EJEEE
https://doi.org/10.62909/ejeee.2024.004 Edison Journal for Electrical and Electronics Engineering
Article
An improved cost function based on Model predictive current
control for five-phase PMSM
Saif Talal Bahar 1, * , Hao Qiu 2, , Deebage Rahman Neama 3, , Fatimah Fawzi Hashim 4, , and Hanaa
Yasseen 5,
1 Department of Electromechanical Techniques, Baquba Technical College, Middle Technical University, Bagh-
dad, Iraq; saif.talal@mtu.edu.iq
2 School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin, China;
haoqiu@guet.edu.cn
3 Department of Renewable Energy Techniques, Baquba Technical Institute, Middle Technical University,
Baghdad, Iraq; deebagerahman@mtu.edu.iq
4 Department of electrical engineering, University Malaya 50603, Kuala Lumpur, Malaysia
5 Department of Electric Power Engineering, Budapest University of Technology and Economics, Budapest,
Hungary; hanaa.yasseen@edu.bme.hu
* Correspondence: saif.talal@mtu.edu.iq
Abstract: In the model predictive control of a five-phase permanent magnet synchronous motor
(PMSM), obtaining weight coefficients through cumbersome calculations is problematic to achieve
optimal system control performance. To address this issue, this paper proposes a cascade model
predictive current control method for a 5-phase PMSM, employing the concept of cascade model
predictive control. First, the mechanism by which the suggested scheme chooses the best voltage
vector is analyzed. Then, by setting the mechanism precedence of the regulated chargeables based
on the characteristics of the 5-phase PMSM, objective function design schemes without weight co-
efficients are proposed: a fundamental current optimization scheme employs a high-amplitude volt-
age vector to improve DC bus voltage utilization and dynamic response capability; and a harmonic
current optimization scheme reduces stator current harmonics to reduce scheme noise and vibra-
tion. Simulation results demonstrate that the offered technique ensures the optimality of the applied
voltage vector, enabling the 5-phase PMSM to achieve excellent performance with a short torque
wave, rapid dynamic reaction, and little harmonic current under different operating situations.
Keywords: five-PMSM; model predictive current control; weight coefficient; voltage vector
1. Introduction
PMSM They are widely used in industrial manufacturing due to their great power
density, small size, and great efficiency [1]. In the context of vigorously developing novel
energy request technologies, the electric drive system collected of 5-phase PMSM and a
power converter contributes to the tendency of novel energy progress [2].
As the number of phases grows, the reliability and fault tolerance of 5-phase PMSM
are enhanced. Even if a two-phase bridge arm fails, it can still work normally, and it has
the characteristics of low voltage, high power, and short torque pulsation. Therefore, 5-
phase PMSM can light the requirements of great concert AC transmission power and pro-
tection and dependability, and has broad demand prospects in novel energy electric cars
and electric momentum airplanes [3]. Model predictive control (MPC) is an enhanced
mechanism technique that has been hotly studied recently. A great number of research
results show that MPC is the third great control mechanism technique for AC motors after
vector control (VC) and direct torque control (DTC), and its comprehensive performance
Citation: Bahar, S. T., et al., An im-
proved cost function based on Model
predictive current control for five-
phase PMSM. 2025. 3: p. 32-38
Academic Editor: Dr. Oladimeji Ibra-
him
Received: 23/08/2025
Revised: 23/09/2025
Accepted: 2/10/2025
Published: 5/10/2025
Copyright: © 2025 by the authors.
Submitted for possible open access
publication under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/license
s/by/4.0/).
EJEEE 2025, Vol.3 33 of 38
is better than VC and DTC [4]. Rendering to different optimization methods, MPC is sep-
arated into MPC and constant set MPC [5]. MPC is a control algorithm built on the dis-
connected numerical type of the inverter. It can choose the finest switching state from a
restricted number of switching states by inventory. Consequently, it does not require a
modulator to create a pulse width modulation (PWM) drive signal, and can also effec-
tively solve the nonlinear delinquent of the inverter [6]. MPC is simple to implement and
has fast dynamic response, making it suitable for controlling multi-variable, nonlinear
PMSM [7].
MPC for PMSMs is primarily divided into two categories: model-predictive torque
control and MPCC, which control flux, torque, and stator dq-axis currents, individually.
MPC uses the current scheme state to calculate the next state and then uses an objective
function to choose the best voltage vector that balances the cost of each controlled variable.
