EJEEE
https://doi.org/10.62909/ejeee.2025.002 Edison Journal for Electrical and Electronics Engineering
Article
Installation of an Electric Car Charger Using the Bald Eagle Op-
timizer Cascaded PI and LQR Controller
Ali Huzbur Hussien 1, *, and Khalid Mohammed Ameen Alazawi 2,
1 Department of Computer Engineering, Faculty of Engineering, Karabuk University, Karabük, Turkey;
2028126031@ogrenci.karabuk.edu.tr
2 Computer and Communication Engineering Department, Faculty of Engineering, Islamic University of Leb-
anon, Beirut, Lebanon; 73535@iul.edu.lb
* Correspondence: Tel.: +90 532 534 43 89
Abstract: The study paper concentrates on the development and execution of a system for an AC to
DC conversion, then followed by an electric vehicle (EV) charger. It enhances the significant power
factor of the power source while minimizing distortion from harmonics. The Golden Eagle optimi-
zation methods are employed to enhance the setting of Proportional-Integral (PI) and Linear Quad-
ratic Regulator (LQR) controller settings for improved conversion efficiency. The optimal strategy
is formulated relying on the eagle's expertise in searching at different angles of circular paths for
obtaining prey. The system converters are developed from the state space version using state space
averaging, and the simplified model is achieved via the current matched technique to decrease com-
puting overhead. The optimize the KP and KI settings of the PI controller and the weighting matrix
Q of the linear quadratic controller. The suggested improvement is executed using MATLAB appli-
cations, and the modeling results indicate a reduction in settling duration, rapid recovery from input
and output fluctuations, decreased Total Harmonic Distortion (THD), and increased permanency.
Keywords: Bald Eagle Optimizer; electric vehicle; Linear Quadratic Regulator; Power factor;
1. Introduction
The worldwide transition to electric vehicles (EVs) is motivated by the necessity to
mitigate considerable ecological problems linked, such as their exhaustion, increasing ex-
penses, and considerable releases of greenhouse gases. The transport industry signifi-
cantly contributes to climate change, with carbon dioxide emissions from combustion en-
gines being a principal factor in the ongoing ecological disaster. Electric vehicles (EVs)
have emerged as a viable solution to mitigate issues related to carbon dioxide emissions
and dependence. Nonetheless, the shift towards extensive electric vehicle adoption en-
counters several obstacles, including the inadequacy of infrastructure for charging.
Aboard steeds are essential in mentioned setting, as they enable the effective and depend-
able recharging of batteries in electric cars. The prevalent method employed by the On-
board charger’s charger involves an AC to DC conversion succeeded by a DC-to-DC con-
verter for battery charging [1, 2].
The adapter is a part of the charging that transforms the AC power from the charging
facility into electrical current for car battery charging. A notable AC to DC, converter
structure is the sequential arrangement of a rectifier and the DC to DC, succeeded by a
diode rectification. The converter has garnered significant attention in solar uses, correc-
tion of power factor converters, and fuel cell systems; nonetheless, it has challenges re-
lated to large parts, the necessity for result filtering, voltage anxiety, and achieving high
effectiveness when the final result exceeds the maximum feed. Buck converters are cost-
effective and very effective; yet, they are significantly impacted by blind angle issues in
Citation: Hussien, A.H. and Alazawi,
K.M.A., Installation of an Electric Car
Charger Using the Bald Eagle Opti-
mizer Cascaded PI and LQR Control-
ler. Edison Journal for Electrical and
Electronics Engineering, 2025. 3: p. 9-
15
Academic Editor: Assoc. Prof. Ad-
ham Hadi Saleh
Received: 23/2/2025
Revised: 4/4/2025
Accepted: 20/4/2024
Published: 25/4/2024
Copyright: © 2024 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 10 of 15
the supply voltage, necessitating the use of a supply voltage filtration [3-5]. The CUK con-
version exhibits the disadvantage of reversing productivity and large fatalities at its
switch and diode components [6].
The standalone converters utilized in AC to DC conversions experience issues related
to dimensions, transducer core the saturation point, and current harmonics [7]. The non-
minimum period features of the flyback converter impede the reaction to transients due
to circuit the inductance, complicating closed-loop correction [8]. The Forward converting
experiences transformer core exhaustion and requires an extra switch to mitigate this is-
sue. Consequently, the system converter is better suited for power factor adjustment in
battery power systems owing to its rapid transient reaction, reduced current delivery re-
verberation that not upsetting results, and capability to execute lowly improvement pro-
cesses. The utilization of system network topology relied power factor converters in cor-
recting power factors devices is on the rise [9].
The latest advances in optimizing for electrical converters encompass numerous es-
sential methods that enhance dynamic performance [10].
This paper presents an innovative method that combines BEO with PI and LQR con-
trollers for power factor correction in system converters utilized in electric vehicle charg-
ing systems. This research's new element is the utilization of BEO to enhance PI and LQR
controllers, overcoming the constraints of conventional optimization techniques. BEO has
exceptional optimization features, resulting in increased accuracy in variable adjustment
and greater system efficiency. The integration of BEO with PI and LQR control techniques
enhances the productivity and permanency of system converters while streamlining con-
troller installation. State space be an average of is used for the system converter, while the
present corresponding strategy streamlines controller development and diminishes the
converter's higher-order move work. To evaluate the reliability and precision of the BEO
method, data points such are contrasted with those of PSO and GWO.
