OPTIMIZED PI CONTROL FOR POWER FLOW AND DC LINK VOLTAGE REGULATION IN A PV-WIND-BATTERY MICROGRID USING GREY WOLF OPTIMIZATION
Microgrids have become essential in modern power systems, enabling reliable and sustainable energy distribution while operating independently or with the main grid. The growing integration of renewable sources like photovoltaic (PV) and wind energy, along with battery storage, necessitates advanced...
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Vidnovluvana energetika| _version_ | 1871104013547601920 |
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| author | Mogilicharla, Veera Narasimha Murthy Gudapati, Sambasiva Rao |
| author_facet | Mogilicharla, Veera Narasimha Murthy Gudapati, Sambasiva Rao |
| author_institution_txt_mv | [
{
"author": "Veera Narasimha Murthy Mogilicharla",
"institution": "University College of Engineering and Technology, Acharya Nagarjuna University, Guntur, Andhra Pradesh, India"
},
{
"author": " Sambasiva Rao Gudapati",
"institution": "R.V.R. & J.C. College of Engineering, Chowdavaram, Guntur, Andhra Pradesh, India"
}
] |
| author_sort | Mogilicharla, Veera Narasimha Murthy |
| baseUrl_str | https://ve.org.ua/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-18T06:32:23Z |
| description | Microgrids have become essential in modern power systems, enabling reliable and sustainable energy distribution while operating independently or with the main grid. The growing integration of renewable sources like photovoltaic (PV) and wind energy, along with battery storage, necessitates advanced control strategies for efficient power management and grid stability. This paper presents an optimized power flow control strategy for a PV-Wind-Battery hybrid microgrid using a Voltage Source Converter (VSC) to regulate active and reactive power while maintaining DC link voltage stability. A Proportional-Integral (PI) controller plays a crucial role in ensuring system performance under varying conditions. However, conventional PI tuning is challenging due to the nonlinear nature of renewable energy sources. To overcome this, an optimized tuning approach based on the Grey Wolf Optimization (GWO) algorithm is proposed. Inspired by the social structure and hunting behaviour of grey wolves, GWO efficiently balances exploration and exploitation to determine optimal control gains. The PV system employs Perturb and Observe (P&O) Maximum Power Point Tracking (MPPT), while an adaptive P&O MPPT strategy is used for wind energy to maximize power extraction. The battery storage system dynamically switches between charging and discharging to maintain power balance. The GWO-based PI controller is compared with conventional methods, including Ziegler-Nichols (ZN), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO). Simulation results demonstrate superior transient response, reduced steady-state error, and minimized power fluctuations. Additionally, Total Harmonic Distortion (THD) analysis confirms lower harmonic distortion, enhancing power quality and system reliability, making GWO a promising approach for microgrid optimization. |
| doi_str_mv | 10.36296/1819-8058.2025.4(83).18-33 |
| first_indexed | 2026-02-08T07:59:26Z |
| format | Article |
| fulltext |
18
Відновлювана енергетика. № 4/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
УДК620.91 https://doi.org/10.36296/1819-8058.2025.4(83).18-33
OPTIMIZED PI CONTROL FOR POWER FLOW AND DC LINK VOLTAGE REGULATION
IN A PV-WIND-BATTERY MICROGRID USING GREY WOLF OPTIMIZATION
Received Mar. 21, 2025; accepted Dec. 09, 2025
Available online Dec. 31, 2025
Veera Narasimha Murthy Mogilicharla1,
Gudapati Sambasiva Rao2
Author for correspondence: Veera Narasimha Murthy Mogilicharla,
e-mail: murthyeps@gmail.com
Abstract. Microgrids have become essential in modern power
systems, enabling reliable and sustainable energy distribution
while operating independently or with the main grid. The
growing integration of renewable sources like photovoltaic
(PV) and wind energy, along with battery storage, necessitates advanced control strategies for efficient power
management and grid stability. This paper presents an optimized power flow control strategy for a PV-Wind-
Battery hybrid microgrid using a Voltage Source Converter (VSC) to regulate active and reactive power while
maintaining DC link voltage stability. A Proportional-Integral (PI) controller plays a crucial role in ensuring system
performance under varying conditions. However, conventional PI tuning is challenging due to the nonlinear nature
of renewable energy sources. To overcome this, an optimized tuning approach based on the Grey Wolf
Optimization (GWO) algorithm is proposed. Inspired by the social structure and hunting behaviour of grey wolves,
GWO efficiently balances exploration and exploitation to determine optimal control gains. The PV system employs
Perturb and Observe (P&O) Maximum Power Point Tracking (MPPT), while an adaptive P&O MPPT strategy is
used for wind energy to maximize power extraction. The battery storage system dynamically switches between
charging and discharging to maintain power balance. The GWO-based PI controller is compared with conventional
methods, including Ziegler-Nichols (ZN), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO).
Simulation results demonstrate superior transient response, reduced steady-state error, and minimized power
fluctuations. Additionally, Total Harmonic Distortion (THD) analysis confirms lower harmonic distortion,
enhancing power quality and system reliability, making GWO a promising approach for microgrid optimization.
Keywords: Grey Wolf Optimization (GWO), PI Controller Tuning, Power Flow Control, DC Link Voltage Regulation,
PV-Wind-Battery Microgrid, Voltage Source Converter (VSC) Control
ОПТИМІЗОВАНЕ ПРОПОРЦІЙНО-ІНТЕГРАЛЬНЕ КЕРУВАННЯ ДЛЯ РЕГУЛЮВАННЯ ПОТОКУ
ПОТУЖНОСТІ ТА НАПРУГИ ПОСТІЙНОГО ЛАНЦЮГА В МІКРОМЕРЕЖІ
PV-ВІТРО-АКУМУЛЯТОРНОГО ТИПУ З ВИКОРИСТАННЯМ АЛГОРИТМУ ОПТИМІЗАЦІЇ «СІРИЙ ВОВК»
Отримано 21 бер. 2025 р.; рекомендовано до публікації 09 груд. 2025 р.
Доступно онлайн 31 груд. 2025 р.
Віра Нарасімха Мурті Могиличарла1,
Гудапаті Самбасіва Рао2
Автор для кореспонденції: Віра Нарасімха Мурті Могиличарла,
e-mail: murthyeps@gmail.com
Анотація. Мікромережі стали невід’ємною складовою
сучасних енергетичних систем, забезпечуючи надійний і
стійкий розподіл електроенергії як у режимі автоном-
ної роботи, так і при підключенні до основної мережі.
Зростання частки відновлюваних джерел енергії, зок-
рема фотоелектричних (PV) і вітрових систем, у поєд-
нанні з акумуляторними сховищами потребує вдосконалених стратегій керування для підвищення ефе-
ктивності енергорозподілу та стабільності мікромережі.
1 Research Scholar
https://orcid.org/0009-0003-4371-2104
2 Professor
https://orcid.org/0000-0001-7410-5911
1 University College of Engineering and
Technology, Acharya Nagarjuna University,
Guntur, Andhra Pradesh, India
2 R.V.R. & J.C. College of Engineering,
Chowdavaram, Guntur, Andhra Pradesh, India
1 канд. наук, доцент
https://orcid.org/0009-0003-4371-2104
2 канд. наук, доцент
https://orcid.org/0000-0001-7410-5911
1 Університетський коледж інженерії та техноло-
гій, Університет Ачар'ї Нагарджуни, Гунтур,
Андхра-Прадеш, Индия
2 Инженерный колледж RVR & JC, Чандрамули-
пурам, Чоудаварам, Гунтур, Андхра-Прадеш,
Индия
19
Відновлювана енергетика. № 4/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
У цій роботі запропоновано оптимізовану стратегію керування потоком потужності для гібридної мі-
кромережі PV-вітро-акумуляторного типу з використанням перетворювача напруги (VSC), який регу-
лює активну та реактивну потужність, а також стабілізує напругу постійного ланцюга. Ключову роль
у забезпеченні стабільної роботи системи відіграє пропорційно-інтегральний (ПІ) регулятор. Проте
традиційне налаштування ПІ-регулятора є складним через нелінійність характеристик відновлюваних
джерел. Для вирішення цієї проблеми запропоновано використати алгоритм оптимізації «Сірий вовк»
(Grey Wolf Optimization, GWO), який ефективно визначає оптимальні коефіцієнти регулятора завдяки
поєднанню пошукової та експлуатаційної поведінки.
У PV-системі реалізовано метод відстеження точки максимальної потужності (MPPT) «збурення та
спостереження» (Perturb and Observe, P&O), тоді як для вітрової системи застосовано адаптивну стра-
тегію P&O MPPT з метою максимізації виробітку енергії. Акумуляторна система автоматично пере-
микається між режимами заряджання та розряджання для підтримання енергетичного балансу.
