Journal of Energy Storage 82 (2024) 110521
Contents lists available at ScienceDirect
Journal of Energy Storage
journal homepage: www.elsevier.com/locate/est
Research papers
Hierarchical control combined with higher order sliding mode control for
integrating wind/tidal/battery/hydrogen powered DC offshore microgrid
Naghmash Ali, Xinwei Shen ∗, Hammad Armghan, Yunfei Du
Tsinghua Shenzhen International Graduate School, Tsinghua University, China
ARTICLE
INFO
Keywords:
Energy storage system
Nonlinear control
Fuel cell
Offshore microgrid
Integral Terminal Sliding Mode Control
ABSTRACT
Due to the intermittent nature of renewable energy sources, energy storage devices play a key role in achieving
power balance for microgrid. To reduce the overall carbon footprint, this paper considers fuel cells and batteries
as auxiliary sources with wind and tidal energy as primary sources. A two-stage control system has been
designed, which has been subdivided into system-level and local-level control systems. The system-level control
includes an energy management system that optimizes load distribution, minimizes system cost, and meets
battery state of charge and hydrogen level constraints. To make the microgrid independent and minimize
transportation costs, on-site hydrogen production has been deployed using an electrolyzer system. At the local
level, a fast reaching law-based terminal sliding mode controller has been implemented for accurate and robust
tracking of the references provided by the system-level control. The stability of the proposed framework has
been validated using the Lyapunov stability criteria. The proposed 600 V and 400 kW microgrid structure
has been realized using MATLAB/Simulink simulations. Furthermore, the effectiveness of the proposed control
scheme has been compared with PID and ITSMC in terms of accuracy and robustness under both power deficit
and surplus modes. Finally, the real-life efficacy has been validated by utilizing controller hardware-in-loop
experiments.
1. Introduction
Currently, the majority (80%) of primary energy consumption is
dependent on non-renewable fossil fuels, with coal power plants alone
accounting for 27% of this consumption [1]. This dependence on fossil
fuels poses the threat to future energy demands due to the finite supply
of these resources and has negative impacts on economic security [2].
To address this challenge, renewable energy sources (RESs) provide
a promising solution for reducing fossil fuel consumption and decarbonizing the energy sector. As of 2020, the global installed capacity of
renewable energy surpassed 2.7 TW, with significant growth in wind
and solar energy [3]. Recent research highlights marine renewable
energy as an emerging avenue for development [4]. Implementation
of marine energy plants on a global scale could potentially generate an
impressive 20,000 TWh of electricity annually [5].
Offshore microgrids (MGs) have been gaining popularity as a means
to achieve carbon-neutral power systems in remote and isolated areas,
thus transforming the paradigm of future electric power systems [6].
By working as a decentralized unit, offshore MGs have the potential to
reduce transmission losses, leading to lower energy cost and improved
energy reliability. Depending on the region requirements, the MG can
be configured with AC Bus, DC Bus or with hybrid AC/DC Bus system.
However, the DC MGs offer several benefits, such as the capability
to connect distributed energy resources (DER), energy storage systems
(ESS), and loads without the need for DC/AC conversions. This leads to
increased efficiency and stability [7,8]. Additionally, the management
and control of DC microgrids are simpler, and they do not face common
power quality issues associated with AC microgrids, such as frequency
synchronization and harmonic currents [9].
Despite the advantages offered by DC MGs, power generation from
offshore RESs, such as wind and tidal energy, is significantly impacted
by environmental conditions, leading to fluctuations and intermittent
power generation [10]. To mitigate these issues, ESSs, such as battery
systems and fuel cells (FCs), have been employed in DC microgrids as
an auxiliary energy source (AES) [11]. To meet the hydrogen requirement for the FC system especially in remote or isolated areas, a local
or on-site hydrogen production system can be implemented using the
power from RESs. This on-site production of hydrogen not only reduces
transportation costs but also makes the overall MGs independent, acting
as a decentralized unit. Several significant offshore wind-to-hydrogen
projects have been launched, including the PosHYdon project in the
∗ Corresponding author.
E-mail addresses: naghmash@sz.tsinghua.edu.cn (N. Ali), xwshen@tsinghua.edu.cn (X. Shen), hammad.armghan@sz.tsinghua.edu.cn (H. Armghan),
duyf23@mails.tsinghua.edu.cn (Y. Du).
https://doi.org/10.1016/j.est.2024.110521
Received 16 September 2023; Received in revised form 3 January 2024; Accepted 7 January 2024
Available online 17 January 2024
2352-152X/© 2024 Elsevier Ltd. All rights reserved.
Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Dutch North Sea, which is the first offshore hydrogen production plant
to deploy at least a 1 MW electrolyzer [12]. The SeaH2Land project
aims to develop one of the world’s largest renewable hydrogen plants,
with 2 GW offshore wind capacity and 1 GW electrolyzer, to supply the
hydrogen demand of the Dutch-Flemish industrial cluster [13]. Furthermore, the Surf ‘n’ Turf project has built the first tidal-powered hydrogen
production system at EMEC’s tidal test site [14]. These projects demonstrate the feasibility of utilizing offshore wind-to-hydrogen technology
as a viable solution to meet the increasing power demand.
Due to integration of multiple RESs and hydrogen production systems, MGs have become more complex, requiring advanced and sophisticated energy management system (EMS) to realize maximum power
from the RESs and distribute the load requirements among individual
DER. To simplify the control mechanism, the EMS can be designed
using advanced hierarchical control methods, splitting it into systemlevel control and local-level control. At system level, the EMS optimizes
energy costs from different sources, manages power system constraints
such as maintaining battery state of charge (SOC) and H2 storage level,
and achieves power balance by distributing the connected load among
interfaced DERs. In [15], the authors have proposed an EMS for a
standalone DC MG comprising a PV/FC/battery system to improve
longevity and reliability of battery system, while also reducing H2
intake. Different operational scenarios and experimental results are
shown to demonstrate efficacy in real-life. However, the authors did not
consider the DC–DC converter dynamics, battery SOC, and hydrogen
storage constraints, such that the final level should meet the initial
level, which is mandatory for a standalone system. Using meta-heuristic
algorithms like the hybrid bat search algorithm [16] and cuckoo search
algorithm [17], the authors have presented an EMS for DC MGs comprised of composite ESS. However, the problem with meta-heuristic
algorithms is that there are scenarios where these algorithms can be
trapped in local maxima, leading to lower system efficiency [18,19]. To
address this limitation, dynamic programming (DP) has been utilized
to design EMS for MGs. Unlike meta-heuristic algorithms, DP ensures
that the global maxima is achieved instead of getting trapped in local
maxima. In [20,21], the authors applied DP to identify the best control
strategy and optimal sizing for distributed energy resources (DERs) in
an electric-hydrogen-based microgrid. This approach not only provides
highly accurate results but also requires less computational power.
However, it is important to note that the authors focused on upperlevel system control and did not consider the local-level control and
power electronics converter dynamics, which play a crucial role in
ensuring grid stability [22]. Based on Fuzzy Logic Control (FLC), the
EMS system for various DC MGs has been presented [23,24]. Although
the authors provided a detailed control system analysis but due to the
limited simulation time window, the article lacks an in-depth analysis
of the connected energy sources. Additionally, the issue with FLC is that
a comprehensive rule-based table is mandatory to achieve satisfactory
results, which incurs high computational costs.
At the local level, robust and intelligent control systems are required to track reference signals provided by the upper system level
EMS. In the case of DC MG, local level control must be capable
of regulating DC bus voltage and track the required current levels
to drive the RESs at their maximum power point (MPP) and regulate the power from AES to meet load requirements. Conventionally,
linear controllers such as PID have been used to track these signals. But these linear PID controllers have limited regulating area
and produce overshoot/undershoot during sudden changes. To overcome these issues, several non-linear controllers have been developed
based on the Lyapunov stability criteria [25–27]. These includes an
integral backstepping technique, presented by the author in [28] for
PV/Wind energy based DC MG. Although these controllers are effective
in tracking required references, the design process is complicated and
cumbersome. Owing to the simplicity and robustness of sliding mode
control (SMC) theory, various high order controller have been devised
for DC–DC converters [29,30]. These higher-order SMCs, such as Terminal SMC (TSMC) [31] and Supertwisting SMC (STSMC) [32], not only
have the ability to be robust to external disturbances but also have a
quick transient response in case of a sudden change in the reference
signal. Additionally, the recent novelties in the reaching laws for these
higher order SMC has greatly reduced the inherent chattering problem
of the SMC [33,34].
The above discussion leads to the conclusion that for an offshore
DC MG having multiple RESs and hydrogen production system, an
advanced hierarchical control based on an optimized EMS and robust
local level tracking should be devised. Based on these objectives, this
study considers Wind Energy System (WES) and Tidal Energy System
(TES) as RESs. These WES and TES are selected on the fact that not
only these RESs can be easily implemented offshore but the predictable
nature of tidal current speed ease up the optimization and planning
process. Additionally, for an in-depth analysis of this MG, the system
level controller has been simulated in hours/minutes and local level
controller in milliseconds. The core objective of this research is to design an optimized two-stage hierarchical control for an offshore DC MG.