2. Materials and Methods
2.1 Decoration, Operation, And Modeling of a System Converter
The system converter depicted in Figure 1 comprises the source voltage, a MOSFET
switch, a diode, input and output inductors, a power assignment capacitor, a production
filter capacitor, and a resistor for the load. The converter functioning has been evaluated
inside the constant conductivity phase. The voltage that results is measured over the load
impedance. It possesses several operational says, which are as follows: Activate Switch
and Deactivate Diode; Deactivate Switch and Activate Diode.
Figure. 1. System converter: (a) wiring schematic, (b) ON condition, (c) OFF condition.
EJEEE 2025, Vol.3 11 of 15
The scientific analysis [11, 12] indicates that an inexpensively conversion chargers’
lightweight electric cars. The subsequent formulas are employed to construct the system
converter [13], and its parts are detailed in Specifications Table 1. The converter's duty
cycles are derived, ripple current, the inductors are computed also, the coupling capaci-
tor's value is determined and the voltage at the input is 240V AC, and the output voltage
is 60V. The maximum frequency effort riddle capacitor and inductor are built using two
formulas as illustrated in Ref. [14].
2.2 Closed-Loop Control of Converter for Power Factor Correction
The system converter employs a sequential control approach for closed-loop regula-
tion. The outer loops use proportional integral regulator for voltage regulation to achieve
the specified electricity, while the inside loop utilizes LQR control for the present control-
ler to enhance the energy ratio on the network lateral. The solitary stage electrical input is
transformed into a pulsing DC output using a diode bridge rectifier, resulting in a subop-
timal power ratio, reduced effectiveness, and elevated distortion from harmonics. The
system converter is employed for power factor alteration, with its final voltage being mon-
itored for comparison to the reference electrical voltage. The incorrect voltage is supplied
as a signal to the PI controller, also known as the voltage controller [15].
Traditional techniques for determining PI controller settings, such as the Routh in-
stability criteria, Ziegler-Nichol’s technique, and pole assignment, are labor-intensive,
may result in increased error in steady-state stability, and carry the risk of system insta-
bility. The traditional Ziegler-Nichols approach determines the KP and KI numbers for
the upper and lower bounds of PI variables and optimization requirements. replacing
these numbers to compute the PI controller. According to Table 2, the proportional in-
crease and the integral gain, the acquired variables exhibit sluggishness in attaining the
steady state, resulting in increased errors. The converter's greatest efficiency relies on the
controller's activity; hence, the controller settings are established via optimization.
Table 1. Proposal constraint
Parameter
Effort Voltage
Production Voltage
Duty cycle ratio
Inductor
Capacitor
Substituting frequency
Effort filter capacitor
Effort filter inductor
Output Power
Table 2. Ziegler Nicholas modification.
Methods
Kp
Ti
Td
P
0.49
NA
NA
PI
0.44
1.19
NA
PID
0.59
0.49
1.19
Utilizing the function of fitness J, appropriate PI variables are identified via the
BEO process, with Table 3 presenting the variety of optimization value ranges. Analyzing
and constructing a great gage prototypical are complex endeavors that necessitate contin-
uous labors to streamline the higher command modeling and mitigate actual computa-
tional demands to yield suitable outcomes from conventional research, modeling, control,
layout, and computational methodologies [16].
The optimal parameters of KP and KI are determined, and the reaction time of the
voltage controller is contrasted with alternative refinements. Furthermore, the results are
presented in Table 4.
EJEEE 2025, Vol.3 12 of 15
Table 3. Limitations for PI optimization
Parameter
Value
Inhabitants size
49
No of repetitions
99
Variety of Kp morals
to five
Variety of Ki morals
to five
Table 4. Efficiency parameters of a closed system
Methods
KP ×10-6
KI ×10-4
Tr ×10-1
PSO
313
191
152
GWO
224
1803
140
BEO
9
1600
80
The T-test is presented for the suggested optimization in comparison to PSO and
GWO in Table 5, indicating that BEO outperforms the three optimization methods. The
statistical variables have been calculated to assess the suggested optimization's correct-
ness and uniformity, and 40 thirty tests are performed.
Traditionally, the price vector of LQR is computed individually, resulting in limited
outcomes. The Q vector is selected for improvement according to the fitness function to
enhance the controller's efficiency. To determine the ideal weightage quantities for Q in
LQR, an optimization technique, namely the Bald Eagle algorithm, is employed to yield
optimized Q values. Furthermore, it reduces the alteration variables while enhancing con-
troller efficiency. The fitness function J is defined as the summation of IAE and ISE, with
the range of Q matrix values specified in Table 6.