Результати моделювання показали, що ПІ-регулятор, налаштований за допомогою алгоритму GWO,
має кращі перехідні характеристики, меншу похибку в сталому режимі та знижені коливання потуж-
ності порівняно з традиційними методами налаштування (Ziegler-Nichols, Genetic Algorithm, Particle
Swarm Optimization). Аналіз гармонічних спотворень (THD) засвідчив нижчий рівень гармонік, що сприяє
підвищенню якості електроенергії та надійності системи.
Таким чином, застосування алгоритму GWO можна вважати перспективним підходом до оптимізації
мікромереж у сфері відновлюваної енергетики.
Ключові слова: алгоритм оптимізації «Сірий вовк» (GWO); ПІ-регулятор; керування потоком потужно-
сті; регулювання напруги постійного ланцюга; мікромережа PV-вітро-акумуляторного типу; керування
перетворювачем напруги (VSC).
1. Introduction
The increasing penetration of renewable energy sources
(RES), such as photovoltaic (PV) and wind energy, into mi-
crogrids has created new challenges in power flow control
due to their intermittent and stochastic nature [1]. Effec-
tive energy management and control strategies are neces-
sary to ensure the reliability, stability, and efficiency of mi-
crogrids integrating PV-wind-battery systems. Traditional
proportional-integral (PI) controllers have been widely
used in power systems due to their simplicity and ease of
implementation [2]. However, selecting optimal PI control-
ler parameters is critical to achieving desired system per-
formance. Conventional tuning methods often fail to pro-
vide optimal performance under dynamic conditions,
leading to the exploration of optimization techniques for PI
tuning [3]. Metaheuristic optimization algorithms have
gained significant attention in control system tuning due to
their ability to efficiently handle nonlinear, multi-objective,
and high-dimensional problems. Grey Wolf Optimization
(GWO) is one such nature-inspired optimization algorithm
that mimics the hunting behaviour of grey wolves [4]. It has
demonstrated superior performance in various engineering
applications due to its exploration-exploitation balance and
fast convergence properties. A traditional PI controller for
power flow control in a hybrid PV-wind-battery microgrid is
proposed in [5]. The study demonstrated satisfactory per-
formance under steady-state conditions but showed limita-
tions in handling dynamic load variations and system uncer-
tainties. The lack of optimization techniques in this study
resulted in suboptimal controller performance during tran-
sient conditions. A PSO-based approach to optimize PI con-
trollers for DC link voltage stabilization was proposed in [6].
While the results showed improved voltage regulation, the
study did not consider the impact of communication delays,
which are critical in real-world microgrid operations. The
use of a Genetic Algorithm (GA) for tuning PI controllers in
a PV-wind-battery microgrid was explored in [7]. The GA-
optimized controllers exhibited better performance com-
pared to conventional PI controllers, but the computational
time required for optimization was significantly high, limit-
ing its practicality for real-time applications. In [8], the au-
thors employed a fuzzy logic-based approach to enhance
the performance of PI controllers. The fuzzy-PI controller
showed improved adaptability to system uncertainties, but
the increased complexity of the design made it less suitable
for large-scale microgrid implementations.
In [9], the authors investigated the application of Artificial
Bee Colony (ABC) optimization for tuning PI controllers in a
microgrid. The study reported improved dynamic response
and reduced oscillations in power flow. However, the ABC al-
gorithm's sensitivity to initial parameters and its tendency to
converge to local optima were significant drawbacks. In [10],
the authors proposed a hybrid optimization technique com-
bining GA and PSO for PI controller tuning. While the hybrid
approach showed promising results, the computational com-
plexity and lack of scalability were major limitations. In [11],
the authors utilized a Simulated Annealing (SA) algorithm to
optimize PI controllers for DC link voltage control. The study
demonstrated improved voltage stability but suffered from
slow convergence and high computational costs. In [12], the
authors focused on the use of Differential Evolution (DE) for
PI controller optimization. The DE-based approach showed
better performance compared to traditional methods, but its
sensitivity to control parameters and difficulty in tuning were
notable drawbacks. The application of Ant Colony Optimiza-
tion (ACO) for tuning PI controllers in a microgrid is investi-
gated in [13]. The ACO-optimized controllers exhibited im-
proved power flow control, but the algorithm's slow
convergence and high computational requirements were
20
Відновлювана енергетика. № 4/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
significant limitations. In [14], proposed a hybrid approach
combining fuzzy logic and PSO for PI controller optimization.
While the results were promising, the increased complexity
and computational overhead made it less practical for real-
time applications. In [15], the authors investigated the use of
a Teaching-Learning-Based Optimization (TLBO) algorithm
for PI controller tuning. The TLBO-based approach showed
improved performance in power flow control and DC link
voltage regulation, but its lack of robustness under varying
operating conditions was a major drawback. In [16], authors
proposed a Harmony Search (HS) algorithm for optimizing PI
controllers. The study reported improved dynamic response,
but the algorithm's sensitivity to parameter settings and slow
convergence were significant limitations.
The use of a Cuckoo Search (CS) algorithm for PI controller
optimization was explored in [17]. The CS-based approach
demonstrated better performance compared to traditional
methods, but its high computational cost and difficulty in
parameter tuning were notable drawbacks. In [18], a hybrid
approach combining GA and fuzzy logic for PI controller
tuning was proposed. While the results were promising, the
increased complexity and computational requirements
made it less suitable for real-time applications. In [19], the
use of a Firefly Algorithm (FA) for optimizing PI controllers
was investigated. The FA-based approach showed im-
proved performance, but its sensitivity to initial parameters
and slow convergence were significant limitations. Despite
the contributions of these studies, many of the proposed
optimization techniques suffer from drawbacks such as
high computational complexity, slow convergence, sensi-
tivity to initial parameters, and lack of robustness under
varying operating conditions. In contrast, the Grey Wolf Op-
timization (GWO) algorithm offers a promising alternative
due to its simplicity, fast convergence, and ability to avoid
local optima. GWO-based approaches can efficiently opti-
mize PI controllers for power flow control and DC link volt-
age regulation in microgrids with PV-wind-battery systems.
GWO's balance between exploration and exploitation,
along with its low computational requirements, makes it a
superior choice for real-time applications. By addressing
the limitations of existing optimization techniques, GWO
can provide a robust and efficient solution for enhancing
the performance of PI controllers in microgrids. This paper
focuses on the application of GWO for optimizing PI con-
troller parameters to improve power flow control in a mi-
crogrid comprising PV, wind, and battery storage. The pro-
posed approach aims to enhance the stability, dynamic
response, and power-sharing efficiency of the system un-
der variable generation and load conditions.
2. HYBRID DG SYSTEM (HDGS)
Fig. 1 illustrates the schematic of the hybrid system, which
integrates a PV-Wind-Battery configuration.
Fig. 1. Management Structure of HDGS with the Proposed Controller
This system comprises a wind turbine, a photovoltaic (PV)
system, and a battery, working together to enable efficient
energy transfer from the DC bus to the grid. The PV gener-
ation system is interfaced with the DC bus via a DC-DC con-
verter operated with Maximum Power Point Tracking
(MPPT). Similarly, the wind generation system is connected
to the DC bus through a rectifier followed by an MPPT-op-
erated DC-DC converter. The battery storage system is
linked to the DC bus through a bidirectional DC-DC con-
verter. The design of the power flow control and manage-
ment modules for the PV-Wind-Battery system is based on
the operational modes of the load and grid. In grid-con-
nected mode, the active and reactive power outputs of the
PV-Wind-Battery system are regulated to match their re-
spective reference values. To ensure optimal performance,
the voltage source inverter (VSI)-based control system
must select an appropriate power control mode. A sinusoi-
dal pulse width modulation (SPWM) technique is employed
to regulate the VSI. To meet varying load demands, the
power contribution from the main grid and the PV-Wind-
Battery system must be dynamically adjusted. Ensuring a
consistent supply of active and reactive power requires
21
Відновлювана енергетика. № 4/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
efficient control of power flow between the PV-Wind-Bat-
tery system, the grid, and the load. Furthermore, a reliable
integration of power from the main grid and the distributed
generation (DG) system is crucial to meeting the load de-
mand [20]. The power balance equation must be satisfied
at both the DC-link and the point of common coupling
(PCC). The total DC power available at the DC bus from the
energy sources in the microgrid is expressed as:
𝑃𝑑𝑐(𝑡) = 𝑃𝑊𝑇(𝑡) + 𝑃𝑃𝑉(𝑡) + 𝑃𝐵𝑎𝑡(𝑡) (1)
𝑃𝑊𝑇: Power generated by the wind generation system, 𝑃𝑃𝑉
: Power generated by the solar generation system, 𝑃𝑏𝑎𝑡:
Battery power measured at the output of the respective
DC/DC converters, 𝑃𝑑𝑐: Total available DC power at the DC
bus. The total power generated by renewable sources is de-
termined using Equation (1) and integrated into the overall
power flow model. The power balance is calculated by ac-
counting for the outputs of the hybrid energy sources and
the load demand at the AC bus.