On the system level EMS, the cost optimization of DERs that includes
offshore WES and TES, battery units, FC and hydrogen production
system has been performed. On the local level control, fast reaching
law based integral terminal sliding mode controller (FRL-ITSMC) has
been designed to track the references from the upper system level EMS
and provide accurate and quick transient response to any disturbance
in real-time. The major contributions can be summarized as follows:
1. The research article describes the detailed mathematical modeling of RESs, FC, battery, hydrogen production system and an
overall unified including the DC bus dynamics.
2. A two-level hierarchical control has been devised, with the upper
system level focusing on EMS of DERs to lower operational costs
and ensure power system stability constraints, while the FRLITSMC on the lower local level generates maximum power from
RES and stabilizes the DC bus by meeting load requirements
from AES.
3. A comparative analysis with existing literature has been presented to validate the robustness of FRL-ITMSC against varying
loads and environmental conditions.
4. Controller hardware-in-loop (C-HIL) simulations are provided to
validate the efficacy in real-life.
The research paper has be categorized as follows: Section 2 outlines
the system configuration. Sections 3 and 4 details the hierarchical
control strategy employed for system level and local level control
respectively. Section 5 discusses the results obtained under different
scenarios, and Section 6 draws the conclusion from the main findings
of this research article.
2. Mathematical modeling of DC MG
Fig. 1 shows the configuration of RESs and AES embedded in the
proposed offshore DC MG. The WES and TES have been considered
as the main energy sources (MES), while the FC, battery, and diesel
generator (DG) have been considered as AES. The WES and TES have
been interfaced with 600 V DC bus by boost converters to realize MPP
from these RESs. The battery system has been configured with a bidirectional DC–DC converter for realizing charging and discharging
modes. Due to uni-directional power flow, the FC has been interfaced
by a boost converter. Finally, the electrolyzer and DG have been linked
via buck converters to generate hydrogen from the renewable energy
and meet the load requirements, respectively. The MES, AES, and load
have been supervised by the proposed hierarchical control strategy to
ensure power system stability.
2
Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Fig. 1. Architecture of DC microgrid under study.
for TES. 𝐶𝑝 is the power coefficient that depends on blade pitch angle
𝛽 and function 𝜆, defined as follows:
𝜆=
𝜔𝑟 𝑅
𝑣𝑡
(2)
where 𝜔𝑟 and 𝑅 represents the rotor angular speed and its radius. By
substitution Eq. (2) into (1), 𝑃𝑚𝑒𝑐ℎ can be simplified as,
)
1 ( 3
𝑃𝑚𝑒𝑐ℎ =
𝜌𝜔𝑟 𝐴𝑅3 𝐶𝑝 (𝜆, 𝛽)
(3)
2𝜆3
The optimal torque control (OTC) technique is utilized in the MPPT
of WES and TES to generate controller reference. This technique involves adjusting the torque of PMSG to achieve the maximum reference
torque of turbine at a particular wind or ocean current speed, resulting
in high accuracy and easy implementation. Assuming optimal tipspeed ratio (𝜆𝑚 ) and maximum power coefficient (𝐶𝑝𝑚𝑎𝑥 ), the maximum
mechanical power (𝑃𝑚𝑝 ) can be yielded as [36],
Fig. 2. Circuit diagram and optimal torque control strategy for wind energy system.
)
1 ( 3
𝜌𝜔𝑟 𝐴𝑅3 𝐶𝑝𝑚𝑎𝑥 = 𝐾𝑝𝑚𝑝 𝜔3𝑟
2𝜆3𝑚
2.1. Modeling of WES and TES
𝑃𝑚𝑝 =
The WES and TES under consideration in this research, comprises
of wind and tidal turbines that interfaces with DC bus using permanent
magnet synchronous generator (PMSG), uncontrolled rectifier and DC–
DC boost converter. The configuration of WES and TES have been
shown in Figs. 2 and 3, respectively. The PMSG-based turbine system is
preferred due to its ease of control, uncomplicated structure, and costeffectiveness. Through the use of turbines and associated PMSG, the
WES and TES harness wind and ocean currents to generate electrical
energy respectively. The mechanical power from WES and TES can be
derived as follows [35]:
According to the power to torque relationship, the maximum attainable torque (𝑇𝑚𝑎𝑥 ) can be derived as,
)
1 ( 2
𝑇𝑚𝑎𝑥 =
𝜌𝜔𝑟 𝐴𝑅3 𝐶𝑝𝑚𝑎𝑥 = 𝐾𝑝𝑚𝑝 𝜔2𝑟
(5)
2𝜆3𝑚
𝑃𝑚𝑒𝑐ℎ =
0.5𝜌𝑣3𝑡 𝐴𝐶𝑝 (𝜆, 𝛽)
(4)
Additionally, the 𝑇𝑚𝑎𝑥 relationship can be utilized to generate the
TES/WES reference current 𝐼𝑟𝑒𝑓 as follows:
𝐼𝑟𝑒𝑓 =
𝑇𝑚𝑎𝑥 𝜔𝑟
𝑉𝑖𝑛
(6)
where 𝑉𝑖𝑛 is the input voltage of the WES/TES. Furthermore, based on
the WES/TES configuration with the DC Bus, the dynamical model can
be derived as:
(
(
))
𝑑𝑖𝑤𝑒𝑠
1
=
𝑉𝑤𝑒𝑠 − 𝑖𝑤𝑒𝑠 𝑅𝐿𝑤𝑒𝑠 − 𝑉𝑜𝑢𝑡 1 − 𝑑1
(7)
𝑑𝑡
𝐿𝑤𝑒𝑠
(1)
where 𝐴 and 𝑣𝑡 represents turbine blade area and wind/ocean current
speed, respectively. 𝜌 denotes air density for WES and water density
3
Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Fig. 3. Circuit diagram and optimal torque control strategy for tidal energy system.
Fig. 4. Configuration of fuel cell system using boost converter.
(
(
))
𝑑𝑖𝑡𝑒𝑠
1
𝑉𝑡𝑒𝑠 − 𝑖𝑡𝑒𝑠 𝑅𝐿𝑡𝑒𝑠 − 𝑉𝑜𝑢𝑡 1 − 𝑑2
=
𝑑𝑡
𝐿𝑡𝑒𝑠
(8)
(
)
𝑖1 = 1 − 𝑑1 𝑖𝑤𝑒𝑠
where 𝐾𝑚 represents modeling constant. Based on the PEMFC configuration with the DC MG, its dynamical model can be derived as
[29]:
(9)
𝑑𝑖𝑓 𝑐
𝑑𝑡
(
)
𝑖2 = 1 − 𝑑2 𝑖𝑡𝑒𝑠
(10)
=
𝑉𝑓 𝑐
−
𝐿𝑓 𝑐
𝑖𝑓 𝑐 𝑅𝐿𝑓 𝑐
𝐿𝑓 𝑐
(
)𝑉
− 1 − 𝑑3 𝑜𝑢𝑡
𝐿𝑓 𝑐
(14)
(15)
𝑖3 = 𝑖𝑓 𝑐 (1 − 𝑑3 )
where 𝑉𝑜𝑢𝑡 , 𝑅𝐿𝑤𝑒𝑠 , 𝑅𝐿𝑤𝑒𝑠 represents the DC bus voltage, WES inductor
(𝐿𝑤𝑒𝑠 ) ESR and TES inductor (𝐿𝑡𝑒𝑠 ) ESR. 𝑑1 and 𝑑2 are WES and TES
converters duty cycles. {𝑉𝑤𝑒𝑠 , 𝑉𝑡𝑒𝑠 } and {𝑖𝑤𝑒𝑠 , 𝑖𝑡𝑒𝑠 } are WES and TES
input voltage and current respectively.
where 𝑅𝐿𝑓 𝑐 , 𝑑3 and 𝑖3 represents inductor (𝐿𝑓 𝑐 ) ESR, converter duty
cycle and PEMFC subsystem output current, respectively.
2.2. Modeling of fuel cell
Electrolyzers are a crucial component of hydrogen energy systems
that utilize electrical power to produce H2 from water. The electrolyzer
has configured with DC bus via a buck converter, presented in Fig. 5.
The mathematical model of the electrolyzer is developed, based on
several assumptions, including the complete saturation of water vapor
in the electrolytic cells, constant temperature and pressure in the gas
flow channels of the cells, and separability of the liquid and gas phases.
The enthalpy of water vapor is assumed to be constant during operation, and energy consumption for water supply and H2 compression is
not taken into account. Additionally, the system’s operation has been
restricted by parasitic current losses, and it cannot operate at maximum
capacity. The current efficiency can be calculated using Faraday’s Law
as follows: [38].
