Torque ripple alleviation of a five-phase permanent magnet synchronous motor using predictive torque control method

International Journal of Power Electronics and Drive Systems (IJPEDS)
Vol. 13, No. 4, December 2022, pp. 2207~2215
ISSN: 2088-8694, DOI: 10.11591/ijpeds.v13.i4.pp2207-2215  2207
Journal homepage: http://ijpeds.iaescore.com
Torque ripple alleviation of a five-phase permanent magnet
synchronous motor using predictive torque control method
Saif Talal Bahar, Riyadh G. Omar
Department Electrical Engineering, University of Mustansiriyah, Baghdad, Iraq
Article Info ABSTRACT
Article history:
Received Aug 1, 2022
Revised Sep 12, 2022
Accepted Sep 30, 2022
The benefits of a five-phase permanent magnet synchronous motor (PMSM)
are its compact size, high fault tolerance, low voltage, and high output. The
drives of this kind of machines can be enhanced using model predictive
direct torque control (MP-DTC) technique. The outcomes of this technique
with additional weighting factors are reduces the complexity of calculation,
and reduction in current harmonics, which present in harmonic subspace in
standard model predictive torque control. Decrease the low-order harmonic
constituents of stator currents and alleviation torque ripple can be achieved
by optimizing the objective function. Adding current limitations and
switching frequency-weighting factor improves the cost function. The
suggested technique can provide superior steady-state performance and keep
the quick transient performing as a possible characteristic of the MP-DTC
scheme. Thus, with the advantageous steady state and dynamic performing
obtained concurrently, the most important aspects of the suggested system
are the reduced mathematical burden, and with simplified objective
functions compared to classic MP-DTC structure. The proposed method
reduced the torque ripple from (3.49%) in a traditional method to (0.58%).
Keywords:
Current ripple
Electrical drives
Predictive torque control
Switching frequency
Torque ripple
This is an open access article under the CC BY-SA license.
Corresponding Author:
Saif Talal Bahar
Department Electrical Engineering, University of Mustansiriyah
Falastin St. Baghdad, Iraq
Email: eema2009@uomustansiriyah.edu.iq
1. INTRODUCTION
Although PMSMs have been around for some time, they have recently been a popular choice for
applications that need faster torque to inertia ratios, efficiency, and a great density of power [1]. This is due
to their numerous advantages over other conventional three-phase motors, including enhanced fault - tolerant
or advantageous reliability, which means fewer stator phase currents and thus lesser converter costs by using
semiconductor switches with smaller current ratings [2], and [3]. Because of these advantages, multi-phase
devices have prospective applications in marine electric propulsion, electric vehicles (EVs), more electric
aircrafts, locomotive tractions, and various power applications [4]. Methods such as field-oriented control
(FOC) with pulse-width modulation (PWM) are provided in the literature to improve the steady state and
dynamic performances of the interior permanent magnet synchronous motor (IPMSM) drive [5]. Depending
on how well the outer and inner control loops function, the FOC-PWM system may be either good or bad.
The low bandwidth of this control method is a major negative since it results in poor transient-state control
performance [6]. To enhance the dynamic performance of ac machines that need quick transient reactions, an
alternative direct torque control (DTC) technique has been presented. By comparing the torque and predicted
stator flux linkage values to the directed signals, the standard DTC technique chooses the ideal stator voltage
vectors [7]. However, the hysteresis bandwidth places constraints on the magnitude of torque and flux