𝑃𝑔(𝑡) = [𝑃𝑙(𝑡) − 𝑃ℎ𝑟𝑒𝑠(𝑡)] (2)
𝑃𝑙(𝑡) = [𝑃ℎ𝑟𝑒𝑠(𝑡) + 𝑃𝑔(𝑡)] (3)
𝑄𝑔(𝑡) = [𝑄𝑙(𝑡) − 𝑄ℎ𝑟𝑒𝑠(𝑡)] (4)
𝑄𝑙(𝑡) = [𝑄ℎ𝑟𝑒𝑠(𝑡) + 𝑄𝑔(𝑡)] (5)
𝑃𝑔: Active power supplied by the grid, 𝑄𝑔: Reactive power
supplied by the grid, 𝑃𝑙: Active power consumed by the
load, 𝑄𝑙: Reactive power consumed by the load, 𝑃ℎ𝑟𝑒𝑠: Ac-
tive power generated by the HDGS, 𝑄ℎ𝑟𝑒𝑠: Reactive power
generated by the HDGS. The battery power of the storage
unit is affected by the discharge duration, during which it
serves as an energy source, and the charging duration,
when it operates as a load. However, maintaining a con-
sistent power balance is challenging due to nonlinear fluc-
tuations on the consumer side and the unpredictable na-
ture of renewable energy sources [21]. To address this
challenge, the system unit requires a high-performance op-
erating mode that facilitates efficient power regulation.
The active and reactive power, calculated using the direct
and quadrature axis voltages and currents, are given by the
equations (6) and (7).
𝑃𝐼(𝑡) =
3
2
[𝑣𝑑 ∗ 𝑖𝑑 + 𝑣𝑞 ∗ 𝑖𝑞] (6)
𝑄𝐼(𝑡) =
3
2
[𝑣𝑞 ∗ 𝑖𝑑 + 𝑣𝑑 ∗ 𝑖𝑞] (7)
𝑣𝑑 and 𝑣𝑞 represent the direct and quadrature axis load
voltages, while 𝑖𝑑 and 𝑖𝑞 denote the direct and quadrature
axis load currents.
3. Modelling of sources
3.1. Mathematical formulation of solar PV module
Fig. 2 shows the simplified circuit representation of a solar
panel. The PV cell can be modelled as an ideal current
source, denoted as 𝑰𝒑𝒉, with series and parallel resistances,
as illustrated in Fig. 2. The output current of an ideal solar
cell is expressed in Equation (8).
𝐼 = 𝐼𝑝ℎ − 𝐼𝑑 (8)
I is PV output current, Id is diode current, Iph photon cur-
rent. In semiconductor theory, the fundamental mathe-
matical equation that describes the I-V characteristics of
the PV cell is the Shockley diode current equation, as shown
in Equation (9).
𝐼𝑑 = 𝐼𝑠 [𝑒𝑥𝑝 (
𝑞𝑉𝑜𝑐
𝑁𝑠 𝐾𝐴𝑇𝑜
) − 1] (9)
then
𝐼𝑑 = 𝐼𝑝ℎ − 𝐼𝑠 [𝑒𝑥𝑝 (
𝑞𝑉𝑜𝑐
𝑁𝑠 𝐾𝐴𝑇𝑜
) − 1] (10)
𝐼𝑠 is the saturation current, q is the electron charge, 𝑉𝑜𝑐is
the open-circuit voltage, 𝑁𝑠 represents the number of se-
ries-connected cells per module, K is Boltzmann’s constant,
and 𝑇𝑜 is the nominal cell temperature in Kelvin.
Fig. 2. Equivalent circuit of real model for PV panel
Due to the sensitivity of photovoltaic (PV) generation out-
put to weather conditions such as irradiance and tempera-
ture, the use of a DC-DC converter is essential for regulating
both the output voltage and power. Fig. 3 highlights the im-
portance of regulating the PV voltage to the maximum
power point voltage (𝑉𝑚𝑝𝑝), a crucial factor in maximizing
the power output from the PV arrays using a DC-DC con-
verter. As shown in Fig. 3, controlling the PV voltage to
reach 𝑉𝑚𝑝𝑝 is crucial for optimizing power extraction from
the PV arrays through the DC-DC converter. The P&O MPPT
(Perturb and Observe Maximum Power Point Tracking) al-
gorithm is used to generate the duty cycle required for the
DC-DC converter to maximize power extraction. Fig. 4
shows the DC-DC converter employed for the PV array.
Fig. 3. I-V and P-V characteristics of PV Array
22
Відновлювана енергетика. № 4/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
The Perturb and Observe (P&O) algorithm is a commonly
used MPPT technique in PV systems. It is a straightforward
and effective method for continuously adjusting the operat-
ing point of a PV system to ensure it operates at its maximum
power point (MPP), where the power output is optimized.
Fig. 4. PV system with boost converter
3.2. PMSG and Wind Turbine
Output power from wind turbine (𝑃𝜔) is given as in Equa-
tion (11)
𝑃𝜔 =
1
2
𝜌𝐴𝐶𝑝(𝜆, 𝛽)𝑉𝜔
3 (11)
ρ is the air density, A is the wind turbine swept area in m2,
λ is the tip speed ratio, and β is the pitch angle. The tip
speed ratio λ is defined as the ratio of the blade tip speed
ω, the wind turbine blade radius r, and the wind speed V,
and it can be expressed by Equation (12).
𝜆 =
𝑟𝜔
𝑉𝜔
(12)
Therefore, the mechanical energy generated by wind tur-
bines can be controlled by adjusting both λ and β. For a
given 𝛽, there is a corresponding power coefficient (Cp) vs.
tip speed ratio (λ) curve, where each curve has an optimal
Cp value, denoted as Cp opt, which corresponds to the opti-
mal tip speed ratio, λ𝑜𝑝𝑡. By controlling these parameters,
the mechanical energy of the turbine can be adjusted to
align with the available wind speed, with the maximum
Cpachieved at the optimized rotational speed when
𝛽equals zero.
The power generated by the PMSG can be regulated using
a DC-DC converter, which is controlled by an MPPT algo-
rithm. Before the DC-DC boost converter takes over the
regulation, the PMSG's output is first connected to a diode
bridge rectifier. To enhance the dynamic performance of
the wind generation system, an adjustable step size (𝑃&𝑂)
algorithm is employed to control and manage the DC-DC
converter. This approach ensures that the system achieves
its peak power output. Unlike traditional P&O algorithms,
this adaptive method addresses several limitations that can
negatively impact the performance of the wind generation
system, particularly in systems with inertia. Traditional P&O
algorithms face significant challenges in selecting the opti-
mal step size for rotor speed adjustments.
The optimal rotor speed can be calculated using Equation
(13), as shown below:
𝜔𝑜𝑝𝑡_𝑚 =
𝜆𝑜𝑝𝑡𝑉𝑤
𝑅
(13)
𝜆𝑜𝑝𝑡 optimal tip speed ratio, 𝜔𝑜𝑝𝑡_𝑚 is directly related to
wind speed expressed in Equation (14)
𝜔𝑜𝑝𝑡_𝑚𝑝
= 𝜔𝑏𝑎𝑠𝑒_𝑚
𝜐𝑤
𝜐𝑏𝑎𝑠𝑒
(14)
𝜐𝑏𝑎𝑠𝑒 refers to the reference wind speed, 𝜔𝑏𝑎𝑠𝑒_𝑚repre-
sents the rotor speed at the reference wind speed,
𝜔𝑜𝑝𝑡_𝑚𝑝
indicates the current optimal generator speed, and
𝜐𝑤 represents the current wind speed. The control system
will make substantial corrections to the rotor speed when
it deviates from the required optimal speed. As the rotor
speed approaches the desired level, the adaptive ratio 𝑅𝑎𝑑𝑝
will decrease until the optimal speed is reached and main-
tained, as shown in Equation (15).
𝑅𝑎𝑑𝑝 = 𝐾𝑝𝑒𝑟 (
𝜔𝑜𝑝𝑡_𝑚𝑝−𝜔𝑚
𝜔𝑜𝑝𝑡_𝑚𝑝
) (15)
The perturbation constant 𝐾𝑝𝑒𝑟determines the accuracy in
achieving the maximum power output. Once the algorithm
determines the ideal rotor speed, a PI controller is used to
generate a reference torque to maintain the PMSG rotor at
its optimal speed 𝜏𝑜𝑝𝑡_𝑚. After that, the input current
Fig. 5. Wind generation system with boost converter
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reference (𝐼𝑤𝑟𝑒𝑓) for the DC-DC converter is calculated from
the torque reference, as shown in Equation (16).