2.3. Modeling of electrolyzer
In the proposed DC MG, the proton exchange membrane fuel cell
(PEMFC) is implemented to convert H2 into electrical energy. Due to
its quick response and reliability, PEMFC has been vital component
of the hydrogen power based MG. The PEMFC is configured with DC
bus via a DC–DC Boost Converter using a current control configuration,
presented in Fig. 4. The PEMFC generated voltage (𝑉𝑓 𝑐 ) and its internal
dynamics can be modeled as follows [37]:
𝑉𝑓 𝑐 = 𝐸𝑐𝑜𝑛 + 𝐸𝑜ℎ𝑚 + 𝐸𝑎 + 𝐸0
(
( ))
𝐸0 = 𝑁 𝐸𝑛 − 𝐴 ln 𝑖𝑒
𝐸𝑎 = ln
(11)
𝐸𝑜ℎ𝑚 = 𝑅𝑖 𝑖𝑓 𝑐
(
)
𝑖𝑓 𝑐 ( 1
)
𝜏𝑆 + 1
𝑖𝑒
𝜂𝑒 = 96.5 × 𝑒
where 𝐸𝑐𝑜𝑛 , 𝐸𝑜ℎ𝑚 , 𝐸𝑎 , 𝐸0 and 𝐸𝑛 represent concentrated voltage, ohmic
voltage, active over-voltage, open-circuit voltage, and Nernst instantaneous voltage, respectively. 𝑁 and 𝑖𝑒 is the total number PEMFCs and
their exchange current, respectively. 𝐴, 𝜏 and 𝑅𝑖 present tafel slope,
response time and its internal resistance. Furthermore, the hydrogen
utilization factor (𝑈H2 ) is a crucial parameter that ensures the smooth
and efficient operation of PEMFC. This factor can be determined by
𝑟𝑐 ) and injected hydrogen (𝑞 𝑖𝑛 ) inside
analyzing levels of reacted (𝑞H
H2
2
tank, as follows:
𝑟𝑐
𝑖𝑛
𝑈H2 = 𝑞H
∕𝑞H
2
2
2𝐾𝑚
≤ 𝑖𝑓 𝑐 ≤
𝑖𝑛
0.9𝑞H
2
2𝐾𝑚
(16)
𝜂𝑒 𝐼𝑒𝑙𝑐 𝑁𝑒𝑙𝑐
(17)
2𝐹
where 𝑁𝑒𝑙𝑐 and 𝐹 represents amount of electrolyzer cells and Faraday constants (96 487 C/mol). Additionally, based on the electrolyzer
configuration with DC MG, its dynamical model has been derived as,
𝑁 H2 =
To improve the PEMFC operating efficiency, 𝑈H2 should lie in
the range from 0.8 to 0.9. Over-utilization of hydrogen (𝑈H2 > 0.9)
will decrease the lifespan of the fuel cell, while under-utilization of
hydrogen (𝑈H2 < 0.8) will result in lower operating efficiency. Utilizing
these constraints, the optimal value of PEMFC current (𝑖𝑓 𝑐 ) constraint
equation can be derived as:
𝑖𝑛
0.8𝑞H
0.09 75.5
−
𝐼𝑒𝑙𝑐 𝐼 2
𝑒𝑙𝑐
where 𝜂𝑒 and 𝐼𝑒𝑙𝑐 denotes current efficiency and electrolyzer operating
current. Furthermore, the relationship between hydrogen production
rate 𝑁H2 (mol/s) and 𝐼𝑒𝑙𝑐 can be derived as,
(12)
2
)
(
𝑁𝐴
𝑑𝑖𝑒𝑙𝑐
𝑉
𝑅 𝑖
𝑑 𝑉
= − 𝑒𝑙𝑐 − 𝑒𝑙𝑐 𝑒𝑙𝑐 + 4 𝑜𝑢𝑡
𝑑𝑡
𝐿𝑒𝑙𝑐
𝐿𝑒𝑙𝑐
𝐿𝑒𝑙𝑐
(18)
𝑖4 = 𝑖𝑒𝑙𝑐 (𝑑4 )
(19)
2.4. Modeling of H2 tank
The H2 generated by electrolyzer has been stored in compressed
gas tank and then utilized by PEMFC for producing electrical energy.
The mathematical model of H2 pressure in tank can be calculated
(13)
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Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Fig. 7. Configuration of diesel generator system using buck converter.
Fig. 5. Configuration of electrolyzer system using buck converter.
of the implemented BESS system can be computed using the methods
described in [39,40].
𝑡
𝑆𝑂𝐶𝑏𝑎𝑡𝑡 = 𝑆𝑂𝐶𝑏0 +
using various factors such as ambient temperature (𝑇 ), the volume of
hydrogen stored (𝑉𝑡 ), and compressibility factor (𝑍 = 1.006).
𝑍𝑁H2 𝑅𝑇
𝑀H 2 𝑉 𝑡
(20)
𝑑𝑉𝑜𝑢𝑡 ( ) 𝑖𝑏𝑎𝑡𝑡
𝑖
= 𝑑56
− 5
𝑑𝑡
𝐶𝑜𝑢𝑡 𝐶𝑜𝑢𝑡
𝑃𝑡𝑎𝑛𝑘
𝑃𝑚𝑎𝑥
(23)
(26)
where 𝑑56 is a virtual control introduced to derive the unified model of
the BESS, calculated as,
(
)
𝑑56 = (1 − 𝛹 ) 𝑑6 + 𝛹 1 − 𝑑5
(27)
(21)
where 𝑀H2 and 𝐿𝐻𝑉 are the H2 molar mass and lower heat value
respectively. Finally, the H2 state of charge (𝑆𝑂𝐶H2 ) for upper system
level EMS can be calculated as the ratio between current tank pressure
𝑃𝑡𝑎𝑛𝑘 and maximum tank pressure 𝑃𝑚𝑎𝑥 .
𝑆𝑂𝐶H2 =
𝑖𝑏𝑎𝑡𝑡
𝑄𝑏𝑎𝑡𝑡
Based on the switch configuration and equation. (24), the dynamical
model of the BESS can be derived as:
( ) 𝑉𝑜𝑢𝑡
𝑑𝑖𝑏𝑎𝑡𝑡
𝑉
𝑅
= 𝑏𝑎𝑡𝑡 − 𝐿𝑏𝑎𝑡𝑡 𝑖𝑏𝑎𝑡𝑡 − 𝑑56
(25)
𝑑𝑡
𝐿𝑏𝑎𝑡𝑡
𝐿𝑏𝑎𝑡𝑡
𝐿𝑏𝑎𝑡𝑡
Additionally, the energy stored capacity (𝐸𝑡𝑎𝑛𝑘 ) of the tank can be
derived as,
𝐸𝑡𝑎𝑛𝑘 = 𝑃𝑡𝑎𝑛𝑘 𝑀H2 𝐿𝐻𝑉
𝜂𝑏𝑎𝑡𝑡
where 𝑄𝑏𝑎𝑡𝑡 , 𝜂𝑏𝑎𝑡𝑡 are battery capacity and ampere hour efficiency and
𝑆𝑂𝐶𝑏𝑎𝑡𝑡 , 𝑆𝑂𝐶𝑏0 denotes battery current and its initial SOC, respectively.
In the configuration in Fig. 6, the BESS consists of an inductor (𝐿𝑏𝑎𝑡𝑡 )
with its ESR (𝑅𝐿𝑏𝑎𝑡𝑡 ), output capacitor 𝐶𝑜𝑢𝑡 , and switches (𝑆5 , 𝑆6 ). The
duty cycles (𝑑5 , 𝑑6 ) for switches (𝑆5 , 𝑆6 ) are generated by the local
controller. The charging and discharging mode are regulated by a
reference signal 𝑖𝑏𝑎𝑡𝑡𝑟𝑒𝑓 which is generated by system level control.
Specifically, when 𝑖𝑏𝑎𝑡𝑡𝑟𝑒𝑓 < 0, the converter operates in the buck mode
for charging BESS, while for 𝑖𝑏𝑎𝑡𝑡𝑟𝑒𝑓 > 0, it operates in the boost mode
for discharging the BESS. To simplify the controller design process, a
new variable 𝛹 has been introduced.
{
1 𝑖𝑏𝑎𝑡𝑡𝑟𝑒𝑓 > 0 (Discharging Mode)
𝛹=
(24)
0 𝑖𝑏𝑎𝑡𝑡𝑟𝑒𝑓 < 0 (Charging Mode)
Fig. 6. Configuration of battery energy storage system using bi-directional buck-boost
converter.
𝑃𝑡𝑎𝑛𝑘 =
∫0
2.6. Modeling of diesel generator
To meet the load power demands, the diesel generator (DG) has
been incorporated with other AES. The generator has been interfaced
with the DC MG via a buck converter to regulate the power delivery
shown in Fig. 7. The dynamical model of the diesel generator in this
configuration can be derived as,
(22)
2.5. Modeling of battery energy storage system
𝑑𝑖𝑑𝑔
To prevent fuel starvation during high load demands, a battery
energy storage system (BESS) has been incorporated with the PEMFC
to satisfy additional load requirements. The BESS has been configured
with the DC bus via a bi-directional buck-boost converter, as shown in
Fig. 6. This DC–DC converter is capable of bi-directional current flow,
allowing the BESS to charge in buck mode or discharge in boost mode
as required by the load current demand.
