a null one during a computation period,

resulting in a modulated predictive current control method.

The method proposed in [17], called OSPC method,

establishes a more appropriate control technique,

corresponding to the application of the optimal voltage vector

during a τ (0<τ<Tm) time. OSPC is similar to MBPC but it

allows combining two states of the VSI within one sample

period. The principle of operation is as follows. For a desired

stator current vector *

si , OSPC proceeds as a MBPC using the

cost function to select a VSI configuration Sioptimum(k+1). Then

a sub modulation problem is solved, computing the time τ that

the active vector is to be applied, being the rest of the sample

time reserved for the null vector. The computation of the sub

modulation period τ is posed as an optimization problem aimed

at minimizing the predicted error. A linearity assumption is

made based on the time scales involved. In this way the

predicted error is obtained as a linear combination of the errors

corresponding to the selected and null voltage, allowing an

analytical expression of τ to be derived.

î0-0(k+1)

î4-5(k+1)

î5-5(k+1)

î5-1(k+1)

î1-1(k+1)

î1-3(k+1)

î3-3(k+1) î3-2(k+1)

î2-2(k+1)

î2-6(k+1)

î6-6(k+1)

î6-4(k+1)

î4-4→Sioptimum

i*(k+1)

iβ [A] Fig. 4. Snapshot of the state vector evolution in the α–β subspace,

depending on the applied switching voltage vector.

Fig. 5. OSPC method in the asymmetrical dual three–phase AC drive.

The time of application of the active voltage vector (τ) is

obtained under the hypothesis that for small periods of time

linearity holds with respect to the application time. In this way,

the state after combining an active vector (Xu) and a null one

(X0) would be:

)1k(X)T()1k(X)1k(XT 0mum +⋅τ−++⋅τ=+⋅ (8)

Similarly, the predicted error would be:

)1k(e)T()1k(e)1k(eT 0mum +⋅τ−++⋅τ=+⋅ (9)

This latter expression allows obtaining the optimal value of τ

setting the derivative of the expected error to zero:

τ (10)

which leads to the following equation:

eee⋅

⋅−=τ (11)

The control method can be summarized with the following

pseudo code:

- Compute the optimal control action (Sioptimum(k+1))

according to cost function J.

- Compute the application time according to (11).

- For the next sampling period apply the selected vector u

during time τ and the null vector during time (Tm-τ).

A consideration must be taken into account. Since the

inverter needs some time to commute between states, the

applications periods must comply with τ>τmin, and (Tm-τ)<τmin,

being τmin the time needed by the inverter to commute safely.

The method proposed in [18], called Predictive–SVPWM

current control technique, combines various states of the VSI

within one sample period. The main idea of this method is to

use the predictive control to substitute the standard PI

controllers but to maintain a conventional modulation

technique. Following that procedure, it is possible to achieve

fixed switching frequency. The principle of operation is as

follows. For a desired stator current vector is*, the proposed

control scheme proceeds as in a MBPC method, using a

predefined cost function to select the VSI switching states. The

minimizer chooses the switching vector Sioptimum that provides

the lower value of J. The selected vector provides the optimum

solution [uαopt, uβ

opt] in terms of currents error in the α–β

subspace, but the x–y subspace is not considered in the cost

function. Consequently, good dynamic performance is

expected using conventional predictive control but at the

expense of lower efficiency due to high x–y Joule losses that

do not generate any torque. Instead of applying the chosen

voltage vector to the multiphase machine during the whole

switching period, which is the procedure in conventional

predictive control schemes, the proposed method uses [uαopt,

uβopt, 0, 0, 0, 0] as the voltage references in the α–β–x–y–z1–z2

subspaces to solve a sub modulation problem. Since x–y

components are undesirable, the inputs for the sub modulation

problem are only the α–β component of the phase voltage, and

the x–y inputs are set to zero. The selected VSI switching

modulation indexes are then obtained from the mathematical

expression of the phase voltages defined in the VSD theory, as

shown in equation (12), where the factor of 1/3 corresponds to

the amplitude invariant criterion adopted in the transformation

matrix. The modulation indexes (τi) associated to VSI phases

have also been included in equation (12), being τi scaled

between 0 and 1.