𝐼𝑤𝑟𝑒𝑓 = 𝜏𝑜𝑝𝑡_𝑚
𝜔𝑚
𝑉𝑑𝑐𝑤
(16)
A DC current regulator with PI control is used to maintain
the output voltage of the DC-DC converter. This regulator
generates the required duty cycle to control the IGBT
switch. Fig. 5 illustrates the wind system with the DC-DC
converter. The output of the 𝑃𝐼1controller is the reference
torque 𝜏𝑜𝑝𝑡_𝑚, which is given in Equation (17).
𝜏𝑜𝑝𝑡𝑚
= 𝐾𝑝1 (𝜔𝑜𝑝𝑡𝑚
(𝑡) − 𝜔𝑚(𝑡)) + 𝐾𝑖1 ∫ (𝜔𝑜𝑝𝑡𝑚
(𝑡) − 𝜔𝑚(𝑡)) 𝑑𝑡 (17)
𝐾𝑝1 and 𝐾𝑖1 are PI controller gains
Output of the 𝑃𝐼2 controller is duty cycle (𝑑𝑤)
required by the converter which is given as
𝑑𝑤 = 𝐾𝑝2 (𝐼𝑊𝑟𝑒𝑓(𝑡) − 𝐼𝑊(𝑡)) + 𝐾𝑖2 ∫ (𝐼𝑊𝑟𝑒𝑓(𝑡) − 𝐼𝑊(𝑡)) 𝑑𝑡 (18)
𝐾𝑝2 and 𝐾𝑖2 are PI controller gains
3.3. Battery energy storage system (BESS)
Fig. 6. Battery storage system with DC-DC converter
Bidirectional DC DC converter of battery storage system
regulate the DC voltage across DC bus. DC bus voltage can
be taken as feedback and compared with reference DC volt-
age to generate reference DC current. As shown in Fig. 6,
the output of the 𝑃𝐼3 controller is the reference battery
current 𝐼𝑏𝑎𝑡𝑟𝑒𝑓, which is given in Equation (19).
𝐼𝑏𝑎𝑡𝑟𝑒𝑓 = 𝐾𝑝3 (𝑉𝑏𝑎𝑡𝑟𝑒𝑓(𝑡) − 𝑉𝑑𝑐𝑏𝑎𝑡(𝑡)) + 𝐾𝑖3 ∫ (𝑉𝑏𝑎𝑡𝑟𝑒𝑓(𝑡) − 𝑉𝑑𝑐𝑏𝑎𝑡(𝑡)) 𝑑𝑡 (19)
𝐾𝑝3 and 𝐾𝑖3 are PI controller gains, 𝑉𝑏𝑎𝑡𝑟𝑒𝑓 battery refer-
ence voltage, 𝑉𝑑𝑐𝑏𝑎𝑡 actual battery voltage,
Output of the 𝑃𝐼4 controller is duty cycle of the switches in
bidirectional converter which is given as in Equation (20)
𝑑𝑏𝑎𝑡 = 𝐾𝑝4 (𝐼𝑏𝑎𝑡𝑟𝑒𝑓(𝑡) − 𝐼𝑏𝑎𝑡(𝑡)) + 𝐾𝑖4 ∫ (𝐼𝑏𝑎𝑡𝑟𝑒𝑓(𝑡) − 𝐼𝑏𝑎𝑡(𝑡)) 𝑑𝑡 (20)
𝐾𝑝4 and 𝐾𝑖4 are PI controller gains, 𝐼𝑏𝑎𝑡𝑟𝑒𝑓 battery reference current, 𝐼𝑏𝑎𝑡 actual battery current,
3.4. Current Control Strategy of DC-AC converter
Fig. 7 presents the control strategy of the DC-AC converter.
Fig. 7. Control Strategy of the DC-AC converter
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Equations (21) and (22) show the reference current used to
achieve the control goal. The two PI controllers in the
power controller work with the external control loop to
generate the reference current vectors 𝑖𝑑𝑟𝑒𝑓 and 𝑖𝑞𝑟𝑒𝑓.
𝑖𝑑𝑟𝑒𝑓 = 𝐾𝑝5 (𝑃𝑟𝑒𝑓(𝑡) − 𝑃(𝑡)) + 𝐾𝑖5 ∫ (𝑃𝑟𝑒𝑓(𝑡) − 𝑃(𝑡)) 𝑑𝑡 (21)
𝑖𝑞𝑟𝑒𝑓 = 𝐾𝑝6 (𝑄𝑟𝑒𝑓(𝑡) − 𝑄(𝑡)) + 𝐾𝑖6 ∫ (𝑄𝑟𝑒𝑓(𝑡) − 𝑄(𝑡)) 𝑑𝑡 (22)
𝐾𝑝5 and 𝐾𝑖5 are PI controller gains, 𝑃𝑟𝑒𝑓 reference active
power, 𝑄𝑟𝑒𝑓 reference reactive power, 𝑃 actual active
power and 𝑄 actual reactive power.
The controller's output is important for accurate tracking
and reducing inverter ripple. This is achieved by using two
PI controllers to correct current errors, along with feedback
from the inverter current and feedforward from the grid
voltage, improving both steady-state and dynamic perfor-
mance. The controller uses a PWM system to generate volt-
age vectors with reduced harmonic distortion. In addition
to the PWM system, it includes a current feedback loop and
a grid voltage feedforward loop to enhance both steady-
state and dynamic performance. These loops help elimi-
nate current errors, ensure precise tracking, and reduce in-
verter drift, as shown in Equations (23) and (24).
𝑣𝑑𝑟𝑒𝑓 = 𝐾𝑝7 (𝑖𝑑𝑟𝑒𝑓(𝑡) − 𝑖𝑑(𝑡)) + 𝐾𝑖7 ∫ (𝑖𝑑𝑟𝑒𝑓(𝑡) − 𝑖𝑑(𝑡)) 𝑑𝑡 (23)
𝑣𝑞𝑟𝑒𝑓 = 𝐾𝑝8 (𝑖𝑞𝑟𝑒𝑓(𝑡) − 𝑖𝑞(𝑡)) + 𝐾𝑖8 ∫ (𝑖𝑞𝑟𝑒𝑓(𝑡) − 𝑖𝑞(𝑡)) 𝑑𝑡 (24)
𝐾𝑝7 and 𝐾𝑖7 are PI controller gains, 𝑖𝑑𝑟𝑒𝑓 reference direct axis
current, 𝑖𝑞𝑟𝑒𝑓 reference quadrature axis current, 𝑖𝑑 actual di-
rect axis current and 𝑖𝑞 actual quadrature axis current.
In grid-connected mode, the HDGS unit controls both the
size and phase of the inverter current to supply the re-
quired active and reactive power to the grid. The control
strategy for active and reactive power in the HDGS unit is
based on frequency and voltage regulation. To assess the
performance of the HDGS unit, the outputs from the PV ir-
radiance, wind turbine, and battery are considered. Tuning
the PI controller gains is important for ensuring effective
and stable control of a system. PI controllers are often used
to regulate a process variable. Heuristic optimization algo-
rithms can be used to automate the process of tuning a PI
controller. These algorithms search through the parameter
space to find the best controller settings that minimize per-
formance issues like integral of time-weighted absolute er-
ror (ITAE), overshoot, or settling time. These algorithms
search for the best controller settings to reduce perfor-
mance issues like ITAE, overshoot, or settling time. When
using heuristic optimization algorithms for tuning a PI con-
troller, it's important to set the objective function based on
the specific performance goals of the control system. Also,
the algorithm parameters (like population size and muta-
tion rate) need to be carefully chosen and adjusted for the
application. Running multiple optimization trials and ana-
lyzing the results can help ensure that the controller set-
tings are both robust and reliable.
The goal of design optimization is to find the best design by
minimizing an objective function, adjusting design varia-
bles, and following given constraints. Sometimes, there are
multiple design criteria or objectives to consider at once. In
these cases, the design problem becomes a multi-objective
optimization challenge. Unlike traditional optimization
methods that focus on one objective, multi-objective opti-
mization is different. Traditional methods can't handle the
complexity of optimizing multiple conflicting objectives at
the same time. That's why specialized techniques for multi-
objective optimization are needed to deal with these com-
plex design problems.
Multi Objective optimization can be defined as shown in
Equations (25) to (28)
min 𝐹(𝑥, 𝑘) = [𝐹1𝐹2 … 𝐹𝑛]𝑇 (25)
𝑢(𝑥, 𝑘) ≤ 0 (26)
𝑣(𝑥, 𝑘) = 0 (27)
𝑥𝑖,𝑙𝑏 ≤ 𝑥𝑖 ≤ 𝑥𝑖,𝑢𝑏(𝑖 = 1,2 … 𝑑) (28)
Consider the objective function vector F, which depends on
the design vector x and a constant parameter vector p. The
inequality and equality constraints are represented by u
and v. Also, 𝑥𝑖,𝑙𝑏 and 𝑥𝑖,𝑢𝑏 show the lower and upper limits
for the ith design variable. The most common method for
multi-objective optimization is the weighted sum method.
The most common method for multi-objective optimization
is the weighted sum method. In this approach, multiple ob-
jectives are combined into one single objective by assigning
a weight to each objective and then adding them together.