The SOC of BESS reflects the amount of charge available relative to
battery peak charging capacity. Monitoring SOC is critical because it
determines which energy storage unit and how much it should be used
by the system level control. For the low level control, the SOC values
𝑑𝑡
=−
𝑉𝑑𝑔
𝐿𝑑𝑔
−
𝑅𝑑𝑔 𝑖𝑑𝑔
𝐿𝑑𝑔
+
𝑑7 𝑉𝑜𝑢𝑡
𝐿𝑑𝑔
𝑖6 = 𝑖𝑑𝑔 (𝑑7 )
(28)
(29)
2.7. Modeling of DC bus dynamics
Based on the configuration of all DERs in the proposed DC MG,
shown in Fig. 8, the load current (𝑖𝐿 ) can be calculated as,
𝑖𝐿 = 𝑖1 + 𝑖2 + 𝑖3 + 𝑖4 + 𝑖5 + 𝑖6
5
(30)
Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Fig. 8. Overall circuit diagram of the microgrid under study.
3. System level energy management system
Substituting values of 𝑖1 , 𝑖2 , 𝑖3 , 𝑖4 and 𝑖6 from Eqs. (9), (10), (15),
(19) and (29), Eq. (30) can be modified as,
3.1. Objective function
𝑖5 = 𝑖𝐿 − ((1 − 𝑑1 )𝑖𝑤𝑒𝑠 + (1 − 𝑑2 )𝑖𝑡𝑒𝑠 + (1 − 𝑑3 )𝑖𝑓 𝑐 + 𝑑4 𝑖𝑒𝑙𝑐 + 𝑑7 𝑖𝑑𝑔 )
(31)
In order to minimize the overall operating cost of the proposed DC
MG, the objective function can be defined as,
Utilizing Eq. (26) and (31), the DC bus dynamics can be modeled
as:
(
)
(
)
(
)
𝑖𝑓 𝑐 1 − 𝑑3
𝑖𝑤𝑒𝑠 1 − 𝑑1
𝑖𝑡𝑒𝑠 1 − 𝑑2
𝑑𝑉𝑜𝑢𝑡
=
+
+
𝑑𝑡
𝐶𝑜𝑢𝑡
𝐶𝑜𝑢𝑡
𝐶𝑜𝑢𝑡
𝑖𝑒𝑙𝑐 𝑑4 𝑖𝑏𝑎𝑡𝑡 𝑑56 𝑖𝑑𝑔 𝑑7
𝑖𝐿
+
+
+
−
𝐶𝑜𝑢𝑡
𝐶𝑜𝑢𝑡
𝐶𝑜𝑢𝑡
𝐶𝑜𝑢𝑡
min 𝐹 = 𝑓𝑑𝑔 + 𝑓𝑚
where 𝑓𝑑𝑔 represents the cost associated with diesel generator and 𝑓𝑚
represents the maintenance cost for the BESS degradation and hydrogen
utilization and production system. These objective functions can be
mathematically defined as follows,
(32)
2.8. Unified modeling of offshore DC MG
𝑓𝑑𝑔 =
To ease the control design process of proposed DC MG, the governing equations of all DERs have been combined and averaged over one
switching cycle.
(
)
𝑥 7 1 − 𝜇1
𝑉
𝑥 𝑅
𝑥̇ 1 = 𝑤𝑒𝑠 − 1 𝐿𝑤𝑒𝑠 −
(33)
𝐿𝑤𝑒𝑠
𝐿𝑤𝑒𝑠
𝐿𝑤𝑒𝑠
(
)
𝑉𝑡𝑒𝑠
𝑥2 𝑅𝐿𝑡𝑒𝑠 𝑥7 1 − 𝜇2
𝑥̇ 2 =
−
−
(34)
𝐿𝑡𝑒𝑠
𝐿𝑡𝑒𝑠
𝐿𝑡𝑒𝑠
(
)
𝑉𝑓 𝑐
𝑥3 𝑅𝐿𝑓 𝑐
𝑥7 1 − 𝜇3
𝑥̇ 3 =
−
−
(35)
𝐿𝑓 𝑐
𝐿𝑓 𝑐
𝐿𝑓 𝑐
𝑉𝑒𝑙𝑐
𝑥 𝑅
𝑥 𝜇
− 4 𝑒𝑙𝑐 + 7 4
𝐿𝑒𝑙𝑐
𝐿𝑒𝑙𝑐
𝐿𝑒𝑙𝑐
(36)
𝑉𝑏𝑎𝑡𝑡
𝑥 𝑅
𝑥 𝜇
− 5 𝐿𝑏𝑎𝑡𝑡 − 7 56
𝐿𝑏𝑎𝑡𝑡
𝐿𝑏𝑎𝑡𝑡
𝐿𝑏𝑎𝑡𝑡
(37)
𝑥̇ 4 = −
𝑥̇ 5 =
𝑉𝑑𝑔
𝑥6 𝑅𝑑𝑔
𝑥 𝜇
𝑥̇ 6 = −
−
+ 7 7
𝐿𝑑𝑔
𝐿𝑑𝑔
𝐿𝑑𝑔
(
)
(
)
(
)
𝑥1 1 − 𝜇1
𝑥2 1 − 𝜇2
𝑥3 1 − 𝜇3
𝑥̇ 7 =
+
+
𝐶𝑜𝑢𝑡
𝐶𝑜𝑢𝑡
𝐶𝑜𝑢𝑡
𝜇4 𝑥4 𝜇56 𝑥5 𝜇7 𝑥6
𝑖𝐿
+
+
+
−
𝐶𝑜𝑢𝑡
𝐶𝑜𝑢𝑡
𝐶𝑜𝑢𝑡
𝐶𝑜𝑢𝑡
(40)
𝑓𝑚 =
𝑇 (
)
∑
𝛼𝑑1 (𝑃𝑡𝑑𝑔 )2 + 𝛼𝑑2 𝑃𝑡𝑑𝑔 ⋅ 𝛥𝑡
𝑡=1
𝑇 (
∑
(
)
)
𝛼𝑚1 𝑃𝑡𝑑𝑖𝑠 + 𝑃𝑡𝑐ℎ𝑔 + 𝛼𝑚2 𝑃𝑡𝑓 𝑐 + 𝛼𝑚3 𝑃𝑡𝑒𝑙𝑐 ⋅ 𝛥𝑡
(41)
(42)
𝑡=1
where 𝛼𝑑1 and 𝛼𝑑2 are the levelized cost for DG and 𝛼𝑚1 , 𝛼𝑚2 and 𝛼𝑚3
are the maintenance cost for BESS, PEMFC and electrolyzer respectively. Furthermore, 𝑃𝑡𝑑𝑔 , 𝑃𝑡𝑓 𝑐 , 𝑃𝑡𝑒𝑙𝑐 , 𝑃𝑡𝑐ℎ𝑔 and 𝑃𝑡𝑑𝑖𝑠 are the power levels
of DG, PEMFC, electrolyzer, BESS charging and discharging power,
respectively.
3.2. System constraints
In order to provide reliable power delivery to end-user and ensure
grid stability, the power system constraints for each individual DER has
to be meet. These constraints associated with each RES and AES have
been defined as follows:
3.2.1. Power balance constraint
To ensure grid stability, the power generated from the WES (𝑃𝑡𝑤𝑒𝑠 ),
TES (𝑃𝑡𝑡𝑒𝑠 ) and AES should meet the load demand (𝑃𝑡𝐿 ). In-addition, if
the power generated from RESs are less, then BESS, PEMFC and DG
have been utilized to cater for load demands. On the contrary, when
there is excess power, then electrolyzer and BESS are used to produce
hydrogen and charge the batteries respectively. Mathematically, the
power balance constraint can be summarized as,
(38)
(39)
where 𝑥1 , 𝑥2 , 𝑥3 , 𝑥4 , 𝑥5 , 𝑥6 and 𝑥7 denotes the averaged states values
of 𝑖𝑤𝑒𝑠 , 𝑖𝑡𝑒𝑠 , 𝑖𝑓 𝑐 , 𝑖𝑒𝑙𝑐 , 𝑖𝑏𝑎𝑡𝑡 , 𝑖𝑑𝑔 and 𝑉𝑜𝑢𝑡 , respectively.
𝑃𝑡𝑤𝑒𝑠 + 𝑃𝑡𝑡𝑒𝑠 + 𝑃𝑡𝑓 𝑐 + 𝑃𝑡𝑑𝑖𝑠 = 𝑃𝑡𝐿 + 𝑃𝑡𝑐ℎ𝑔 + 𝑃𝑡𝑒𝑙𝑐
6
(43)
Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Fig. 9. Overview of hierarchical control structure using system and local level controllers.