 ISSN: 2088-8694
Int J Pow Elec & Dri Syst, Vol. 13, No. 4, December 2022: 2207-2215
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ripples. Recently, it has been shown that model predictive control (MPC) is an effective method for dealing
with the constraints and non - linarites of plants with many inputs and outputs. In order to determine a desired
switching state, the MPC system uses a straightforward and optimum control structure that reduces control
parameter errors. Model predictive direct torque control (MP-DTC) combines this with the standard DTC to
provide superior PMSM drive control. In contrast to traditional DTC and FOC with SVM, the MP-DTC
technique is founded on the idea of optimum control [8]. The optimal switching states may be obtained by
designing an objective function to reduce torque and stator flux control inaccuracy. There has been a lot of
interest in MP-DTC owing to its slight control construction and rapid dynamic response [9]. The torque and
flux of the motor are used as the control variables in this algorithm. If currents are sampled from each
possible voltage vector, then torque and flux may be predicted at a future interval. The computed error values
may be utilized to select which voltage vectors have the greatest impact on the cost function. The cost
function may be used to select the best nominee voltage vector for the following interval. However, the
process of verifying all possible voltage vectors is a computationally intensive one [10]. The cost function's
torque and flux terms should be given a weighting factor to account for the two quantities varying sizes.
Various weighting factors will have an impact on the performance of the control [11], [12]. Flux and torque
errors are included in the cost function and may be used to assess the relative importance of various voltage
vector candidates [13]. For the next interval, the voltage vector with the lowest cost function may be picked
as the best option. As a result, it requires a lot of computer capabilities to go through all possible voltage
vectors [14]. A proper weighting factor should be included to account for the differing lengths of Torque and
Flux in the objective function. The performance of a control system may be affected by the weighting factor
used. In MP-DTC [15]. Even with this, the test of all voltage vectors is a time-consuming and cumbersome
procedure. To make the control group more effective, [16], [17] offered a streamlined technique for doing so.
A low-complexity MP-DTC method was presented in [18], [19].
In this paper, an enhanced MPTC approach with reduced computational overhead is suggested for
five-phase permanent magnet synchronous motor (PMSM) driving systems. Initially, to get rid of harmonic
currents and cut down on computing complexity. Secondly, the suggested MPTC approach may preserve a
quick dynamic reaction while further reducing computing complexity by excluding redundant switching
states from every control period. Finally, simulation compares the suggested MP-DTC's control performance
to that of the conventional MP-DTC schemes.
2. MP-DTC WORKING STEPS AND SYSTEM MODEL
2.1. Five-phase inverter model
Figure 1 depicts the structure of a two-level inverter powering a five-phase PMSM, where the
inverter's DC supply voltage (Vdc). The leg's switching states are represented by the binary states
variables( 𝑆𝑎, 𝑆𝑏, 𝑆𝑐, 𝑆𝑑, 𝑆𝑒). These variables indicate the leg switching states in order: leg a (S1–S2), leg b
(S3–S4), leg c (S5–S6), leg d (S7-S8) and leg e (S9-S10). To avoid a DC link short, the switches on each leg
should operate in tandem. Switches “1” and “0” indicate which switch is on and which is off; “1” indicates
the highest switch is on and “0” indicates the lowest switch is off [20], [21]. The voltage vectors that
correspond to the varying configurations of switching states are specified [22]. There are 32 voltage vectors
in all, containing 30 effective voltage vectors and 2 zero-voltage vectors [23].
Figure 1. Five-phase inverter
Two zero voltage vectors and thirty active voltage vectors make up the 32 switching states of a five-
phase inverter. Both d1-q1 and d3-q3 are 2D subspaces that include all five phases' variables. The 2
subspaces and the corresponding switching vectors are shown in Figure 2. There are 30 voltage vectors in the
active space; they are divided into three groups based on their amplitudes: large (U1-U10), medium (U11-
U20), and small (U21–U30). Figure 2 displays the space plane design divided into 10 equal sections.