In short, the combined objective function is a weighted sum
of the individual objectives, creating a unified optimization
criterion represented as 𝐹𝑜𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒in Equation (29).
𝐹𝑜𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 = 𝑎1𝐹1 + 𝑎2𝐹2 + ⋯ + 𝑎𝑛𝐹𝑛 (29)
Where 𝑎1, 𝑎2 … , 𝑎𝑛 are the weights for each objective func-
tion. If the sum of the weights equals 1 ∑ 𝑎𝑖
𝑛
𝑖=1 = 1 and
0 ≤ 𝑎𝑖 ≤ 1, the weighted sum is a convex combination of
the objectives. In this case, each optimization of a single ob-
jective finds a specific optimal solution along the Pareto
front. The weighted sum method then adjusts the weights
to explore different solutions, producing various optimal
points. In this study, the optimization of PI controller gains
is performed by using the Integral of Time-weighted Abso-
lute Error (ITAE) as the sole objective function. The objec-
tive function to be minimized is defined as the sum of the
integral of the absolute error multiplied by time for each
individual PI controller. The optimization aim is to minimize
the total ITAE, improving the dynamic response and overall
performance of the control system. The final objective
function to be minimized is expressed in Equation (30).
𝐹𝑜𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 = 𝑎1𝐼𝑇𝐴𝐸1 + 𝑎2𝐼𝑇𝐴𝐸2 + ⋯ + 𝑎𝑛𝐼𝑇𝐴𝐸𝑛 (30)
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The Grey Wolf Optimization is used to optimize the Propor-
tional-Integral (PI) controller gains (proportional gain and
integral time constant). The goal of this optimization is to
improve the dynamic response of the system. The goal is to
optimize all eight PI controller gains: two PI controllers reg-
ulate the boost converter in the wind generation system,
another two control the bidirectional converter in the bat-
tery storage system, and the remaining four manage the
DC-AC converter. This optimization aims to improve control
overactive and reactive power, as well as enhance the reg-
ulation of DC and AC side voltages. The PI controller gains
to be optimized include 𝐾𝑝1, 𝐾𝑝2, … 𝐾𝑝8representing the
eight proportional gains, and 𝐾𝑖1, 𝐾𝑖2, … 𝐾𝑖8which repre-
sent the integral time constants.
4. Grey Wolf Optimizer
The Grey Wolf Optimizer (GWO) is a population-based me-
taheuristic algorithm inspired by the social behaviour of
grey wolves, first introduced by Mirjalili et al. in 2014 [22].
This algorithm simulates both the leadership structure and
the cooperative hunting strategies of grey wolves in their
natural habitat. Grey wolves typically live in packs with a
distinct hierarchy, as depicted in Fig. 8.
Fig. 8. Hierarchy of a grey wolf pack (Mirjalili et al., 2014)
[22]
4.1. Mathematical model
Let M represent the number of wolves in the pack and let
𝑋𝑖 = [𝑋1, 𝑋2, … , 𝑋𝑘] denote the position vector of the i-th
wolf, where K is the dimensionality of the problem being
addressed. The model used to update each wolf's position
based on the encircling behaviour is given by Equations (31)
and (32).
𝐷 = |𝐶. 𝑋𝑃(𝑡) − 𝑥(𝑡)| (31)
𝑥(𝑡 + 1) = 𝑋𝑃(𝑡) − 𝐴. 𝐷 (32)
Here, t represents the current iteration, 𝑥(𝑡) denotes the
wolf's current position, and 𝑋𝑃(𝑡) is the prey's position. The
vectors A and C are calculated using Equations (33) and
(34), respectively.
𝐴 = 2. 𝑎𝑟1 − 𝑎 (33)
𝐶 = 2. 𝑟2 (34)
𝑎 = 2 − (𝑖𝑡𝑒𝑟 × (
2
𝑀𝑎𝑥𝑖𝑡𝑒𝑟
)) (35)
Here, 𝑟1 and 𝑟2 are random vectors with values in the range
[0,1], and a is a vector whose components decrease linearly
from 2 to 0 throughout the algorithm's execution. Fig. 9(a)
shows the encircling behaviour of wolves during a hunt in a
2D scenario. Each wolf updates its position based on the
estimated location of the prey and can move to various new
positions depending on the vectors A and C. However, the
precise location of the prey (i.e., the optimal solution to the
problem at hand) remains unknown. As previously noted,
the hunting process is directed by the α, β, and δ wolves.
To model this characteristic, the GWO algorithm assumes
that the α, β, and δ wolves—representing the candidate so-
lutions with the best fitness values—have a more precise
understanding of the prey's location. Consequently, the po-
sition of each wolf is updated based on the positions of the
α, β, and δ wolves, as illustrated in Equations (36–42).
𝐷𝛼 = |𝐶1. 𝑋𝛼 − 𝑋| (36)
𝐷𝛽 = |𝐶1. 𝑋𝛽 − 𝑋| (37)
𝐷𝛿 = |𝐶1. 𝑋𝛿 − 𝑋| (38)
𝑋1 = 𝑋𝛼 − 𝐴1𝐷𝛼 (39)
𝑋2 = 𝑋𝛽 − 𝐴2𝐷𝛽 (40)
𝑋3 = 𝑋𝛿 − 𝐴3𝐷𝛿 (41)
𝑋(𝑡 + 1) = 𝑋1+𝑋2 + 𝑋3 (42)
(a)
(b)
Fig. 9. (a) Encircling behaviour of a pack (b) Position up-
date in the grey wolf optimizer algorithm (adapted from
Mirjalili et al., 2014)
Fig. 9 (b) depicts the process of updating the positions of
the wolves. Algorithm 1 provides the pseudocode for im-
plementing the GWO algorithm.
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Grey Wolf Optimization (GWO) Algorithm
Initialize population (𝑋) of grey wolves randomly in search space
Define maximum number of iterations (𝑀𝑎𝑥_𝑖𝑡𝑒𝑟), the number of wolves (𝑛) and problem dimension (𝑑)
Calculate fitness of each wolf in the population
Identify 𝑋𝛼 (best), 𝑋𝛽(second best), and 𝑋𝛿 (third best) wolves
Start main optimization loop
for 𝑖𝑡𝑒𝑟 = 1 𝑡𝑜 𝑀𝑎𝑥_𝑖𝑡𝑒𝑟
Update the positions of the remaining wolves for each wolf i in the population for each dimension j
for each wolf 𝑖 in the population
for each dimension 𝑗
Compute coefficients 𝑎, 𝐴 𝑎𝑛𝑑 𝐶
Compute distances to 𝛼, 𝛽 𝑎𝑛𝑑 𝛿 (𝐷𝛼, 𝐷𝛽 𝑎𝑛𝑑 𝐷𝛿)
Compute new position 𝑋𝑛𝑒𝑤 using 𝑋1, 𝑋2 𝑎𝑛𝑑 𝑋3
end
end
Apply boundary constraints
Evaluate new fitness values
Update 𝑋𝛼 (best), 𝑋𝛽(second best), and 𝑋𝛿 (third best) based on new fitness values
Replace old population with new positions
Store the best solution found so far
Best Solution = Alpha
end
Output the best solution
Return Best Solution
5. Simulation Results
This section presents simulation results validating the ef-
fectiveness of the proposed GWO-based control method. A
key performance metric is maintaining DC bus voltage and
active/reactive power within specified ranges under differ-
ent Microgrid (MG) operating modes. Simulations are con-
ducted in MATLAB/SIMULINK, with system specifications
shown in Table 1. To demonstrate superiority, GWO is com-
pared with Genetic Algorithm [23], PSO [24], and Ziegler-
Nichols (ZN) [25]. The control strategy from Section 3 is ap-
plied to the system in Fig. 1, using optimized PI gains. Table
2 presents these gains for different algorithms. Three test
cases evaluate the proposed method: (1) Irradiance, tem-
perature and wind speed changes, (2) reference active and
reactive power changes, and (3) Load changes. Fig. 10 (a)
presents the comparison of active and reactive power
tracking performance with proposed GWO and conven-
tional ZN, GA and PSO algorithms. Fig. 10 (b) presents the
comparison of DC link voltage tracking performance with
proposed GWO and conventional ZN, GA and PSO algo-
rithms. Tuned PI controller gains are presented in Table 2.
Comparison of performance indices between proposed al-
gorithm and conventional algorithms from literature is pre-
sented in Table 3.