Therefore, state prediction and best voltage vector choice are key technologies for MPC
implementation. In the MPC cost function, due to the different dimensions of the con-
trolled variables, reasonable weight coefficients must be matched to achieve system sta-
bility.
However, current research still struggles to create a numerical relationship between
the weight coefficients and the regulated variables. Therefore, the weight coefficients can-
not be obtained analytically and are primarily determined through trial-and-error adjust-
ments in simulations or experiments [8]. The main drawbacks of this trial-and-error
method are its complexity and limited versatility. The weight coefficients must be read-
justed when system parameters and operating conditions change. Therefore, the adjust-
ment of weight coefficients is a research difficulty in model predictive control, which lim-
its the request and expansion of MPCC in the arena of motor regulator [9].
2. Materials and Methods
2.1 Model of a 5-Phase PMSM
The 5-phase PMSM drive circuit is displayed in Figure 1. The inverter's DC source
voltage is Udc. By regulating the switching of the inverter's 5-phase link legs, the inverter's
AC output side generates 5-phase AC power with a phase shift of 72°, creating a round
revolving magnetic field in the planetary to drive the 5-phase PMSM.
Assume that the stator winding comprises only the basic and 3rd harmonics, disre-
garding the effects of additional greater-order harmonics. Based on the organized conver-
sion, the 5-phase currents abcde can be equal to the currents d1, q1d3q3 In the
revolving organizational scheme. Their dynamic equations can be expressed as follows:
(1)
(2)
(3)
(4)
Where: 、 , 、 Are the d-axis and q-axis mechanisms of the stator cur-
rent and voltage in the important frequency space; 、 , 、 Are the dq-axis
mechanisms of the stator current and voltage in the 3rd harmonic frequency space; Rs is
the stator resistance; Ld and Lq are the dq-axis stator inductances, correspondingly; Lls is
the stator leakage inductance; is the rotor electrical angular velocity; Is the flux
linkage of the permanent magnet.
2.2 Space voltage vector of a 2-level 5-phase inverter
The two-level 5-phase inverter can provide 32 spatial voltage vectors, counting 30
effective voltage vectors and 2 zero voltage vectors [10]. Define (Sa, Sb, Sc, Sd, Se) (S
EJEEE 2025, Vol.3 34 of 38
represents the state of each bridge arm, S 1 when on and S 0 when off). Figures 2 show
the distribution of these spatial voltage vectors in the d1-q1 (two-phase stationary coordi-
nate system when the rotation speed is zero) and d3-q3 coordinate systems. According to
the magnitude of the voltage vector in the d1-q1 coordinate system, it is divided into four
categories, as shown in Table 1. The large vector and small vector in the d1-q1 coordinate
system are mapped to the small vector and large vector in the d3-q3 coordinate system,
respectively [11]. The rich voltage vectors in the five-phase inverter provide more options
for the selection of the control set in the FCS-MPTC algorithm.
Figure 1. 5-phase PMSM system
Figure 2. Voltage vector of a 5-phase inverter
2.3 Traditional MPCC of 5-Phase PMSM
The block illustration of the MPCC architecture for a 5-phase PMSM is illustrated in
Figure 3. The regulated adjustable comprises speed, basic currents id1 and iq1, and 3rd sym-
pathetic currents . Speed is controlled via a PI regulator, while the basic and sym-
pathetic currents are optimized, consuming an objective function. Model-predictive cur-
rent control periodically monitors stator current, predicts system states, and selects the
optimal voltage vector, achieving online progressive optimization [12]. First, the current
speed mistake is calculated, and the speed regulator converts the error signal into a stator
q-axis current reference command i*q1. Second, the current stator current is measured, and
the basic and 3rd harmonic currents for the subsequent instant are intended based on the
current forecast model [13]. Third, the forecast current and its reference command are fed
into the objective function to choose the best voltage vector that balances the current of
the stator basic and 3rd sympathetic currents. Lastly, the best voltage vector is trans-
formed into the regulator indication for the heavy 5-phase PMSM.
Based on the Euler method, the constant typical of the 5-phase PMSM is discretized.