3.2.2. RES and DG constraints
The EMS constraints for the power generated from WES, TES and
DG can be defined as follows:
3.2.4. Hydrogen utilization and production constraints
In order to switch between the hydrogen production or utilization
mode, the binary variables 𝑦𝑒𝑙𝑐 and 𝑦𝑓 𝑐 have been defined as follows,
𝑤𝑒𝑠
0 ≤ 𝑃𝑡𝑤𝑒𝑠 ≤ 𝑃𝑚𝑎𝑥
(44)
𝑦𝑒𝑙𝑐 + 𝑦𝑓 𝑐 = 1
(53)
𝑡𝑒𝑠
0 ≤ 𝑃𝑡𝑡𝑒𝑠 ≤ 𝑃𝑚𝑎𝑥
(45)
𝑒𝑙𝑐
0 ≤ 𝑃𝑡𝑒𝑙𝑐 ≤ (𝑃𝑚𝑎𝑥
) ⋅ (𝑦𝑒𝑙𝑐 )
(54)
𝑑𝑔
0 ≤ 𝑃𝑡𝑑𝑔 ≤ 𝑃𝑚𝑎𝑥
(46)
𝑓𝑐
0 ≤ 𝑃𝑡𝑓 𝑐 ≤ (𝑃𝑚𝑎𝑥
) ⋅ (𝑦𝑓 𝑐 )
(55)
𝑓𝑐
𝑃𝑚𝑎𝑥
𝑒𝑙𝑐 and
where 𝑃𝑚𝑎𝑥
are maximum power levels for electrolyzer and
PEMFC. Additionally, Eqs. (53) to (55) ensure that the hydrogen system
either work in production mode or utilization mode. Furthermore, H2
levels in the storage tank can be calculated as,
𝑤𝑒𝑠 , 𝑃 𝑡𝑒𝑠 and 𝑃 𝑑𝑔 are maximum power generation limit for
where 𝑃𝑚𝑎𝑥
𝑚𝑎𝑥
𝑚𝑎𝑥
the WES, TES, and DG respectively.
3.2.3. BESS constraints
To ensure BESS is either in charging or discharging modes, the
binary variables 𝑦𝑐ℎ𝑔 and 𝑦𝑑𝑖𝑠 are introduced,
𝑐ℎ𝑔
𝑑𝑖𝑠
𝑦
+𝑦
0≤
𝑃𝑡𝑐ℎ𝑔
≤
H2
𝐸𝑡
(47)
=1
𝑐ℎ𝑔
(𝑃𝑚𝑎𝑥
) ⋅ (𝑦𝑐ℎ𝑔 )
H
𝑐ℎ𝑔
𝑑𝑖𝑠 denotes maximum charging and discharging
where 𝑃𝑚𝑎𝑥
and 𝑃𝑚𝑎𝑥
power of BESS respectively. Furthermore, SOC level of the BESS can
be calculated as,
𝑐ℎ𝑔
𝑆𝑂𝐶
𝐸𝑡𝑆𝑂𝐶 = 𝐸𝑡−1
+ 𝑃𝑡−1
⋅ 𝜂𝑐ℎ𝑔 −
𝑆𝑂𝐶
𝑆𝑂𝐶
𝐸𝑚𝑖𝑛
≤ 𝐸𝑡𝑆𝑂𝐶 ≤ 𝐸𝑚𝑎𝑥
𝜂𝑑𝑖𝑠
𝑃𝑡𝑒𝑙𝑐 ⋅ 𝜂𝑒𝑙𝑐 −
𝑃𝑡𝑑𝑖𝑠
𝜂𝑑𝑖𝑠
=0
𝜂𝑓 𝑐
H
2
≤ 𝐸𝑚𝑎𝑥
(56)
(57)
𝑃𝑡𝑓 𝑐
𝜂𝑓 𝑐
=0
(58)
(50)
4. Local level controller design and stability analysis
(51)
The configuration of hierarchical control structure using FRL-ITSMC
for the proposed DC MG has been presented in Fig. 9. The primary
control objective of the local-level controller is to drive the WES and
TES at its MPP and regulate the power from the AES to meet the load
demands by tracking the references generated by the system level EMS.
The control objectives can be summarized as follows:
where 𝜂𝑐ℎ𝑔 and 𝜂𝑑𝑖𝑠 represents charging and discharging efficiency
𝑆𝑂𝐶 and 𝐸 𝑆𝑂𝐶 denotes the set-points for minimum and
of BESS. 𝐸𝑚𝑖𝑛
𝑚𝑎𝑥
maximum charge level of the BESS. Furthermore, the constraint to
ensure the initial and final level of SOC level to be same can be defined
as:
𝑃𝑡𝑐ℎ𝑔 ⋅ 𝜂𝑐ℎ𝑔 −
𝑓𝑐
𝑃𝑡−1
where 𝜂𝑒𝑙𝑐 and 𝜂𝑓 𝑐 are the electrolyzer and PEMFC efficiency for the
H2
H2
hydrogen system. 𝐸𝑚𝑖𝑛
and 𝐸𝑚𝑎𝑥
denotes the minimum and maximum
H2 storage level respectively. Additionally, to ensure that final H2 level
at the end of day meet the initial level, the following equation must be
satisfied:
(49)
𝑑𝑖𝑠
𝑃𝑡−1
H2
2
𝐸𝑚𝑖𝑛
≤ 𝐸𝑡
(48)
𝑑𝑖𝑠
0 ≤ 𝑃𝑡𝑑𝑖𝑠 ≤ (𝑃𝑚𝑎𝑥
) ⋅ (𝑦𝑑𝑖𝑠 )
H
𝑒𝑙𝑐
2
= 𝐸𝑡−1
+ 𝑃𝑡−1
⋅ 𝜂𝑒𝑙𝑐 −
• Tracking of WES and TES current {𝑖𝑤𝑒𝑠 , 𝑖𝑡𝑒𝑠 } to {𝑖𝑤𝑟𝑒𝑓 , 𝑖𝑡𝑑𝑟𝑒𝑓 } to
attain MPPT from these RESs.
(52)
7
Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
• Regulation of power from AES {𝑖𝑓 𝑐 , 𝑖𝑒𝑙𝑐 , 𝑖𝑏𝑎𝑡𝑡 , 𝑖𝑑𝑔 } to EMS generated references {𝑖𝑓 𝑐𝑟𝑒𝑓 , 𝑖𝑒𝑙𝑐𝑟𝑒𝑓 , 𝑖𝑏𝑎𝑡𝑡𝑟𝑒𝑓 , 𝑖𝑑𝑔𝑟𝑒𝑓 } to meet load demands and power system constraints.
• Accurate and tight regulation of DC bus voltage against variations
in connected load and power from RESs.
• Ensuring asymptomatic stability of FRL-ITSMC using Lyapunov
stability criteria.