Int J Pow Elec & Dri Syst ISSN: 2088-8694 
Torque ripple alleviation of a five-phase permanent magnet synchronous motor using … (Saif Talal Bahar)
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(a) (b)
Figure 2. The 30 effective voltages vector on (a) (𝑑1 − 𝑞1 𝑎𝑥𝑖𝑠), and (b) (𝑑3 − 𝑞3 𝑎𝑥𝑖𝑠)
2.2. Five-phase PMSM model
It is shown in many literatures that the five-phase PMSM has a good performance due to: minimal
core saturation, exclusion of eddy current. The following equations describe the 5- phase surface-mounted
PMSM with sinusoidal distributed windings in a synchronous rotating frame [24], [25]:
𝑉𝑠𝑞1 = 𝑅𝑠 ∗ 𝑖𝑞1 + 𝑤𝑟 ∗ Φ𝑑1 +∗
𝑑
𝑑𝑡
𝛷𝑞1 (1)
𝑉𝑠𝑑1 = 𝑅𝑠 ∗ 𝑖𝑑1 − 𝑤𝑟 ∗ Φ𝑞1 +∗
𝑑
𝑑𝑡
Φ𝑑1 (2)
𝑉𝑠𝑞3 = 𝑅𝑠 ∗ 𝑖𝑞3 +∗
𝑑
𝑑𝑡
Φ𝑞3 (3)
𝑉𝑠𝑑3 = 𝑅𝑠 ∗ 𝑖𝑑3 +∗
𝑑
𝑑𝑡
Φ𝑑3 (4)
Φ𝑠𝑞 = 𝐿𝑞 ∗ 𝑖𝑞 (5)
Φ𝑠𝑑 = 𝐿𝑑 ∗ 𝑖𝑑 + Φ𝑓 (6)
𝑇𝑒 = 2.5 ∗ 𝑝 ∗ 𝑖𝑞 ∗ Φ𝑓 (7)
where, Φ𝑑1 and 𝛷𝑞1 are the flux in 𝑑1 − 𝑞1 axis Φ𝑑3 and Φ𝑞3 are the harmonic flux in 𝑑3 − 𝑞3 axis.
2.3. Predictive current
The motor d-q currents can be discretized according to the core idea of predictive control. The
sample period 𝑇𝑠 is used, at the same time; the (𝑘 + 1)time current is a prediction of that one at the (𝑘)
period. The discrete linear (time-consistent) system is developed in (8) and (9).
𝑖𝑑(𝑘 + 1) = (1 −
𝑅𝑠∗𝑇𝑠
𝐿𝑑
) 𝑖𝑑 + (
𝑤𝑟∗𝐿𝑞∗𝑇𝑠
𝐿𝑑
) 𝑖𝑞 + (
𝑇𝑠
𝐿𝑑
)𝑉𝑠𝑑 (8)
𝑖𝑞(𝑘 + 1) = (1 −
𝑅𝑠∗𝑇𝑠
𝐿𝑞
) 𝑖𝑞 − (
𝑤𝑟∗𝐿𝑑∗𝑇𝑠
𝐿𝑞
) 𝑖𝑑 + (
𝑇𝑠
𝐿𝑑
) 𝑉
𝑠𝑞 −
𝑤𝑟∗Φ𝑓∗𝑇𝑠
𝐿𝑞
(9)
2.4. Predictive torque
To obtain a discrete equation representing the motor torque, another use of the Euler method is
utilized. If the sampling time is 𝑇𝑠, and the motor current is predicted at (k+1) time, while the actual one is
measured at the instant (k).

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Φ𝑠𝑞(𝑘 + 1) = 𝐿𝑞 ∗ 𝑖𝑠𝑞(𝑘 + 1) (10)
Φ𝑠𝑑(𝑘 + 1) = 𝐿𝑑 ∗ 𝑖𝑠𝑑(𝑘 + 1) + Φ𝑓 (11)
Φ𝑠(𝑘 + 1) = √(Φ𝑠𝑑(𝑘 + 1))2 + (Φ𝑠𝑞(𝑘 + 1))2 (12)
𝑇𝑒(𝑘 + 1) =
5
2
(
𝑝
2
)(Φ𝑠𝑑(𝑘 + 1) ∗ 𝑖𝑠𝑞(𝑘 + 1) − Φ𝑠𝑞(𝑘 + 1) ∗ 𝑖𝑠𝑑(𝑘 + 1)) (13)
3. THE CONVENTIONAL MP-DTC METHOD
The model prediction method only affects the system's performance once the prediction model has
been established. Because the (𝑑3 − 𝑞3 ) subspace affects the five-phase motor differently from the three-
phase one, it is required to regulate the flux not only using the (𝑑1 − 𝑞1) subspace, but also using the
(𝑑3 − 𝑞3 ) subspace as well. You may use a prediction step to determine which voltage vector will best
control the target after establishing the objective function. The full procedures are as follows, with a control
block diagram of the traditional MP-DTC system shown in Figure 3. Therefore, in the 5 phase -PMSM
system, the objective function (𝑔) will be selected as:
𝑔 = (
𝑇𝑟𝑒𝑓−𝑇𝑒(𝑘+1)
𝑇𝑟𝑒𝑓
)2
+ λ1 . (
Φ𝑟𝑒𝑓− Φ𝑠1(𝑘+1)
Φ𝑟𝑒𝑓
)2
+ 𝜆2 . (
𝛷𝑟𝑒𝑓3− 𝛷𝑠3(𝑘+1)
𝛷𝑟𝑒𝑓3
)2
(14)
λ1 = Ten
𝛙en
, λ2 = Ten𝟏
𝛙en𝟏
, Where, λ1, and λ2 are the weight coefficients of flux linkage.
The procedure control of traditional MP-DTC: i) Measure stator currents; ii) Measure rotor speed; iii) Tuning
PI controller; iv) Calculate predictive current; v) Calculate predictive torque; vi) Calculate the cost function
value for each prediction; and vii) Select the voltage vector that can reduce objective function.
Figure 3. The traditional five-phase motor MP-DTC system
4. THE PROPOSED MP-DTC METHOD
Figure 4 depicts the control circuit for the proposed MP-DTC method. In a sinusoidally wound five-
phase permanent magnet synchronous motor (PMSM), only the fundamental components in (𝑑1 − 𝑞1)
subspace is implicated in the electromechanical energy conversion process, and the voltages in (𝑑3 − 𝑞3 )
subspace will generate enormous harmonic currents, leading to stator current distortion and the additional
copper losses. It is possible to get rid of the (𝑑3 − 𝑞3 ) subspace harmonics. As a result, the harmonic terms
( 𝛷𝑠3(𝑘 + 1)) are no longer obligatory in the cost function. The full procedures are as follows, with a control
block diagram of the proposed MP-DTC system shown in Figure 4. Two more constraint on the cost-function
are added to these papers as a suggested improvement. The over-current protection term, is represented by
the first one (𝐼𝑚), which is current upper limit. The switching frequency weighting factor (𝑆𝑤) is used to
improve the objective function as a second. The final objective function (𝑔) equation is specified in this
proposed procedure is:
𝑔 = (
𝑇𝑟𝑒𝑓−𝑇𝑒(𝑘+1)
𝑇𝑟𝑒𝑓
)2
+ λ1 . (
Φ𝑟𝑒𝑓− Φ𝑠1(𝑘+1)
Φ𝑟𝑒𝑓
)2
+ (𝑖𝑑𝑟𝑒𝑓 − 𝑖𝑑(𝑘 + 1)) 2
+ 𝐼𝑚 + 𝑆𝑤 (15)
𝑆𝑤 = |𝑆𝑎(𝑘 + 1) − 𝑆𝑎(𝑘)| + |𝑆𝑏(𝑘 + 1) − 𝑆𝑏(𝑘)| + |𝑆𝑐(𝑘 + 1) − 𝑆𝑐(𝑘)| + |𝑆𝑑(𝑘 + 1) −
𝑆𝑑(𝑘)| + |𝑆𝑒(𝑘 + 1) − 𝑆𝑒(𝑘)| (16)