Table 5. T-test for BEO optimization with
GWO and PSO
Test
method
PSO Vs BEO
GWO Vs
BEO
t-Test
2890.57
3869.7
Table 6. Optimization restrictions for LQR
Parameter
Value
Population
To Thousand
Iteration
To Handed
Range of Q matrix
To five Thousand
2.3 Bald Eagle Optimization for Utilized Controller
This algorithm replicates the fishing actions of bald eagles when pursuing food. The
formulated optimizer's hunting conduct consists of three separate stages: 1) choosing an
area where the eagle identifies a location with a greater likelihood of encountering prey
compared to alternatives. 2) Conducting an investigation inside the area traversed by the
eagle to the already designated location to execute the discovery procedure. 3) Dive in
which the fisherman identifies the optimal location to capture the animal and proceeds
directly to it utilizing data gathered in the stage before it. For more information about this
matter and how connect employed system with this algorithm search, see Ref. [17]
3. Results
The simulation is conducted using the MATLAB/SIMULINK 2025 software. The sub-
sequent converter settings are taken into account for modeling: The input AC energy volt-
age is 220 Vrms, the target voltage at the output is 59.9 V, the resultant current is 7.69 A,
and the equipment's impedance is 7.9 Ω.
3.1 Closed Loop Reaction
The open-loop modeling outcomes of the conversion, the overall distortion of har-
monics is 45%, as seen in Figure. 3, and the power factor is 0.95. The improved PI and LQR
cascading closed-loop calculations in Figure. 4 demonstrate that the supplied flow is
nearly in sync with the voltage, resulting in the entire harmonic distortion that has de-
creased to 1.64% with significant scales.
EJEEE 2025, Vol.3 13 of 15
Figure. 2 Convergence curve of GWO, GWO and
PSO.
Figure. 3 Open loop reaction of the converter
Figure 5 demonstrates that the converters effectiveness remains relatively stable with
varying load, sustaining excellent performance throughout a wide spectrum of results du-
ties, indicative of little losses. Figure 6 illustrates how the converter substantially reduces
the total harmonic noise as the load current escalates, with reduced source current har-
monic attaining elevated load electrical currents. In Figure. 7, the power factor improves
as the load current rises. 5.8 A, resulting in a power factor that approaches unison. In Fig-
ure. 5, the total harmonic distortion escalates as the effort voltage rises from 179V to 239V.
The Total Harmonic Distortion is Below one percent at 179 V and elevated to 2.5 percent
at 220V.
Figure. 4 Closed-loop reaction of the converter in BEO
Figure. 5 Load and efficiency relationship
Figure. 6 Load current and THD relationship
Figure. 7 Power factor and load current relationship
0.05
0.1
0.15
0.2
0.25
0.3
020 40 60 80 100
Fitness Value
Iterations
PSO GWO GEO
0
0.2
0.4
0.6
0.8
1
1.2
0100 200 300 400 500 600 700 800 900
mag
frequency
0
0.005
0.01
0.015
0.02
0.025
0.03
0100 200 300 400 500 600 700 800 900
mag
frequency
96.5
96.7
96.9
97.1
97.3
97.5
97.7
97.9
98.1
98.3
6.7 7.4 7.7 8.7 10 12
Effecincey
Load Current
0.01
0.015
0.02
0.025
0.03
180 190 200 210 220 230 240
THD
Input Voltage
0.99928
0.99938
0.99948
0.99958
0.99968
0.99978
0.99988
5 5.5 6 6.5 7 8 9 10 11 12
Load Current
Power Factor
EJEEE 2025, Vol.3 14 of 15
Table 7 illustrates the converter's reaction to the suggested optimization strategies in
comparison to the current approach. The BEO outperforms PSO and GWO in criteria like
profit border, getting duration, power ratio, and effectiveness.
Table 7. Evaluation of the system converter with
current approaches.
Methods
Source Current
PF
η
PSO
2.62
0.995
97.30%
GWO
2.409
0.9983
97.51%
BEO
1.73
0.9984
97.61%
5. Conclusions
This paper employs the BEO method to improve PI and LQR transmitted supervisors
for voltage regulation and improvement of power factors in a system converter. The study
utilizes a summary instruction concept derived from the instant corresponding approach
to alleviate computing requirements. The BEO rely on PI and LQR cascade controllers
have been replicated in MATLAB/Simulink, demonstrating substantial enhancements
compared to conventional PI controllers. The improved controllers exhibited accelerated
static reactions, less overshoot, and attained a power factor, approaching unison. The
equipment demonstrated an efficiency and a total harmonic distortion present. In com-
parison to GWO and PSO, the BEO technique decreased excessive currents in diodes and
MOSFETs, facilitating the use of low-current rated and economically viable switches. This
adjustment reduces energy loss and total harmonic distortion. It enhances the AC arrange-
ment, fosters energy efficiency, and guarantees steady output voltage amidst fluctuating
load and input circumstances. The suggested approach provides actual cost savings and
increases in manufacturing excellence, illustrating its significance in boosting converter
efficiency and dependability.
Acknowledgments: the main authors thank his university to support this work by software but this
no any grant for this effort.
Conflicts of Interest: Declare conflicts of interest or state “The authors declare no conflict of inter-
est.”
EJEEE 2025, Vol.3 15 of 15
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