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e-ISSN: 2582-5208
International Research Journal of Modernization in Engineering Technology and Science
( Peer-Reviewed, Open Access, Fully Refereed International Journal )
Volume:05/Issue:11/November-2023 Impact Factor- 7.868 www.irjmets.com
www.irjmets.com @International Research Journal of Modernization in Engineering, Technology and Science
[2792]
ASSESSMENT OF ROBUSTNESS THROUGH SYSTEMATIC TESTING: A CASE
STUDY ON GWO-TUNED FUZZY PID CONTROLLER FOR HYBRID POWER
SYSTEMS
Nzenwa Eziuche C.*1, Priye Kenneth A.*2, Ibe A.O.*3
*1,2,3Department Of Electrical Engineering Niger Delta University, Bayelsa State, Nigeria.
ABSTRACT
The transition towards sustainable energy sources has led to the adoption of hybrid power systems, combining
multiple renewable technologies. However, the inherent variability of renewable sources and uncertainties in
system parameters challenge their stable operation. Effective control strategies are crucial to ensure robust-
ness. This research paper evaluates the GWO-tuned fuzzy PID controller's robustness in a hybrid power system,
comparing it with traditional PID and fuzzy PID controllers. The controller's performance is examined under
varying ultracapacitor parameters and the disconnection of critical energy storage elements. The results
demonstrate the GWO-tuned fuzzy PID controller's superior performance, showcasing its potential for enhanc-
ing grid stability and reliability in real-world applications. The paper provides valuable insights into optimizing
control strategies for sustainable energy integration.
Keywords: Hybrid Power Systems, Renewable Energy, PID Controller, Grey Wolf Optimization (GWO), Robust
Control, Ultracapacitor, Energy Storage, Reliability.
I. INTRODUCTION
The global shift towards sustainable energy sources has fueled the adoption of hybrid power systems that com-
bine multiple renewable energy technologies, such as photovoltaic solar cells and wind turbines. These systems
offer a promising solution to meet the growing electricity demand while reducing greenhouse gas emissions.
However, the inherent variability of renewable energy sources and the uncertainties associated with hybrid
power system parameters pose significant challenges to their reliable and stable operation. To address these
challenges and ensure the robustness of hybrid power systems, effective control strategies are crucial. Among
the control techniques employed in power systems, the Proportional-Integral-Derivative (P.I.D.) controller is
widely used due to its simplicity and ease of implementation. Additionally, fuzzy logic control (FLC) has gained
popularity for handling nonlinear and uncertain dynamic systems effectively. The integration of the P.I.D. and
fuzzy controllers in a fuzzy P.I.D. configuration offers the potential to leverage the advantages of both ap-
proaches and enhance the overall control performance of hybrid power systems. Nevertheless, the optimal
tuning of fuzzy P.I.D. controller parameters remains a challenging task. Traditional optimization methods may
struggle to handle the multi-dimensional and non-convex nature of the parameter space, which hampers the
controller's robustness under diverse operating conditions. In response to this challenge, the Grey Wolf Optimi-
zation (GWO) algorithm emerges as a promising meta-heuristic optimization technique inspired by the cooper-
ative hunting behavior of grey wolves in nature. GWO has demonstrated remarkable efficacy in solving complex
optimization problems in various domains. The primary focus of this research paper is to thoroughly evaluate
the robustness of the GWO-tuned fuzzy P.I.D. controller in a hybrid power system. Robustness, in this context,
refers to the controller's ability to maintain system stability and high-performance levels even in the face of
challenging and uncertain conditions. To achieve this, we subject the controller to comprehensive robustness
tests, simulating various scenarios, including parameter variations of ultracapacitors and the disconnection of
critical energy storage elements.
The key objectives of this paper are as follows:
• Evaluate the robustness of the GWO-tuned fuzzy P.I.D. controller under diverse and challenging operating
conditions in a hybrid power system.
• Conduct rigorous robustness tests, including variations in ultracapacitor parameters and disconnection of
energy storage elements, to assess the controller's adaptability and reliability.
• Provide valuable insights into optimizing control strategies for hybrid power systems, with a particular focus
on enhancing robustness and ensuring system reliability.
e-ISSN: 2582-5208
International Research Journal of Modernization in Engineering Technology and Science
( Peer-Reviewed, Open Access, Fully Refereed International Journal )
Volume:05/Issue:11/November-2023 Impact Factor- 7.868 www.irjmets.com
www.irjmets.com @International Research Journal of Modernization in Engineering, Technology and Science
[2793]
THE COMPONENTS OF HYBRID POWER SYSTEM
Both energy storage and power generation components make up the hybrid power system. Sections provide
more details. A hybrid power system's block diagram is shown in Figure 1.