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𝐼𝑚 = {
0, 𝑖𝑠(𝑘 + 1) < 𝑖𝑚𝑎𝑥
∞, 𝑖𝑠(𝑘 + 1) > 𝑖𝑚𝑎𝑥
}
𝑖𝑠(𝑘 + 1) = √𝑖𝑑(𝑘 + 1)2 + 𝑖𝑞(𝑘 + 1)2 where, 𝑖𝑠(𝑘 + 1) maximum anticipated stator current, that is
permitted. The term 𝑇𝑒𝑛 is the rated torque, and 𝜓𝑒𝑛 is the PM flux linkage. 𝑇𝑟𝑒𝑓 Denotes to the torque
reference. 𝑇𝑒(𝑘 + 1)Moreover, Φ𝑠(𝑘 + 1) are the predictive electromagnetic torque, and stator flux
predictive value. While λ1 is a weighting factor, (Φ𝑟𝑒𝑓) represents the reference flux value, 𝑖𝑑𝑟𝑒𝑓 is the
current reference, and 𝑖𝑑(𝑘 + 1) represents the predictive current.
Figure 4. The proposed five-phase motor MP-DTC system
5. RESULTS AND DISCUSSION
The simulation is carried out via MATLAB/Simulink 2021 package. Figure 5 shows the proposed
circuit for MP-DTC, the simulation scheme has six principal components: PI control, switching frequency
weighting factor, Rotation calculation, predictive torque control algorithm, converter model, and the 5-phase
PMSM Model. The system parameters are: rated speed (wm) = 700 rpm, DC-link voltage = 150 V, p = 4,
Ld = 12.4 mH, Lq = 14.3 mH, Rs = 0.5 Ω, load torque = 10 Nm, PM flux = 0.09 wb, frequency = 50 Hz,
𝐽 = 0.02 𝑘𝑔.𝑚2
,Ts = 2μs. The parameters of PI controller proportional gain Kp = 300, integral gain Ki = 2.
A MATLAB function linked with the prediction algorithm to execute it. Depending on the system model, this
component performs the objective functions of the optimization process. The reference flux, rotor speed, and
actual stator currents are all inputs to this sub-system, whereas the gates indications to the converter are the
outputs. Figure 6 shown the reference speed and actual speed.
Figure 5. Block diagram of the proposed system