Table 1. Parameters of the Hybrid DG system
Parameter Value
PV Array
Manufacturer and Model LG, LG350N2W-B3
Open Circuit Voltage (𝑉𝑜𝑐) 48,1 V
Short Circuit Current (𝐼𝑠𝑐) 9,74 A
Parameter Value
Maximum power point
voltage (𝑉𝑚𝑝𝑝)
37,9 V
Maximum power point
current (𝐼𝑚𝑝𝑝)
9,24 A
Series-connected modules
per string
43
Parallel strings 10
PMSG
Stator Resistance 0,8634
Stator Inductance 0,8121 µH
Torque Constant 4,82
Inertia 0,0027
Wind Turbine
Mechanical output power 150 kW
Base wind speed 11 m/s
Rotor diameter 24,5 m
Swept rotor area 480 m2
Battery
Nominal voltage 600
Rated capacity 800
Grid 11 kV, 50 Hz
6.1. Case 1: Analysis of Irradiance, Temperature, and Wind
Speed Variations
In this case, variations in irradiance, temperature, and wind
speed are analysed to assess their impact on the generated
power from the photovoltaic (PV) and wind energy sys-
tems. The power output from the PV system is directly in-
fluenced by the irradiance and temperature levels, while
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the power generated by the wind system depends on the
variations in wind speed. The irradiance and temperature
start at 200 W/m² and 30°C, respectively, from 0 to 4 sec-
onds. These values then increase to 400 W/m² and 32°C,
followed by further increments to 600 W/m² and 34°C be-
tween 4 to 8 seconds. The irradiance continues to rise to
800 W/m² and 36°C between 8 to 12 seconds and finally
reaches 1000 W/m² and 38°C at 12 to 20 seconds.
Table 2. Optimized gains of PI controllers using proposed and various algorithms
Algorithm 𝐾𝑝1, 𝐾𝑖1 𝐾𝑝2, 𝐾𝑖2 𝐾𝑝3, 𝐾𝑖3 𝐾𝑝4, 𝐾𝑖4 𝐾𝑝5, 𝐾𝑖5 𝐾𝑝6, 𝐾𝑖6 𝐾𝑝7, 𝐾𝑖7 𝐾𝑝8, 𝐾𝑖8
Proposed
GWO
0,8221
5,9568
1,8265
4,4410
0,9588
1,0731
1,7920
2,2863
0,2962
1,4625
1,0033
1,4135
0,9098
2,5126
0,5197
2,2459
PSO
0,4517
7,9595
2,1464
5,1731
0,7417
1,0570
1,6142
2,.6405
0,1328
1,5571
0,7457
2,4346
1,5295
1,9126
1,1673
1,9816
GA
0,6283
7,3236
2,0684
5.0611
0,7837
1,6274
1,0361
2,5383
0,3039
1.8097
0,49590
2.09410
1,6852
2.9816
1,3414
2.7502
Ziegler Nich-
olas
0,6695
7,7959
1,63765
4,4723
0,7403
1,1844
0,6690
2,9526
0,33917
2,2928
0,5989
2,0129
1,4019
3,2008
1,6861
2,7817
Table 3. Comparison of performance indices between proposed algorithm and previous algorithms from literature
Algo-
rithm
DC Bus Voltage Active Power Reactive Power
IAE ISE ITAE ITSE IAE ISE ITAE ITSE IAE ISE ITAE ITSE
Pro-
posed
GWO
0,0514 0,0279 0,0167 0,01264 0,0598 0,0477 0,0149 0,0037 0,0451 0,0342 0,0135 0,0146
PSO 0,0456 0,0212 0,0213 0,0056 0,0353 0,0354 0,0028 0,0037 0,0381 0,01827 0,01588 0,01957
GA 0,04881 0,03369 0,01573 0,01690 0,04378 0,03715 0,01100 0,00872 0,04631 0,02157 0,01105 0,01088
Ziegler
Nicho-
las
0,12596 0,05242 0,03170 0,02325 0,17925 0,09551 0,04475 0,00988 0,19109 0,096691 0,054999 0,01500
Similarly, the wind speed varies dynamically over time, be-
ginning at 8 m/s from 0 to 3 seconds, increasing to 9 m/s
between 3 to 6 seconds, and further rising to 10 m/s from
6 to 8 seconds. It continues increasing to 11 m/s between 8
to 12 seconds and peaks at 12 m/s from 12 to 15 seconds.
After this peak, the wind speed starts decreasing, first drop-
ping to 10 m/s between 15 to 18 seconds, and finally reduc-
ing back to 8 m/s from 18 to 20 seconds. These variations
in irradiance, temperature, and wind speed are illustrated
in Fig. 11 (a). The impact of these variations on the power
generated by the PV and wind systems is shown in
Fig. 11 (b). The power output from the PV system is directly
proportional to irradiance and temperature, while the wind
power is proportional to wind speed. As the irradiance and
temperature increase, the PV system generates more
power, and similarly, the wind system produces higher
power as wind speed increases. However, the battery
power output is governed by the reference active and reac-
tive power settings provided to the voltage source con-
verter (VSC). In the initial phase, when the total power gen-
erated by PV and wind systems is insufficient to meet the
reference power demand of the VSC, the battery discharges
to supply the shortfall. This is indicated by the positive bat-
tery terminal power before 8 seconds, which implies that
(a) (b)
Fig. 10. (a) active and reactive power comparison (b) DC link voltage comparison
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the battery is in a discharging state. As the irradiance and
wind speed continue to increase, leading to higher power
generation from PV and wind sources, the total generated
power exceeds the reference value after 8 seconds. At this
point, the battery enters a charging state, and its terminal
power turns negative. The battery’s state of charge (SOC)
increases during this phase, as shown in Fig. 14, whereas
during the discharging phase, the SOC decreases.
The reference active and reactive power values provided to
the VSC control strategy are set at 150 kW and 100 kVAr,
respectively, as depicted in Fig. 12 (a). To maintain these
power levels at the VSC AC terminals, the sum of power
from PV, wind, and battery must match these reference
values. Up to 8 seconds, when PV and wind generation are
lower than the reference demand, the battery compen-
sates by discharging. After 8 seconds, as PV and wind gen-
eration exceed the reference requirement, the battery
starts charging. The effectiveness of the VSC in maintaining
the reference power levels is further validated through
Fig. 12 (b), which illustrates the active and reactive power
consumed by the connected load. The load power require-
ments are 250 kW of active power and 120 kVAR of reactive
power. However, the VSC provides only 150 kW and 100
kVAR, as dictated by the reference inputs. The remaining
power required by the load is sourced from the grid, as
demonstrated in Fig. 13 (a).
(a) (b)
Fig. 11. (a) Irradiance, temperature input to the PV system and wind speed input to the wind generation system (b)
generated power from PV, wind and terminal power of the battery
Maintaining a stable DC link voltage is crucial for the
proper operation of the VSC and the overall system.
Fig. 13 (b) shows the DC link voltage and its reference
value. The VSC control strategy effectively regulates the
DC voltage, ensuring that it remains within acceptable
limits despite fluctuations in power generation and de-
mand. Additionally, power quality is an essential aspect of
system performance. The total harmonic distortion (THD)
levels of different components in the system are pre-
sented in Fig. 15 (a–c).
(a) (b)
Fig. 12. (a) Reference and actual active and reactive power converted by the VSC (b) Load active and reactive powers
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Відновлювана енергетика. № 4/2025 | Комплексні проблеми енергетичних систем на основі НВДЕ
The THD of the load current is 1.99%, the THD of the VSC
current is 1.94%, and the THD of the grid current is 1.28%.
These values indicate that the proposed control strategy
ensures minimal distortion, thereby improving the overall
power quality of the system. The analysis of Case 1 demon-
strates the impact of irradiance, temperature, and wind
speed variations on a hybrid energy system comprising PV,
wind, and battery storage. The system effectively balances
power generation and demand by utilizing battery storage to
compensate for generation shortfalls and surplus energy.
The VSC maintains reference active and reactive power lev-
els while ensuring stable DC link voltage. Moreover, the THD
values confirm the effectiveness of the control strategy in
maintaining power quality within permissible limits.
(a) (b)
Fig. 13. (a) Active and reactive powers provided by the grid (b) DC Link Voltage
Fig. 14. State of charge of the battery in %
(a)
(b)
(c)
Fig. 15. (a) load current (b) VSC current and (c) grid current
THDs
6.2. Case 2: Analysis of reference active and reactive
power variations
In this case, the irradiance, temperature, and wind speed
are considered constant throughout the simulation. As a re-
sult, the power generated from both the photovoltaic (PV)
and wind energy systems remains unchanged. The primary
objective of this case is to evaluate the efficacy of the tuned
PI controller gains optimized using the GWO algorithm by
varying the reference active and reactive power inputs to
the control strategy of the VSC.As shown in Fig. 16 (a), the
system operates under a constant irradiance of 1000 W/m²,
a temperature of 34°C, and a wind speed of 12 m/s. These
constant environmental conditions ensure that the power
outputs from the PV and wind generation systems remain
stable, eliminating any fluctuations caused by external
weather changes. This allows for a focused assessment of
the PI controller’s performance under dynamically chang-
ing power reference conditions.