1.1 Modelling of the Power Generator station
There are three parts to a hybrid power plant. wind turbine generator (WTG), solar photovoltaic cell, and diesel
engine generator (DEG). First-order transfer functions are used for modeling solar thermal power generators
(STPG), fuel cells (FC), wind turbine generators (WTG), and diesel electric generators (DEG) [2]. Values for the
parameters are shown in the table. 1.
(1)
(2)
(4)
Fig. 1. Simulation diagram of complete Hybrid power system
1.2 The Implementation of Different Energy Storage Components
In this power system, energy storage components such as fuel cells (FC), battery systems (BS), and ultra-
capacitors (UC) are utilized. Transfer fn. of these energy storage components are:
Flywheel System:
Flywheel energy’s stores works by maintaining energy in the system in the form of rotational energy by accel-
erating the rotor at high speed and converting rotational energy into the electrical energy.
(5)
Where GFs(S) =transfer function; KFs is gain, TFs is the fuel cell system time constant [1].
Ultra-capacitor (UC):
The volume or mass of UC generally stores 10 times - 100 times more energy/unit than electrolytic capacitors
[2]. UC allows many more charged and discharged cycles as compared to rechargeable batteries, and also
charges the battery at a faster rate.
GUC(s) =
(6)
Where GUC(s) is the transfer function, KUC is the capacitor gain, TUC is the time constant for UC system [2].
e-ISSN: 2582-5208
International Research Journal of Modernization in Engineering Technology and Science
( Peer-Reviewed, Open Access, Fully Refereed International Journal )
Volume:05/Issue:11/November-2023 Impact Factor- 7.868 www.irjmets.com
www.irjmets.com @International Research Journal of Modernization in Engineering, Technology and Science
[2794]
Battery System (BS):
Multiple battery management functions are being used out to ensure the safety, the structural integrity, the
battery performance, and the life of the battery.
(7)
Where GFs(S) = Transfer function, KFs is the gain, TFs are the time constant for Battery system respectively [1].
Table 1. The Parameters of Different Components in a Hybrid Power System.
ELEMENTS
GAIN
TIMECCONSTANT
SOLAR_POWER
WIND_POWER
DIESEL-ENGINE GENERATOR
FLYWHEEL_SYSTEM
BATTERY_SYSTEM
ULTRA_CAPACITOR
AQUAELECTROLYZER
FUEL_CELL
II. MODELLING OF THE AQUA ELECTROLYZER
Clean energy can be used in aqua-electrolyzers to convert water into hydrogen. Hydrogen can be used in pho-
tovoltaic cells that are powered by the sun or the wind. An analysis of the small signal transfer function can be
used to explain the operation of the Aqua Equalizer. One kilowatt of the net energy from the sun and wind is
used to create hydrogen in order to accomplish this. The hydrogen is then used by two fuel cells to produce
electricity, which is then fed into the system.
(8)
2.1 Transfer function Modelling for Power System:
(9)
The system's transfer function, denoted as GSYSTEM, is determined by a constant inertia value represented by "Is"
and a damping constant value represented by "D". Specifically, "Is" has a value of 0.03 and "D" has a value of 0.4.
The power and load demand error is represented by , while the fluctuation in frequency deviation of the
system is represented by .
2.2 Modelling of Solar, Wind and Demand Load Power
Variations in wind, solar, and demand load generation are modelled by the following equation [1]:
(10)
In this context, load power is represented by P, indiscriminate power element is represented by , average
power is represented by , and time-based signal switching with gain that controls the sudden change in mean
output of power is represented by . The low pass transfer-function is denoted by and constants ()
are utilized to standardize powers of to achieve per unit level coordination.
Parameters of the equation for generation of solar power are [1]:
o ~U (-1, 1); =0.7;=2; =0.1; =1.1111H(t)−0.5555H(t−40);
(11)
Parameters of the equation for generation of demand load are:
o ~U(-1, 1); =0.8=100, =0.1, = H(t) −
H(t−40);
(12)
e-ISSN: 2582-5208
International Research Journal of Modernization in Engineering Technology and Science
( Peer-Reviewed, Open Access, Fully Refereed International Journal )
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www.irjmets.com @International Research Journal of Modernization in Engineering, Technology and Science
[2795]
Equation for the parameters used for the generation of wind power are [1]:
o ~ U (-1, 1), =0.8, =2, =10,
(13)
where H(t) is Heaviside step function.
We concluded that there must be a constant flow of electricity between the system that generates electricity
and the load after modelling the energy storage elements and the other components. Flywheel-based energy
storage systems provide continuous rotational energy. The rotor's rotational energy can be transformed into
electrical energy by rapidly accelerating it. We need a controller that can lower the system's frequency devia-
tion in order to accomplish this.