introduced in [41], that can be stated as,
( )
𝜗 𝑠𝑔𝑛 𝑆 −1
𝑆̇ 𝑖 = −𝛼𝑖 𝑠𝑔𝑛 𝑆𝑖 − 𝛽𝑖 𝑆𝑖 − 𝛾𝑖 ||𝑆𝑖 || 𝑖 (| 𝑖 | ) 𝑆𝑖
where {𝛼𝑖 , 𝛽𝑖 , 𝛾𝑖 , 𝜗𝑖 } > 0 are the FRL control parameters. The dynamic
response of the FRL to the varying ITSMC can be calculated as,
{
𝜗
𝑆𝑖 > 1 𝑆̇ 𝑖 = −𝛼𝑖 − 𝛽𝑖 𝑆𝑖 − 𝛾𝑖 ||𝑆𝑖 || 𝑖 𝑆𝑖
(65)
( )
−𝜗
𝑆𝑖 < 1 𝑆̇ 𝑖 = −𝛼𝑖 𝑠𝑔𝑛 𝑆𝑖 − 𝛽𝑖 𝑆𝑖 − 𝛾𝑖 ||𝑆𝑖 || 𝑖 𝑆𝑖
4.1. Designing of FRL-ITSMC
It can be deduced from Eq. (65) that when the system is far away
from the sliding surface (𝑆𝑖 > 1), the convergence speed is faster
with respect to common exponential law [42]. Additionally, when the
system states are near to sliding surface (𝑆𝑖 < 1), the reaching rate
decreases to reduce chattering [41]. Utilizing the Eqs. (63) to (65), the
control laws (𝜇1 , 𝜇2 ) for minimization of errors (𝑒1 , 𝑒2 ) and to drive the
WES and TES at their MPP can be derived as,
(
(
)
𝑥 7 1 − 𝜇1
𝐿
𝑉𝑤𝑒𝑠
𝑥 𝑅
𝜇1 =1 − 𝑤𝑒𝑠
− 1 𝐿𝑤𝑒𝑠 −
− 𝑖̇ 𝑤𝑟𝑒𝑓
𝑥7
𝐿𝑤𝑒𝑠
𝐿𝑤𝑒𝑠
𝐿𝑤𝑒𝑠
( 𝑡
)𝛤1 −1 )
(66)
+ 𝜉1 𝛤1 𝑒1
𝑒1 𝑑𝑡
∫0
(
)
( )
𝐿
𝜗 𝑠𝑔𝑛 𝑆 −1
+ 𝑤𝑒𝑠 −𝛼1 𝑠𝑔𝑛 𝑆1 − 𝛽1 𝑆1 − 𝛾1 ||𝑆1 || 1 (| 1 | ) 𝑆1
𝑥7
(
(
)
𝑥 7 1 − 𝜇2
𝐿𝑡𝑒𝑠 𝑉𝑡𝑒𝑠
𝑥 𝑅
𝜇2 = 1 −
− 2 𝐿𝑡𝑒𝑠 −
− 𝑖̇ 𝑡𝑑𝑟𝑒𝑓
𝑥7
𝐿𝑡𝑒𝑠
𝐿𝑡𝑒𝑠
𝐿𝑡𝑒𝑠
)
( 𝑡
)𝛤2 −1
(67)
+ 𝜉2 𝛤2 𝑒2
𝑒2 𝑑𝑡
∫0
)
( )
𝐿 (
𝜗 𝑠𝑔𝑛 𝑆 −1
+ 𝑡𝑒𝑠 −𝛼2 𝑠𝑔𝑛 𝑆2 − 𝛽2 𝑆2 − 𝛾2 ||𝑆2 || 2 (| 2 | ) 𝑆2
𝑥7
To achieve the control objectives and regulate power levels, the
error signals 𝑒𝑖 have been defined for individual DER as follows,
⎡𝑒1 ⎤ ⎡ 𝑥1 − 𝑖𝑤𝑟𝑒𝑓 ⎤
⎥
⎢𝑒 ⎥ ⎢ 𝑥 − 𝑖
𝑡𝑑𝑟𝑒𝑓 ⎥
⎢ 2⎥ ⎢ 2
⎢𝑒3 ⎥ ⎢ 𝑥3 − 𝑖𝑓 𝑐𝑟𝑒𝑓 ⎥
𝑒 = ⎢𝑒4 ⎥ = ⎢ 𝑥4 − 𝑖𝑒𝑙𝑐𝑟𝑒𝑓 ⎥
⎥
⎢ ⎥ ⎢
⎢𝑒5 ⎥ ⎢𝑥5 − 𝑖𝑏𝑎𝑡𝑡𝑟𝑒𝑓 ⎥
⎢𝑒6 ⎥ ⎢ 𝑥6 − 𝑖𝑑𝑔𝑟𝑒𝑓 ⎥
⎥
⎢ ⎥ ⎢
⎣𝑒7 ⎦ ⎣𝑥7 − 𝑉𝑜𝑢𝑡𝑟𝑒𝑓 ⎦
(64)
(59)
In order to converge these errors signals to zero and achieve system
stability, a sliding surface is required. The objective of the sliding
surface is to converge the error in the vicinity of the surface and then
slide it to bring it the equilibrium point. Based on this Integral Terminal
SMC (ITSMC) theory, the sliding surface 𝑆𝑖 for the convergence of error
to zero (𝑒𝑖 → 0) is defined as follows:
{
(
)𝛤𝑖
𝑡
(60)
𝑖 = {1, 2..., 6}
𝑆𝑖 = 𝑒𝑖 + 𝜉𝑖 ∫0 𝑒𝑖 𝑑𝑡
where 𝜉𝑖 and 𝛤𝑖 are ITSMC surface control parameters, defined as,
{
𝜉𝑖 > 0
𝑖 = {1, 2..., 6}
(61)
1 < 𝛤𝑖 < 2 𝑖 = {1, 2..., 6}
Furthermore, the control laws (𝜇3 , 𝜇4 ) for the hydrogen utilization
and production system can be calculated by substituting Eq. (64) into
(63) respectively,
(
(
)
𝐿𝑓 𝑐 𝑉𝑓 𝑐
𝑥3 𝑅𝐿𝑓 𝑐
𝑥 7 1 − 𝜇3
𝜇3 = 1 −
−
−
− 𝑖̇ 𝑓 𝑐𝑟𝑒𝑓
𝑥7
𝐿𝑓 𝑐
𝐿𝑓 𝑐
𝐿𝑓 𝑐
)
( 𝑡
)𝛤3 −1
(68)
+ 𝜉3 𝛤3 𝑒3
𝑒3 𝑑𝑡
∫0
)
𝐿𝑓 𝑐 (
( )
𝜗 𝑠𝑔𝑛 𝑆 −1
+
−𝛼3 𝑠𝑔𝑛 𝑆3 − 𝛽3 𝑆3 − 𝛾3 ||𝑆3 || 3 (| 3 | ) 𝑆3
𝑥
The inclusion of error integral action in ITSMC surface enables it
to minimize the SMC chattering effect and achieve a fast transient
response to sudden changes in reference value. To incorporated the MG
dynamics into surface 𝑆𝑖 , its time derivative can be derived as,
{
(
)𝛤𝑖 −1
𝑡
(62)
𝑆̇ 𝑖 = 𝑒̇ 𝑖 + 𝜉𝑖 𝛤𝑖 𝑒𝑖 ∫0 𝑒𝑖 𝑑𝑡
𝑖 = {1, 2..., 6}
In order to derive the control laws (𝜇1 , 𝜇2 , 𝜇3 , 𝜇4 , 𝜇5 6, 𝜇7 ), the MG
dynamics from Eqs. (33) to (38) has been substituted into Eq. (62). The
modified surface dynamics for each individual DER can be calculated
as,
(
)
(
)𝛤1 −1 ⎤
𝑥1 𝑅𝐿𝑤𝑒𝑠 𝑥7 1 − 𝜇1
⎡ 𝑉𝑤𝑒𝑠
𝑡
−
−
− 𝑖̇ 𝑤𝑟𝑒𝑓 + 𝜉1 𝛤1 𝑒1 ∫0 𝑒1 𝑑𝑡
⎢𝐿
⎥
𝐿𝑤𝑒𝑠
𝐿𝑤𝑒𝑠
⎢ 𝑤𝑒𝑠
⎥
⎢
⎥
(
)
(
)𝛤2 −1 ⎥
⎡𝑆̇ 1 ⎤ ⎢ 𝑉
𝑥2 𝑅𝐿𝑡𝑒𝑠 𝑥7 1 − 𝜇2
𝑡
𝑡𝑒𝑠
⎥
⎢ ⎥ ⎢
−
−
− 𝑖̇ 𝑡𝑑𝑟𝑒𝑓 + 𝜉2 𝛤2 𝑒2 ∫0 𝑒2 𝑑𝑡
𝐿𝑡𝑒𝑠
𝐿𝑡𝑒𝑠
⎥
⎢ ⎥ ⎢ 𝐿𝑡𝑒𝑠
⎢𝑆̇ 2 ⎥ ⎢
⎥
(
)
⎢ ⎥ ⎢ 𝑉
⎥
(
)
𝛤
−1
𝑥
𝑅
𝑥
1
−
𝜇
3
3 𝐿𝑓 𝑐
3
𝑡
⎢ ⎥ ⎢ 𝑓𝑐 − 7
⎥
̇
∫
−
−
𝑖
+
𝜉
𝛤
𝑒
𝑒
𝑑𝑡
̇
𝑓
𝑐𝑟𝑒𝑓
3
3
3
3
0
⎢𝑆3 ⎥ ⎢ 𝐿𝑓 𝑐
⎥
𝐿𝑓 𝑐
𝐿𝑓 𝑐
⎢ ⎥=⎢
⎥
⎢ ̇ ⎥ ⎢
(
)𝛤4 −1 ⎥⎥
𝑉𝑒𝑙𝑐
𝑥4 𝑅𝑒𝑙𝑐
𝑥7 𝜇4
⎢𝑆4 ⎥ ⎢
𝑡
+
− 𝑖̇ 𝑒𝑙𝑐𝑟𝑒𝑓 + 𝜉4 𝛤4 𝑒4 ∫0 𝑒4 𝑑𝑡
⎢ ⎥ ⎢ −𝐿 − 𝐿
⎥
𝐿𝑒𝑙𝑐
𝑒𝑙𝑐
𝑒𝑙𝑐
⎢ ̇ ⎥ ⎢
⎥
𝑆
⎢ 5⎥ ⎢
⎥
(
)
𝛤
−1
𝑉
𝑥
𝑅
𝑥
𝜇
5
⎢ ⎥ ⎢ 𝑏𝑎𝑡
⎥
𝑡
− 5 𝐿𝑏𝑎𝑡𝑡 − 7 56 − 𝑖̇ 𝑏𝑎𝑡𝑡𝑟𝑒𝑓 + 𝜉5 𝛤 𝛤5 𝑒5 ∫0 𝑒5 𝑑𝑡
⎢𝑆̇ ⎥ ⎢ 𝐿
⎥
𝐿𝑏𝑎𝑡𝑡
𝐿𝑏𝑎𝑡𝑡
⎣ 6 ⎦ ⎢ 𝑏𝑎𝑡𝑡
⎥
⎥
⎢
(
)
𝛤6 −1
𝑥6 𝑅𝑑𝑔
𝑉𝑑𝑔
⎢
⎥
𝑥7 𝜇7
𝑡
̇
−
−
+
− 𝑖𝑑𝑔𝑟𝑒𝑓 + 𝜉6 𝛤6 𝑒6 ∫0 𝑒6 𝑑𝑡
⎢
⎥
𝐿𝑑𝑔
𝐿𝑑𝑔
𝐿𝑒𝑙𝑐
⎦
⎣
7
𝐿
𝜇4 = 𝑒𝑙𝑐
𝑥7
+
𝐿𝑒𝑙𝑐
𝑥7
(
( 𝑡
)𝛤4 −1 )
𝑉𝑒𝑙𝑐
𝑥4 𝑅𝑒𝑙𝑐
𝑥 7 𝜇4
̇
−
−
+
− 𝑖𝑒𝑙𝑐𝑟𝑒𝑓 + 𝜉4 𝛤4 𝑒4
𝑒 𝑑𝑡
∫0 4
𝐿𝑒𝑙𝑐
𝐿𝑒𝑙𝑐
𝐿𝑒𝑙𝑐
(
)
( )
𝜗 𝑠𝑔𝑛 𝑆 −1
−𝛼4 𝑠𝑔𝑛 𝑆4 − 𝛽4 𝑆4 − 𝛾4 ||𝑆4 || 4 (| 4 | ) 𝑆4
(69)
Finally, utilizing (64) and (63), the FRL-ITSMC laws (𝜇56 , 𝜇7 ) for
BESS and DG can be calculated as,
(
𝐿
𝑉𝑏𝑎𝑡
𝑥 𝑅
𝑥 𝜇
𝜇56 = 𝑏𝑎𝑡𝑡
− 5 𝐿𝑏𝑎𝑡𝑡 − 7 56 − 𝑖̇ 𝑏𝑎𝑡𝑡𝑟𝑒𝑓
𝑥7
𝐿𝑏𝑎𝑡𝑡
𝐿𝑏𝑎𝑡𝑡
𝐿𝑏𝑎𝑡𝑡
(
)𝛤 −1 )
𝑡
+ 𝜉5 𝛤5 𝑒5
∫0
5
𝑒5 𝑑𝑡
(70)
)
( )
𝐿𝑏𝑎𝑡𝑡 (
𝜗 𝑠𝑔𝑛 𝑆 −1
−𝛼5 𝑠𝑔𝑛 𝑆5 − 𝛽5 𝑆5 − 𝛾5 ||𝑆5 || 5 (| 5 | ) 𝑆5
𝑥7
(
( 𝑡
)𝛤6 −1 )
𝐿𝑑𝑔
𝑉𝑑𝑔
𝑥6 𝑅𝑑𝑔
𝑥 𝜇
𝜇7 =
−
−
+ 7 7 − 𝑖̇ 𝑑𝑔𝑟𝑒𝑓 + 𝜉6 𝛤6 𝑒6
𝑒6 𝑑𝑡
∫0
𝑥7
𝐿𝑑𝑔
𝐿𝑑𝑔
𝐿𝑒𝑙𝑐
)
𝐿𝑑𝑔 (
( )
𝜗 𝑠𝑔𝑛 𝑆 −1
+
−𝛼6 𝑠𝑔𝑛 𝑆6 − 𝛽6 𝑆6 − 𝛾6 ||𝑆6 || 6 (| 6 | ) 𝑆6
𝑥7
+
(63)
In order to increase the convergence speed and improve transient
response against abrupt changes, a fast reaching law (FRL) has been
(71)
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Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Fig. 10. (a) Wind speed and power generated (b) Tidal current speed and power generated.