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(a) (b)
Fig. 16. (a) Irradiance, temperature input to the PV system and wind speed input to the wind generation system (b) gen-
erated power from PV, wind and terminal power of the battery
The power outputs from the PV and wind systems, along with
the battery terminal power, are illustrated in Fig 16 (b). Since
the power generated from PV and wind remains constant, the
battery terminal power is adjusted dynamically based on the
reference power inputs to the VSC control strategy. The refer-
ence active and reactive power values are varied as follows: 0
to 3 seconds: 50 kW and 40 kVAr, 3 to 6 seconds: 80 kW and
60 kVAr, 6 to 9 seconds: 120 kW and 90 kVAr, 9 to 12 seconds:
150 kW and 140 kVAr, 12 to 15 seconds: 180 kW and 140 kVAr,
15 to 18 seconds: 240 kW and 200 kVAr, After 18 seconds: 150
kW and 120 kVAr. To achieve these reference power levels at
the AC terminals of the VSC, the battery's terminal power must
be adjusted accordingly, as depicted in Fig. 16(b). The battery’s
operation depends on the relationship between the total
power generated from PV and wind and the reference power
demand. Before 15 seconds and after 18 seconds, the total
power generated by PV and wind exceeds the reference
power demand. As a result, the excess power is stored in the
battery, putting it in a charging mode. However, between 15
to 18 seconds, the reference power demand surpasses the
power generated by PV and wind. In this scenario, the battery
enters a discharging mode, supplying the additional required
power. This dynamic adjustment ensures that the system
maintains a balance between power generation and con-
sumption. The reference and actual powers converted by the
VSC are presented in Fig. 17 (a).
(a) (b)
Fig. 17. (a) Reference and actual active and reactive power converted by the VSC (b) Load active and reactive powers
The tuned PI controller ensures that the VSC closely tracks
the reference power values, demonstrating the effectiveness
of the GWO-optimized gains in achieving accurate power
conversion. The load's active and reactive power require-
ments are illustrated in Fig. 17 (b). Since the converted
power by the VSC exceeds the actual load demand, the sur-
plus power is directed to the grid, as shown in Fig. 18 (a).
This highlights the system’s capability to efficiently manage ex-
cess power and contribute it to the grid when required. The
State of Charge (SOC) of the battery, represented in
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percentage, is depicted in Fig. 18 (b). During the period be-
tween 15 to 18 seconds, when the battery is in discharging
mode, the SOC decreases as stored energy is used to compen-
sate for the additional reference power demand. At all other
time instances, the SOC increases as the battery remains in
charging mode, storing the surplus power generated by the PV
and wind systems. This controlled charging and discharging
operation ensures efficient energy management and en-
hances the stability of the system. This case demonstrates the
effectiveness of the GWO-optimized PI controller gains in
regulating the power flow within the system. By maintaining
constant environmental conditions, the impact of dynamically
changing reference power inputs on the system’s perfor-
mance was evaluated. The battery efficiently transitions be-
tween charging and discharging modes based on the power
demand, ensuring system stability. Furthermore, the VSC ef-
fectively tracks the reference power values, and any surplus
energy is successfully transferred to the grid. The results vali-
date the robustness of the control strategy, optimizing energy
utilization while maintaining system reliability.
(a) (b)
Fig. 18. (a) Active and reactive powers provided by the grid (b) State of charge of the battery in %
6.3. Case 3: Analysis of Load Variation and System Response
In this case, the impact of load variation on system perfor-
mance is analysed. The active and reactive power demands
of the load fluctuate over time, as illustrated in Fig. 20 (a).
The variation in load power demand is structured as fol-
lows: 0 to 3 seconds: 50 kW and 40 kVAr, 3 to 6 seconds:
120 kW and 90 kVAr, 6 to 9 seconds: 180 kW and 120 kVAr,
9 to 12 seconds: 250 kW and 240 kVAr, 12 to 15 seconds:
300 kW and 250 kVAr, 15 to 18 seconds: 220 kW and
190 kVAr, After 18 seconds: 200 kW and 180 kVAr. Unlike
the previous case, where power reference values were al-
tered, in this scenario, the irradiance, temperature, and
wind speed remain constant throughout the simulation, as
shown in Fig. 19 (a). Consequently, the power outputs from
the PV and wind generation systems remain constant, as
depicted in Fig. 19 (b).
For this case, the reference active and reactive power val-
ues are set to a constant 150 kW and 140 kVAr, respec-
tively. Since these values remain unchanged, the power
converted by the VSC also remains constant, as illustrated
in Fig. 20 (a). The VSC ensures that the power delivered to
the system remains at the specified reference levels, irre-
spective of fluctuations in the load demand. The actual ac-
tive and reactive power consumption of the load is illus-
trated in Fig. 20 (b). Since the load demand varies over time
while the VSC-converted power remains constant, a power
balance mechanism is established through the interaction
with the grid. The grid active and reactive power flows are
depicted in Fig. 21 (a), which illustrates how the power
exchange between the system and the grid occurs based on
the load demand.
When the load requirement is lower than the power con-
verted by the VSC, the surplus power is exported to the grid.
Conversely, when the load requirement exceeds the power
converted by the VSC, the grid supplies the additional power
needed to meet the demand. This dynamic power exchange
ensures that the system remains stable and that the load al-
ways receives the required power. The State of Charge (SOC)
of the battery is presented in Fig. 21 (b).
Since the reference power (150 kW and 140 kVAr) is set
lower than the combined power generated by the PV and
wind systems, the battery remains in charging mode
throughout the simulation. This results in a continuous in-
crease in the SOC over time, as excess energy from the gen-
eration sources is stored in the battery. The charging behav-
ior of the battery ensures efficient utilization of surplus
power, preventing unnecessary wastage and enhancing sys-
tem efficiency. This case demonstrates the response of the
system to load variations while keeping the generation con-
ditions constant. The VSC effectively maintains constant
power conversion based on reference values, ensuring a sta-
ble power supply. The grid plays a crucial role in balancing
the power demand by either absorbing surplus energy or
supplying additional power when needed. The battery re-
mains in charging mode due to the surplus energy generated
from PV and wind sources, leading to an increase in SOC over
time. These results highlight the system’s ability to manage
load fluctuations efficiently while optimizing energy utiliza-
tion through battery storage and grid interaction.
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(a) (b)
Fig. 19. (a) Irradiance, temperature input to the PV system and wind speed input to the wind generation system (b) gen-
erated power from PV, wind and terminal power of the battery
(a) (b)
Fig. 20. (a) Reference and actual active and reactive power converted by the VSC (b) Load active and reactive powers
(a) (b)
Fig. 21. (a) Active and reactive powers provided by the grid (b) State of charge of the battery in %
33
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7. Conclusion
This study presents the application of Grey Wolf Optimiza-
tion (GWO) for tuning Proportional-Integral (PI) controllers
in a PV-Wind-Battery-based microgrid to enhance power
flow control and DC link voltage regulation. The integration
of renewable energy sources introduces dynamic and non-
linear variations in power generation, making conventional
PI tuning methods inadequate for achieving optimal system
performance. To address this challenge, the GWO algo-
rithm is employed to optimize the PI controller gains, lever-
aging its superior exploration and exploitation capabilities.
The proposed GWO-tuned PI controllers are implemented
in the Voltage Source Converter (VSC) control strategy,
where active and reactive power control is adopted for ef-
ficient energy distribution. Additionally, Perturb & Observe
(P&O) MPPT is used for PV power extraction, while an adap-
tive P&O MPPT is applied to the wind generation system to
ensure maximum power tracking under varying environ-
mental conditions. The performance of the GWO-based PI
controller is evaluated through extensive simulations and is
compared with conventional Ziegler-Nichols (ZN), Genetic
Algorithm (GA), and Particle Swarm Optimization (PSO)
based tuning approaches. Simulation results demonstrate
that the GWO-optimized PI controllers significantly im-
prove dynamic response, steady-state accuracy, and power
balance within the microgrid. The optimized controllers
achieve faster response times, reduced overshoot, and im-
proved DC link voltage stability, leading to enhanced sys-
tem reliability. Furthermore, battery charging and discharg-
ing behaviour is effectively regulated based on real-time
power generation and load variations, ensuring efficient
energy management. The GWO-based PI tuning approach
proves to be an effective optimization technique for power
flow control and DC link voltage regulation in microgrid sys-
tems with multiple renewable energy sources. The findings
of this study contribute to the advancement of intelligent
microgrid control strategies, enabling more resilient, sta-
ble, and efficient integration of renewable energy into
modern power systems. Future work can explore hybrid
optimization techniques and real-time hardware imple-
mentation to further validate the effectiveness of GWO-
based controllers in practical applications.