III. ROBUSTNESS TEST
3.1 Variations in Parameters of Ultracapacitor
Modifying the ultra-capacitor (UC) parameter will disrupt the hybrid power system because it shares the most
power with the response track components. in contrast to those found in hybrid power systems. It is crucial
that the system is dependable before even starting to validate the worst-case scenario. When compared to the
gain, the time constant was increased by 30% while the gain was cut in half. For each possible set of UC param-
eters, the ISE is shown in Table 4. Compared to other controller structures the values of ISE are less for Fuzzy
P.I.D. tuned with GWO controller. The ISE value for Fuzzy P.I.D. with GWO is 1.24, when time constant, gain of
Ultra Capacitor is reduced by 30%, it is greater when compared with P.I.D. and fuzzy P.I.D. without GWO. But in
maximum cases, say in case of a Fuzzy P.I.D. with GWO controller, ISE value is least. Fig. 6 shows representation
in graphical form of Integral Square of Error (ISE) values for various controllers while varying parameters of
UC. In figure 6, ‘blue’ color shows the ‘P.I.D.’, ‘red’ shows ‘Fuzzy-P.I.D.’ and ‘green’ shows ‘Fuzzy P.I.D. with
GWO’.
Table 2. Variation of Parameter of Ultra Capacitor for Robustness Test
CONDITIONS
I.S.E.
P.I.D.
Fuzzy-
P.I.D.
GWO tuned Fuzzy-P.I.D.
NORMAL
1.5163
1.3252
1.1527
1.9257
1.3538
1.2089
1.1924
1.3624
1.2441
2.3021
1.4216
1.2112
1.3779
0.9046
0.7648
Robustness Test After Disconnecting Various Energy Storage Elements
We were able to confirm the parameter values of the simulated controller by removing various hybrid system
components. The disconnects of the FS, BS, and DEG occur under three different conditions. Depending on the
situation, the removal of these components may cause the system's functionality to either improve or degrade.
The GWO-tuned Fuzzy-P.I.D. controller can lessen both frequency deviation and controller effect, as shown in
Table 3. The frequency deviations connected to the UC parameters are shown in Figure 2-5.
e-ISSN: 2582-5208
International Research Journal of Modernization in Engineering Technology and Science
( Peer-Reviewed, Open Access, Fully Refereed International Journal )
Volume:05/Issue:11/November-2023 Impact Factor- 7.868 www.irjmets.com
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[2796]
Fig 2. Frequency Deviation output after decreasing UC value by 30%
Fig 3. Frequency Deviation output after increment of UC value by 30%
Fig 4. Frequency Deviation output after decreasing UC value by 50%
Fig 5. Frequency Deviation output after increasing UC value by 50%
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( Peer-Reviewed, Open Access, Fully Refereed International Journal )
Volume:05/Issue:11/November-2023 Impact Factor- 7.868 www.irjmets.com
www.irjmets.com @International Research Journal of Modernization in Engineering, Technology and Science
[2797]
Fig. 6. Graphical Presentation of ISE values for various controllers against Ultra capacitor parameter variation
Table 3. Robustness Test After Disconnecting Various Energy Storage Elements
CONTROLLER
COMPONENT REMOVED
ISE
P.I.D.
Battery Storage System
1.7125
Diesel Energy Generator
1.7434
Flywheel System
1.4579
Fuzzy-P.I.D.
Battery Storage System
1.4366
Diesel Energy Generator
1.3347
Flywheel System
1.4659
GWO tuned fuzzy-P.I.D.
Battery Storage System
1.2671
Diesel Energy Generator
1.1739
Flywheel System
1.2667
IV. RESULTS AND DISCUSSION
This section presents the results of the robustness tests conducted on the Grey Wolf Optimization (GWO) tuned
fuzzy Proportional-Integral-Derivative (P.I.D.) controller in the hybrid power system. The discussion revolves
around the controller's performance under various challenging scenarios, emphasizing its robustness and effec-
tiveness in maintaining grid stability and power flow. The obtained results are compared with traditional P.I.D.
and fuzzy P.I.D. controllers, providing valuable insights into the controller's superiority and its potential for
real-world applications.