⋅⋅+⋅⋅=

1 1 1 0 0 0

0 0 0 1 1 1

Once the references for the sub modulation problem are set,

the calculation of the duty cycles for each VSI leg can be

performed in a standard manner, and the modulation indexes

are obtained using equation (12) as follows:

⋅⋅⋅+⋅

f,e,d,c,b,ax;x =τ

⋅⋅⋅+⋅

optimum

Fig. 6. Predictive current control method in the asymmetrical dual three–phase

induction machine proposed in [18].

A detailed block diagram of the proposed technique is

provided in Fig. 6. The proposed method is a hybrid solution

between MBPC and standard field oriented control,

maintaining interesting features of both schemes. Specifically,

the use of predictive instead of PI controllers allows

minimizing the current error considering future values, avoids

the tuning of PI controllers and provides enhanced flexibility

through the definition of the cost function (which can minimize

not only the current error but also the number of

commutations, the switching losses or the DC link unbalance

in multilevel converters [21], [22]). On the other hand,

maintaining the modulation process helps to obtain fixed

switching frequency, adequate harmonic spectrum and lower

x–y components.

B. Enhanced Predictive Current Control Method (ePCC)

The principle of operation of ePCC is as follows: for a

desired stator current vector is*, the proposed control scheme

proceeds as in an OSPC method, using a predefined cost

function to select the VSI switching states. The minimizer

chooses the switching vector Sioptimum that provides the lower

value of J. The selected vector provides the optimum solution

[uαopt, uβ

opt] in terms of currents error in the α–β subspace.

Then, the sub modulation problem of the OSPC method is

solved, computing the on time of the active voltage vector (τ).

Afterwards, a second sub modulation problem corresponding

to the predictive control method proposed in [18] is also

solved, using [τ·uαopt, τ·uβ

opt, 0, 0, 0, 0] as the voltage

references in the α–β–x–y–z1–z2 subspaces. The selected VSI

switching modulation indexes τi are then obtained from

equation (13). A detailed block diagram of the proposed

technique is provided in Fig. 7.

f,e,d,c,b,ax;x =τ

⋅⋅⋅+⋅

optimum

Fig. 7. ePCC method in the asymmetrical dual three–phase induction machine.

IV. OBTAINED RESULTS

An experimental test rig has been used for obtaining

experimental results. The test–rig is based on a conventional 36

slots, 2 pairs of poles, 10kW 3–phase induction machine whose

stator has been rewound to construct a 36 slots, 3 pairs of

poles, dual 3–phase induction machine. Two sets of stator 3–

phase windings spatially shifted by 30 electrical degrees have

been included. A diagram and photos of the complete system

are shown in Figs. 8 and 9. Table I shows the parameters of the

machine used to obtain the experimental results.

POWER ELECTRONIC CONVERTERDUAL THREE-PHASE

INDUCTION MOTOR

Hall effect

current sensorDrivers

Diagnostics

Analog

InterfaceDSP

TMS320R2812

RS232 Serial Port

CONTROL BOARDS

Dc_link A B

Encoder

switch

Fig. 8. Scheme of the experimental set–up.

Fig. 9. Photographs of the experimental setup including, 1) the power

electronics, 2) the windings, 3) the stator connection grid, and 4) the machine

test rig.

TABLE I

PARAMETERS OF THE ASYMMETRICAL DUAL 3–PHASE INDUCTION MACHINE

Parameter Value

Stator resistance Rs (Ω) 1.63

Rotor resistance Rr (Ω) 1.08

Stator inductance Ls (H) 0.2792

Rotor inductance Lr (H) 0.2886

Mutual inductance Lm (H) 0.2602

Inertia J (kg. m2) 0.109

Pairs of poles P 3

Friction coefficient B (kg. m2/s) –

Nominal frequency ωe (Hz) 50

0 0.05 0.1 0.15-4

iα, i*α

i x, i y

0.01 0.02 0.031.5

0 0.05 0.1 0.15-4

iα, i*α

0.01 0.02 0.03

0 0.05 0.1 0.15-4

i x, i y

0 0.05 0.1 0.15-4

0.01 0.02 0.03

iα, i*α

0 0.05 0.1 0.15-4

0.01 0.02 0.032

0 0.05 0.1 0.15-4

iα, i*α

0 0.05 0.1 0.15-4

iα, i*α

i x, i y

Fig. 10. Experimental results for 2.5A – 12 Hz reference stator current tracking in α–β and x-y subspaces. Predicted stator current in the α component is shown in

the upper side (zoom graphs, green curves). From left to right: PI-PWM technique, MBPC (proposed in [15] and [16]), the improved predictive control methods