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Even though it is incorporated in the cost function, harmonic current with the (𝑑3) and (𝑞3) axes is
not adequately reduced when using a conventional MP-DTC. Although the stator current seems to be
generally sinusoidal in Figure 7, there is a degree of distortion. As shown in Figure 7, torque exhibits large
fluctuations as well show in Figure 8. Figures 9 and 10 shows the improvement in MP-DTC stator current
and torque. The (𝑑3 − 𝑞3)subspace may be neglected. In this way, it is evident that the stator current has a
perfect sine wave, but its distortion has been nearly completely reduced, resulting in an overall smooth
waveform. At the same period, the torque ripple has been much decreased as well.
Figure 6. Reference speed and actual speed
Figure 7. Measured 5-phase motor currents without constraint
Figure 8. The actual torque in conventional MP-DTC
Actual speed
Reference speed

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Figure 9. Measured 5-phase motor currents with constraint
Figure 10. The actual torque in the proposed MP-DTC method
Figures 11 and 12, illustrate the increase in the harmonic currents content represented by total
harmonic distortion (THD) when the conventional MP-DTC and decrease THD when the proposed constraint
is applied. The proposed method in Figure 5 gives a less ripple in the torque and low THD (7.11%) for
current. The result was compared with another reference [26]; the value of ripple in torque is higher than the
proposed method. In addition, THD for current is large. The ratio of the difference between the greatest and
smallest torque peaks of each control technique and the average torque values are used to determine the
torque ripples:
𝑇𝑒, 𝑟𝑖𝑝 =
𝑇𝑒,𝑚𝑎𝑥−𝑇𝑒,𝑚𝑖𝑛
𝑇𝑒,𝑎𝑣𝑒
(17)
Figure 11. THD for current with constraint
Actual Torque Te

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Figure 12. THD for current without constrain
6. CONCLUSION
For applications like aerospace and electric cars, five-phase permanent magnet synchronous motors
(PMSMs) include the advantages of rapid fault tolerance and rapid torque per ampere. However, designing a
controller for a complicated machine model presents a number of issues. In addition, with Thirty-two voltage
vectors with varying impacts on current and torque. This paper presents a low-complexity MP-DTC approach
that can produce quick dynamic response and good steady state performance in a 5-phase PMSM drive
system. The enhanced MP-DTC may greatly minimize the motor's torque ripple and the distortions in the
stator currents. This can be verified in the simulation outcomes. In order to develop the motor performance,
the accuracy of the procedure is confirmed. By adjusting the weighting factor SW the importance of the
switching frequency can be set. In situations where the switching losses are important SW can be increased to
fulfil these requirements. The weighting factor's value must be determined experimentally, via trial and error.
The constraints are a safety feature, which limits the current output magnitude. Can be added to the cost
function. The benefits of the suggested MP-DTC system may be described in light of a comparison with the
conventional MP-DTC method, as follows: The proposed technique has advantageous stator currents, notably
for reducing low-order harmonics, it achieves low torque ripple and has outstanding steady-state performance
over the whole speed range. Furthermore, it features top-notch dynamic performance and Decrease
calculation complexity and it can remove the (d3-q3) subspace harmonics and improve the objective
functions.
ACKNOWLEDGEMENTS
To the teachers of Mustansiriyah University, the writers would like to express their thanks for their
aid and advice.
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BIOGRAPHIES OF AUTHORS
Saif Talal Bahar received his BSc. degree in Power and Electrical Machine
Engineering from Diayla University, Diayla, Iraq. He is currently pursuing his MSc. degree in
Electrical Engineering at Mustansiriyah University, Baghdad, Iraq. He was working Electrical
Engineer in the Electrical Department of Baquba Technical Institute at Middle Technical
University, Baghdad, Iraq. His research interests include Power Electronics & Electrical
Machine. He can be contacted at email: eema2009@uomustansiriyah.edu.iq.
Riyadh G. Omar is an Assist. Prof. in the Electrical Engineering Department,
Mustansiriyah University, Baghdad-Iraq, for 18 years in Power System Analysis & Power
Electronics. He is a member of the electrical engineering department council. He has many
publications mainly in power electronics and predictive control. He can be contacted at email:
riyadh.g.omar@uomustansiriyah.edu.iq.

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