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| id | veorgua-article-572 |
| institution | Vidnovluvana energetika |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:17:21Z |
| publishDate | 2025 |
| publisher | Institute of Renewable Energy National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | veorgua/b0/c816272691406025278d8a0d895ddab0.pdf |
| spelling | veorgua-article-5722026-07-18T06:32:23Z OPTIMIZED PI CONTROL FOR POWER FLOW AND DC LINK VOLTAGE REGULATION IN A PV-WIND-BATTERY MICROGRID USING GREY WOLF OPTIMIZATION ОПТИМІЗОВАНЕ ПРОПОРЦІЙНО-ІНТЕГРАЛЬНЕ КЕРУВАННЯ ДЛЯ РЕГУЛЮВАННЯ ПОТОКУ ПОТУЖНОСТІ ТА НАПРУГИ ПОСТІЙНОГО ЛАНЦЮГА В МІКРОМЕРЕЖІ PV-ВІТРО-АКУМУЛЯТОРНОГО ТИПУ З ВИКОРИСТАННЯМ АЛГОРИТМУ ОПТИМІЗАЦІЇ «СІРИЙ ВОВК» Mogilicharla, Veera Narasimha Murthy Gudapati, Sambasiva Rao Grey Wolf Optimization (GWO), PI Controller Tuning, Power Flow Control, DC Link Voltage Regulation, PV-Wind-Battery Microgrid, Voltage Source Converter (VSC) Control алгоритм оптимізації «Сірий вовк» (GWO); ПІ-регулятор; керування потоком потужності; регулювання напруги постійного ланцюга; мікромережа PV-вітро-акумуляторного типу; керування перетворювачем напруги (VSC). Microgrids have become essential in modern power systems, enabling reliable and sustainable energy distribution while operating independently or with the main grid. The growing integration of renewable sources like photovoltaic (PV) and wind energy, along with battery storage, necessitates advanced control strategies for efficient power management and grid stability. This paper presents an optimized power flow control strategy for a PV-Wind-Battery hybrid microgrid using a Voltage Source Converter (VSC) to regulate active and reactive power while maintaining DC link voltage stability. A Proportional-Integral (PI) controller plays a crucial role in ensuring system performance under varying conditions. However, conventional PI tuning is challenging due to the nonlinear nature of renewable energy sources. To overcome this, an optimized tuning approach based on the Grey Wolf Optimization (GWO) algorithm is proposed. Inspired by the social structure and hunting behaviour of grey wolves, GWO efficiently balances exploration and exploitation to determine optimal control gains. The PV system employs Perturb and Observe (P&O) Maximum Power Point Tracking (MPPT), while an adaptive P&O MPPT strategy is used for wind energy to maximize power extraction. The battery storage system dynamically switches between charging and discharging to maintain power balance. The GWO-based PI controller is compared with conventional methods, including Ziegler-Nichols (ZN), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO). Simulation results demonstrate superior transient response, reduced steady-state error, and minimized power fluctuations. Additionally, Total Harmonic Distortion (THD) analysis confirms lower harmonic distortion, enhancing power quality and system reliability, making GWO a promising approach for microgrid optimization. Мікромережі стали невід’ємною складовою сучасних енергетичних систем, забезпечуючи надійний і стійкий розподіл електроенергії як у режимі автономної роботи, так і при підключенні до основної мережі. Зростання частки відновлюваних джерел енергії, зокрема фотоелектричних (PV) і вітрових систем, у поєднанні з акумуляторними сховищами потребує вдосконалених стратегій керування для підвищення ефективності енергорозподілу та стабільності мікромережі.У цій роботі запропоновано оптимізовану стратегію керування потоком потужності для гібридної мікромережі PV-вітро-акумуляторного типу з використанням перетворювача напруги (VSC), який регулює активну та реактивну потужність, а також стабілізує напругу постійного ланцюга. Ключову роль у забезпеченні стабільної роботи системи відіграє пропорційно-інтегральний (ПІ) регулятор. Проте традиційне налаштування ПІ-регулятора є складним через нелінійність характеристик відновлюваних джерел. Для вирішення цієї проблеми запропоновано використати алгоритм оптимізації «Сірий вовк» (Grey Wolf Optimization, GWO), який ефективно визначає оптимальні коефіцієнти регулятора завдяки поєднанню пошукової та експлуатаційної поведінки.У PV-системі реалізовано метод відстеження точки максимальної потужності (MPPT) «збурення та спостереження» (Perturb and Observe, P&O), тоді як для вітрової системи застосовано адаптивну стратегію P&O MPPT з метою максимізації виробітку енергії. Акумуляторна система автоматично перемикається між режимами заряджання та розряджання для підтримання енергетичного балансу.Результати моделювання показали, що ПІ-регулятор, налаштований за допомогою алгоритму GWO, має кращі перехідні характеристики, меншу похибку в сталому режимі та знижені коливання потужності порівняно з традиційними методами налаштування (Ziegler-Nichols, Genetic Algorithm, Particle Swarm Optimization). Аналіз гармонічних спотворень (THD) засвідчив нижчий рівень гармонік, що сприяє підвищенню якості електроенергії та надійності системи.Таким чином, застосування алгоритму GWO можна вважати перспективним підходом до оптимізації мікромереж у сфері відновлюваної енергетики. Institute of Renewable Energy National Academy of Sciences of Ukraine 2025-12-27 Article Article application/pdf https://ve.org.ua/index.php/journal/article/view/572 10.36296/1819-8058.2025.4(83).18-33 Vidnovluvana energetika ; No. 4(83) (2025): Scientific and applied Journal renewable energy ; 18-33 Возобновляемая энергетика; ##issue.no## 4(83) (2025): Scientific and applied Journal renewable energy ; 18-33 Відновлювана енергетика; № 4(83) (2025): Науково-прикладний журнал Відновлювана енергетика; 18-33 2664-8172 1819-8058 10.36296/1819-8058.2025.4(83) en https://ve.org.ua/index.php/journal/article/view/572/483 Copyright (c) 2025 Veera Narasimha Murthy Mogilicharla, Sambasiva Rao Gudapati https://creativecommons.org/licenses/by-nc-nd/4.0 |
| spellingShingle | Grey Wolf Optimization (GWO) PI Controller Tuning Power Flow Control DC Link Voltage Regulation PV-Wind-Battery Microgrid Voltage Source Converter (VSC) Control Mogilicharla, Veera Narasimha Murthy Gudapati, Sambasiva Rao OPTIMIZED PI CONTROL FOR POWER FLOW AND DC LINK VOLTAGE REGULATION IN A PV-WIND-BATTERY MICROGRID USING GREY WOLF OPTIMIZATION |
| title | OPTIMIZED PI CONTROL FOR POWER FLOW AND DC LINK VOLTAGE REGULATION IN A PV-WIND-BATTERY MICROGRID USING GREY WOLF OPTIMIZATION |
| title_alt | ОПТИМІЗОВАНЕ ПРОПОРЦІЙНО-ІНТЕГРАЛЬНЕ КЕРУВАННЯ ДЛЯ РЕГУЛЮВАННЯ ПОТОКУ ПОТУЖНОСТІ ТА НАПРУГИ ПОСТІЙНОГО ЛАНЦЮГА В МІКРОМЕРЕЖІ PV-ВІТРО-АКУМУЛЯТОРНОГО ТИПУ З ВИКОРИСТАННЯМ АЛГОРИТМУ ОПТИМІЗАЦІЇ «СІРИЙ ВОВК» |
| title_full | OPTIMIZED PI CONTROL FOR POWER FLOW AND DC LINK VOLTAGE REGULATION IN A PV-WIND-BATTERY MICROGRID USING GREY WOLF OPTIMIZATION |
| title_fullStr | OPTIMIZED PI CONTROL FOR POWER FLOW AND DC LINK VOLTAGE REGULATION IN A PV-WIND-BATTERY MICROGRID USING GREY WOLF OPTIMIZATION |
| title_full_unstemmed | OPTIMIZED PI CONTROL FOR POWER FLOW AND DC LINK VOLTAGE REGULATION IN A PV-WIND-BATTERY MICROGRID USING GREY WOLF OPTIMIZATION |
| title_short | OPTIMIZED PI CONTROL FOR POWER FLOW AND DC LINK VOLTAGE REGULATION IN A PV-WIND-BATTERY MICROGRID USING GREY WOLF OPTIMIZATION |
| title_sort | optimized pi control for power flow and dc link voltage regulation in a pv-wind-battery microgrid using grey wolf optimization |
| topic | Grey Wolf Optimization (GWO) PI Controller Tuning Power Flow Control DC Link Voltage Regulation PV-Wind-Battery Microgrid Voltage Source Converter (VSC) Control |
| topic_facet | Grey Wolf Optimization (GWO) PI Controller Tuning Power Flow Control DC Link Voltage Regulation PV-Wind-Battery Microgrid Voltage Source Converter (VSC) Control алгоритм оптимізації «Сірий вовк» (GWO) ПІ-регулятор керування потоком потужності регулювання напруги постійного ланцюга мікромережа PV-вітро-акумуляторного типу керування перетворювачем напруги (VSC). |
| url | https://ve.org.ua/index.php/journal/article/view/572 |
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