(proposed in [17] and [18]), and ePCC technique.

The control system is based on the TMS320LF2812 Texas

Instruments digital signal processor (DSP) and the MCK2812

system. The control code is written in C, performing closed

loop current control, and using an optimized sampling

frequency of 5kHz, obtained after using specialized floating–

point mathematical libraries and many source–code and

compiler optimizations. A comparative study has been done

between conventional PWM technique, MBPC technique

proposed in [15] and [16], the improved predictive control

methods proposed in [17] and [18], and the proposed predictive

current control technique have been implemented. A series of

tests are performed in order to examine the control properties.

Figures 10 to 12 show the obtained results.

First, a 2.5A reference stator current at 12Hz is established.

Figure 10 depicts the current tracking in the α–β–x–y

subspaces using the proposed ePCC method (right side), PI-

PWM current control technique and other PC techniques.

0 0.1 0.2 0.3 0.4 0.5-8

0 0.1 0.2 0.3 0.4 0.5-4

iα, i*α

0 0.1 0.2 0.3 0.4 0.5 0.6-8

time[s]

0 0.1 0.2 0.3 0.4 0.5 0.6-4

time[s]

0 0.1 0.2 0.3 0.4 0.5 0.6-8

time[s]

0 0.1 0.2 0.3 0.4 0.5 0.6-4

time[s]

iα, i*α

Fig. 11. Experimental results applying simultaneous amplitude (from 2.5A to

3.5A) and frequency (from 12Hz to 36Hz) tracking.

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1-8

0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1-4

0.6 0.7 0.8 0.9 1 1.1-8

time[s]

0.6 0.7 0.8 0.9 1 1.1-4

time[s]

iα, i*α

0.6 0.7 0.8 0.9 1 1.1-8

time[s]

0.6 0.7 0.8 0.9 1 1.1-4

time[s]

iα, i*α

Fig. 12. Experimental results applying simultaneous amplitude (from 3.5A to

2.5A) and frequency (from 36Hz to 12Hz) tracking.

Better stator current tracking is obtained in the α–β subspace

using the proposed method, while the stator current x–y

components highly decrease. Simultaneous amplitude (from

2.5A to 3.5A) and frequency (from 12Hz to 36Hz) tracking is

also investigated for PI-PWM, Predictive SVPW and ePCC.

Figures 11 and 12 show the obtained results. Again, better

stator current tracking is obtained in the α–β subspace, being

near zero the stator currents in the x–y subspace. The obtained

results prove that the proposed predictive control technique is a

good alternative in comparison to previous predictive control

methods.

V. CONCLUSIONS

The area of multiphase induction motor drives has

experienced a substantial growth in recent years. Research has

been conducted worldwide and numerous interesting

developments have been reported in the literature, particularly

in the current control of the VSI–driven asymmetrical dual

three–phase AC machine. PC techniques have been recently

applied to power converter and drives due to their advantages

and the appearance of fast microprocessors. In this paper, a

variant of the predictive control strategy is proposed for the

current control of VSI–driven asymmetrical dual three–phase

AC drives. The proposed ePCC method provides better

performance (lower stator current harmonic components) for

real–time applications than previous predictive current control

techniques. Experimental results confirm the viability of the

proposed current control method.

ACKNOWLEDGMENT

The authors gratefully acknowledge support provided by the

Spanish Ministry of Education and Science within the I+D+I

national project with reference DPI2005/04438.

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Enhanced predictive current control method for the asymmetrical dual\u0026#x2014;three phase...

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