Fig. 11. Power levels of connected energy sources and user connected load under different cases.
4.2. Stability analysis
The stability of FRL-ITSMC has been analyzed by Lyapunov stability
criteria (LSC). Using LSC theory, the composite candidate function 𝑉𝑐
can be defined as.
𝑉𝑐 =
6
∑
𝑉𝑆𝑖 =
𝑖=1
6
1∑
(𝑆 )2
2 𝑖=1 𝑖
(72)
According to LSC, the system can be considered asymptotically
stable if each candidate function 𝑉𝑆𝑖 > 0 and its derivative 𝑉̇ 𝑆𝑖 ≤ 0.
To determine the dynamics of the Lyapunov function, we can take the
time derivative of Eq. (72).
Fig. 12. Hydrogen storage level in the tank.
𝑉̇ 𝑆𝑖 = 𝑆𝑖 𝑆̇ 𝑖
(73)
To analyze the dynamics of surface 𝑆1 , the Lyapunov function 𝑉𝑆1
can be derived by utilizing Eqs. (64) and (73),
𝑉̇ 𝑆1 = 𝑆1 𝑆̇ 1
(
)
( )
𝜗 𝑠𝑔𝑛 𝑆 −1
= 𝑆1 −𝛼1 𝑠𝑔𝑛 𝑆1 − 𝛽1 𝑆1 − 𝛾1 ||𝑆1 || 1 (| 1 | ) 𝑆1
( )
𝜗 𝑠𝑔𝑛 𝑆 −1
= −𝛼1 𝑆1 𝑠𝑔𝑛 𝑆1 − 𝛽1 𝑆12 − 𝛾1 𝑆12 ||𝑆1 || 1 (| 1 | )
(74)
≤0
By applying a similar stability method. 𝑉̇ 𝑆2 to 𝑉̇ 𝑆6 for surfaces 𝑆2 to
𝑆6 , can be made negative definite, provided {𝛼𝑖 , 𝛽𝑖 , 𝛾𝑖 , 𝜗𝑖 } > 0.
Fig. 13. State of charge of battery energy storage system.
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Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Fig. 14. Tracking of DC bus voltage by different controllers.
Fig. 15. Current tracking of different energy sources by local level controller.
Fig. 16. Overview of controller hardware in loop configuration using Matlab and Delfino F28379D Launchpad.
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Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Table 1
Power levels analysis under different cases.
5. Results & Discussions
To validate the effectiveness of the proposed hierarchical control scheme, the offshore DC MG has been simulated using MATLAB/Simulink 2023a. The specifications of the implemented WES, TES
are provided in Table 3. The specifications of the AES and FRL-ITSMC
control parameters are listed in Tables 4, and 5 respectively. For
detailed analysis of the hierarchical control structure, the simulations
have been divided into further subsections.
RESs
BESS
DG
H2
Case 1
Case 2
Case 3
Surplus
Charging
Idle
Production
Deficit
Fully charged
Lowest
Maximum level
Deficit
Discharging
High
Utilization
5.1. System level control simulation
The system level control presented in Section 3 has been modeled
using Yalmip toolbox and solved using CPLEX 12.10 and MATLAB
2023a for a 24-h window to generate the reference signals for each
individual energy resource. The MG system has been simulated against
a 400 kW varying load to provide the effectiveness of proposed control
scheme and to assess both power deficit and excess modes.
The WES and TES output power can be analyzed in Figs. 10(a)
and 10(b), respectively. The simulated power curves of each RES and
AES for a 24 h time-window have been presented in Fig. 11. Furthermore, the H2 levels and battery SOC can be presented in 12 and 13,
respectively. Based on the power levels at different time-stamps, the
24-h simulation window can be divided into 3 cases, where each case
represents a different scenario.
Fig. 17. DC bus regulation using controller hardware in loop simulation.
additional 66 kW load power demand. Finally, it can be concluded from
Figs. 11, 12, and 13 that the DG has been utilized effectively not only
to cater for additional load demand but also to satisfy the constraint
that battery SOC and H2 levels should match the initial levels at the
end of the daily cycle. For ease of readability, these cases have been
summarized in Table 1.
5.1.1. Case 1:
It can be deduced from Fig. 11 that from 𝑡 = 1 to 6 h, the load
demand (130 kW to 150 kW) is lower compared to the power generated
from the WES and TES. The average power generated from WES and
TES in this time window is approximately 75.5 kW and 101 kW respectively. In this excess mode, the additional power has been delivered
to the electrolyzer and BESS to produce H2 and charge the battery
to provide power for the rest of the day. The charging and hydrogen
production phenomenon can be validated from the fact that power from
BESS and PEMFC has been negative in the time frame. Furthermore, the
increased H2 level and battery SOC for this time period can be analyzed
from Figs. 12 and 13, respectively. Additionally, the power generated
from the DG has been at its lowest level to minimize operating costs.
5.2. Local level control simulation
The configuration of the implemented hierarchical control scheme
has been presented in Fig. 9. The local level control was achieved using
FRL-ITSMC control laws, derived in Section 4. The MG structure and
the derived control laws have been modeled in MATLAB/Simulink. For
detailed analysis, the modeled system has been simulated using ode45
with a step size of 0.1 ms.