The differential of the stator current can be articulated using a discrete-time model: where
Ts, k, are the mechanism period, the current time, and the earlier time, correspondingly
[14]. Moving the current time k forward by one time, the stator current prediction model
at time k+1 is attained:
(5)
(6)
(7)
EJEEE 2025, Vol.3 35 of 38
(8)
Where , Are the forecast currents in the fundamental and 3rd
harmonic spaces, correspondingly. 、 , 、 Are the output
voltages of the 5-phase inverter.
Objective Function: After completing the predictions for apiece regulated variable,
the cost function combines the forecast and orientation values of all regulated adjustable
into a function to quantify the difference between the system's next state and the desired
state, thereby selecting the optimal state and its corresponding voltage vector [15]. The
objective function g is constructed by subtracting , from their respec-
tive reference commands and match them with the corresponding weight coefficients:
(9)
Where: λ is the weight coefficient of the 3rd sympathetic current;
、
,
、
.
hese are the reference values of the basic current and the 3rd sympathetic current, respec-
tively. Since the harmonic space of the surface-mounted 5-phase PMSM does not partici-
pate in the electromechanical energy conversion, to suppress the 3rd harmonic current,
. The objective function value for a piecewise voltage vector is intended
spending Equation (8). The lesser the objective function value, the lesser the sum of the
stator current mistakes and the healthier the mechanism concert of the scheme. So, the
voltage vector with the least objective function value is the best voltage vector for the
scheme.
2.4 Improved MPCC of 5-Phase PMSM
The MPCC algorithm, based on an improved cost function, eliminates third-har-
monic voltages during virtual voltage vector synthesis. For a 5-phase PMSM with a sinus-
oidal stator winding distribution and no third-harmonic permanent magnets, no third-
harmonic current is generated. This simplifies the prediction equation and evaluation
function:
(10)
(11)
(12)
3. Results and Discussion
A 5-phase PMSM simulation platform was built in MATLAB/Simulink to confirm the
precision of the projected technique. The factors of the 5-phase PMSM are in Table 1. To
address the relevant issues in the above research, this paper proposes an MPCC method
to improve the performance of a five-phase PMSM driven by a two-level voltage source
inverter (VSI). First, a five-phase PMSM operating model is established under natural op-
eration.
Non-zero switching states that generate large voltage vectors in the d-q subspace are
selected as candidate states. Based on the selected voltage vectors, an SVM method is pro-
posed. Finally, a simulation platform is built to verify the effectiveness of the proposed
method.
By selecting the value function vector and performing non-analytical optimization,
MPCC was achieved over a wide speed range, thereby ensuring that the motor operates
stably in a predetermined manner within different speed ranges and improving the
steady-state performance of the system. However, the duty cycle control or MPCC control
strategy in the above studies cannot eliminate the voltage vector error.
Figures 4 and 5 show that both conventional MPCC and improved MPCC have good
dynamic performance, but improved MPCC has lower torque ripple and stator current
EJEEE 2025, Vol.3 36 of 38
harmonic content. The torque ripple for conventional MPCC is 9.66%, while that for im-
proved MPCC is 1.96%. Improved MPCC on the torque ripple discount.
Figure 3. Block illustration of the MPCC of the 5-phase
PMSM.
Figure 4. Torque traditional MPCC
(a) Figure 5. Torque with improved MPCC
Figure 6. Measured 5-Phase PMSM Currents with tradi-
tional MPCC
EJEEE 2025, Vol.3 37 of 38
Table 1. This System factors of MPCC for
5-phase PMSM
Parameter
Value
Unit
TL
12
N.m
Udc
300
V
p
3
-
Rs
0.5
Ω
Ld=Lq
12.4
mH
J
0.02
. 2
flux
0.09
Wb
Figure 7. Measured 5-Phase PMSM Currents with improved MPCC
5. Conclusions
This paper proposes an MPC for a 5-phase PMSM, addressing the cumbersome
weight coefficient tuning problem. By setting the control priority of the basic and har-
monic currents, a cost function is established for the structure. This objective function se-
lects the best voltage vector that balances fundamental and harmonic current performance
without requiring weight coefficients. The cost function structure can be modified based
on system performance requirements, including a fundamental current optimization
scheme to improve output torque and a harmonic current optimization scheme to elimi-
nate the third harmonic of the stator current. Simulation results demonstrate that the pro-
posed method, which eliminates the need for weight coefficients when controlling a five-
phase PMSM, achieves superior current harmonic suppression and dynamic response
speed compared to traditional MPC.
EJEEE 2025, Vol.3 38 of 38
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