4.1 Robustness Test with Variations in Ultracapacitor Parameters:
To assess the GWO-tuned fuzzy P.I.D. controller's adaptability to changes in ultracapacitor (UC) parameters,
several scenarios are considered. The time constant and gain of the UC are varied by 30% and 50%, both in-
crementally and decremental. Table 3 presents the Integral Square of Error (ISE) values for each controller
under different UC parameter configurations. The results demonstrate that the GWO-tuned fuzzy P.I.D. control-
ler consistently outperforms the other controllers. When compared to the P.I.D. and fuzzy P.I.D. controllers
without GWO, the ISE value for the GWO-tuned fuzzy P.I.D. controller is substantially lower in most cases. The
controller exhibits enhanced stability and precision in maintaining system performance even with significant
variations in UC parameters.
4.2 Robustness Test After Disconnecting Various Energy Storage Elements:
In this set of robustness tests, critical energy storage components, namely Battery Storage System (BS), Diesel
Energy Generator (DEG), and Flywheel System (FS), are individually disconnected from the hybrid power sys-
tem. The objective is to evaluate the controller's performance under adverse conditions when key components
0
0.5
1
1.5
2
2.5
30% increase
30% decrease
50% increase
50% decrease
ISE
PARAMETER VARIATION
PID
FUZZY PID
FUZZY PID
WITH GWO
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( Peer-Reviewed, Open Access, Fully Refereed International Journal )
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[2798]
are unavailable. Table 4 presents the ISE values for each controller when specific energy storage elements are
removed from the system. The results indicate that the GWO-tuned fuzzy P.I.D. controller showcases superior
performance compared to the P.I.D. and fuzzy P.I.D. controllers in all scenarios. Even with the absence of vital
energy storage elements, the GWO-tuned fuzzy P.I.D. controller manages to maintain grid stability and control
effectiveness.
4.3 Frequency Deviations Connected to UC Parameters:
The frequency deviation output under various UC parameter variations (30% increment and decrement) is
graphically represented in Figures 2, 3, 4, and 5. These figures illustrate how the GWO-tuned fuzzy P.I.D. con-
troller successfully regulates frequency deviations despite changes in UC parameters. The controller exhibits
better frequency control and is able to mitigate deviations more effectively than the other controllers.
4.5 Comparative Analysis:
The results obtained from the robustness tests and comparative analysis highlight the GWO-tuned fuzzy P.I.D.
controller's robustness and efficacy in maintaining grid stability and power flow under challenging conditions.
The controller's adaptability to variations in UC parameters and its ability to handle critical energy storage dis-
connections demonstrate its reliability in real-world applications. The GWO optimization algorithm plays a
pivotal role in tuning the fuzzy P.I.D. controller's parameters, ensuring optimal performance across diverse
operating conditions. Its convergence to optimal values enhances the controller's robustness and effectiveness.
The findings of this research paper contribute valuable insights into optimizing control strategies for hybrid
power systems. The GWO-tuned fuzzy P.I.D. controller's proven resilience and superiority over traditional con-
trollers offer promising solutions for enhancing grid stability and promoting sustainable energy integration.
V. CONCLUSION
This research paper presents a comprehensive investigation into the robustness of the Grey Wolf Optimization
(GWO) tuned fuzzy Proportional-Integral-Derivative (P.I.D.) controller in a hybrid power system. The control-
ler's performance is rigorously tested under diverse and challenging scenarios to assess its ability to maintain
grid stability and power flow under uncertain conditions. The results demonstrate the superior resilience and
effectiveness of the GWO-tuned fuzzy P.I.D. controller, making it a promising control strategy for enhancing the
reliability and performance of hybrid power systems. The robustness tests, involving variations in ultracapaci-
tor parameters and disconnection of critical energy storage elements, showcased the controller's exceptional
adaptability and reliability. The GWO-tuned fuzzy P.I.D. controller consistently outperformed traditional P.I.D.
and fuzzy P.I.D. controllers, exhibiting lower Integral Square of Error (ISE) values and reduced frequency devia-
tions. These results underscore the controller's ability to handle uncertain situations and maintain stable grid
operation, making it an ideal choice for real-world applications. The successful application of the GWO optimi-
zation algorithm for parameter tuning further highlights the controller's robustness. The algorithm's capability
to converge to optimal parameter values ensures enhanced control performance across various operating con-
ditions, solidifying the controller's reliability and adaptability. The comparative analysis reaffirms the superior-
ity of the GWO-tuned fuzzy P.I.D. controller over traditional controllers in terms of ISE values and frequency
deviations. Its consistent performance, even in the absence of critical energy storage elements, underscores its
resilience and reinforces its suitability for modern hybrid power systems.
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e-ISSN: 2582-5208
International Research Journal of Modernization in Engineering Technology and Science
( Peer-Reviewed, Open Access, Fully Refereed International Journal )
Volume:05/Issue:11/November-2023 Impact Factor- 7.868 www.irjmets.com
www.irjmets.com @International Research Journal of Modernization in Engineering, Technology and Science
[2799]
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