The DC bus regulation and current tracking of the RES and AES
by FRl-ITSMC have been presented in Figs. 14 and 15, respectively. It
can be deduced from Fig. 14(a) that the FRL-ITSMC ensured tight DC
bus voltage regulation to 600 V throughout the complete simulation
window. Fig. 14(b) showcases the initial controller response which
shows that the controller achieve the steady state in around 0.08 s
Furthermore, at 𝑡 = 10 s and 𝑡 = 17 s, when there is an abrupt
requirement from PEMFC and BESS, there is a dip in DC bus voltage
but the FRL-ITSMC quickly recover and reach the steady state. This
transient response and the minimal steady state error can be analyzed
from Fig. 14(c) and (d), respectively. In-addition, the individual current
tracking of each RES and AES can be analyzed from Fig. 15. It can be
deduced from these sub-figures that the FRL-ITSMC not only tracked
the reference signal accurately but it also exhibit a very quick response.
In order to validate the effectiveness of the proposed FRL-ITSMC
scheme against prior control schemes, the performance has been compared against conventional PID and ITSMC. Based on the DC bus
voltage regulation provided in Fig. 14, the detailed analysis has been
carried out and is presented in Table 2. It can be seen that out of
these three controllers, the ITSMC has quickest rise time but it exhibit
overshoot in the initial tracking. The PID on the other-hand has not only
the slowest response but it also have larger undershoot and settling time
compared to FRL-ITSMC and ITSMC. From the comparison provided
in Fig. 14(b), (c) and (d) and the analysis presented in Table 2, it
can be concluded that the FRL-ITSMC achieved our control objectives
efficiently and accurately.
5.1.2. Case 2:
From 𝑡 = 6 to 10 h, there has been a sharp increase in the load
demand, i.e., from 129 kW to 290 kW. The average power generated
from the WES and TES systems is 140 kW and 76 kW, respectively.
Additionally, from 𝑡 = 6 to 9 h, it can be observed from Fig. 10(a)
that WES power has increased from 95 kW to a maximum of 155.5 kW.
However, there is a dip in power generated from WES to 142 kW. To
cater for this dip and meet the battery and H2 level constraints, there
is an increment in DG power (44 kW). Additionally, it can be analyzed
from Figs. 12 and 13 that the H2 level and battery SOC have reached
their maximum levels. The BESS and electrolyzer system have been in
an idle state.
5.1.3. Case 3:
In this scenario, we will discuss how AES will be used to meet power
demands when there are random changes in connected load. It can
be observed that at 𝑡 = 18 h, the load reaches its maximum value of
400 kW. Furthermore, the power generated from WES and TES reaches
a maximum of 236 kW and 112 kW, respectively. In this power deficit
mode, it can be observed from Figs. 12 and 13 that the hydrogen and
battery SOC levels have been reduced to meet the additional power
demand. Furthermore, whenever there is a dip in power demand, such
as at 𝑡 = 19 h, the excess power has been used to generate H2 using
the electrolyzer. At 𝑡 = 20 h, when the power output from the WES
(210 kW) and TES (77 kW) decreases, the PEMFC reaches its maximum
output of 40 kW, and the BESS and DG have been utilized to meet the
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Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Fig. 18. Controller hardware in loop simulation of local level controller.
Table 3
Wind and tidal energy systems parameters.
Table 2
Performance comparison of proposed controller with prior control techniques.
PID
ITSMC
FRL-ITSMC
Rise time
(ms)
Settling
time (ms)
Percent
overshoot (%)
Steady-State
error (%)
60
35
52
98.8
121.4
81.2
0.287
0.16
0.07
0.06
0.05
0.005
Parameter
Value
Air density (𝜌𝑎𝑖𝑟 )
Water density (𝜌𝑠𝑒𝑎𝑤𝑎𝑡𝑒𝑟 )
Wind speed at rated power
Tidal current speed at rated power
WES power at rated speed
TES power at rated speed
Maximum power coefficient (𝐶𝑝𝑚𝑎𝑥 )
Optimal tip-speed ratio (𝜆𝑚 )
1.225 kg/m3
1025 kg∕m3
5 m∕s
2 m∕s
150 kW
80 kW
7.5
0.43
5.3. C-HIL simulation
Table 4
Auxiliary energy sources parameters.
The configuration of C-HIL has been elaborated in Fig. 16. The
control unit comprises of a 3060Ti GPU based Ryzen 5600X PC for
modeling the proposed MG system and solving the system level controller using MATLAB. The FRL-ITSMC has been implemented using the
Texas Instruments Delfino F28379D Launchpad. The connection of the
launchpad has been established with the control unit through analog
to digital (ADC) and digital to analog (DAC) interfaces. Furthermore,
to code the FRL-ITSMC on to the launchpads, the MATLAB C2000
Embedded encoder has been utilized.
To ensure consistency, the simulations has been repeated under
similar environmental conditions and same load profile. The DC bus
regulation and the current tracking of individual RES and AES has been
presented in Figs. 17 and 18. The inclusion of the minor noise in the
results is due to the ADC and DAC conversions. It can be concluded
that the simulation results are consistent with the C-HIL validating the
efficacy of the proposed control scheme for real-life application.
Symbol
Parameter
Value
𝑉𝑓 𝑐
𝐼𝑓 𝑐𝑚𝑎𝑥
PEMFC nominal voltage
PEMFC maximum current
400 V
100 A
𝑓𝑐
𝑃𝑚𝑎𝑥
𝑉𝑒𝑙𝑐
PEMFC maximum power
Electrolyzer nominal voltage
40 kW
405 V
𝑒𝑙𝑐
𝑃𝑚𝑎𝑥
𝑉𝑏𝑎𝑡𝑡
𝜂𝑏𝑒𝑠𝑠
𝐼𝑏𝑒𝑠𝑠𝑚𝑎𝑥
Electrolyzer maximum power
BESS nominal voltage
BESS efficiency
BESS maximum current
50 kW
480 V
90%
105 A
𝑏𝑎𝑡𝑡
𝑃𝑚𝑎𝑥
BESS maximum power
50 kW
𝑑𝑔
𝑃𝑚𝑎𝑥
𝜂𝑑𝑔
DG maximum power
DG efficiency
60 kW
40%
of the proposed FRL-ITSMC controller. However, it should be noted that
the FRL-ITSMC controller has multiple control parameters that need
to be optimized for efficient system performance. Furthermore, the
effectiveness of the proposed framework was validated through realtime C-HIL experiments, which showed consistency with simulation
results and confirmed the effective performance of the FRL-ITSMCbased microgrid system in real-world applications. Future work could
focus on optimizing the control parameters of the FRL-ITSMC controller using meta-heuristic algorithms to further enhance the system’s
performance.
6. Conclusion
This study presented a hierarchical control system designed for
an offshore DC microgrid. The proposed control strategy not only
minimized operating costs by optimizing the usage of DG, PEMFC,
and BESS but also ensured MPPT from wind and tidal energy system.
The control framework demonstrated accurate tracking and compliance
with system constraints during both power deficit and surplus modes. A
comparison with ITSMC and PID controllers confirmed the superiority
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Journal of Energy Storage 82 (2024) 110521
N. Ali et al.
Table 5
DC–DC converters and controller parameters.
Symbol
Parameter
Value
𝑓𝑐𝑠
𝜂𝑐𝑠
[𝐿𝑤𝑒𝑠 , 𝐿𝑡𝑒𝑠 , 𝐿𝑓 𝑐 ]
[𝐿𝑒𝑙𝑐 , 𝐿𝑑𝑔 , 𝐿𝑏𝑎𝑡𝑡 ]
[𝑅𝐿𝑤𝑒𝑠 , 𝑅𝐿𝑡𝑒𝑠 , 𝑅𝐿𝑓 𝑐 ]
[𝑅𝐿𝑒𝑙𝑐 , 𝑅𝐿𝑏𝑎𝑡𝑡 , 𝑅𝐿𝑑𝑔 ]
𝐶𝑜𝑢𝑡
[𝛼{1,2,..6} , 𝛽{1,2,..6} , 𝛾{1,2,..6} ]
[𝜗{1,2,..6} , 𝛤{1,2,..6} , 𝜉{1,2,..6} ]
Converters switching frequency
Converters efficiency
Inductors
150 kHz
96%
[3.3 mH, 3.5 mH, 4.3 mH]
[2.3 mH, 3.8 mH, 4.5 mH]
[∼35 mΩ, ∼45 mΩ, ∼25 mΩ]
[∼25 mΩ, ∼35 mΩ, ∼40 mΩ]
2500 μF
[650, 1500, 400]
[0.3, 1.5, 0.7]
Inductors ESR
Output filter capacitor
FRL-ITSMC parameters
CRediT authorship contribution statement
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Naghmash Ali: Writing – original draft, Software, Methodology,
Conceptualization. Xinwei Shen: Writing – review & editing, Validation, Supervision, Resources, Funding acquisition. Hammad Armghan:
Validation, Formal analysis. Yunfei Du: Writing – review & editing,
Visualization.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Data availability
Data will be made available on request.
Acknowledgments
This work is supported in part by National Natural Science Foundation of China (No. 52007123), and Basic and Applied Basic Research
Funding of Guangdong with Offshore Wind (No. 2022A1515240019)
(Corresponding author: Xinwei Shen, sxw.tbsi@sz.tsinghua.edu.cn).
Appendix
See Tables 3–5.
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