A Novel Approach to Energy Management with Power Quality Enhancement in Hydrogen Based Microgrids through Numerical Simulation

Abstract

A hydrogen-based microgrid (MG) is an energy system that uses hydrogen as a primary energy carrier within a localized grid. Numerous alternative approaches and concepts are found concerning the management of renewable energy systems. This study proposes a novel approach to assess the energy management system (EMS) and optimal hydrogen-based Energy Storage Systems (HBESS) at minimal total cost, employing particle swarm optimization (PSO) and fuzzy control in stand-alone microgrids. Together, these methods effectively address control and management challenges within hybrid microgrids (HMGs). This has been proposed to enhance energy management and to improve power quality. The findings reveal that PSO is the most advantageous and efficient approach. Its utilization proves instrumental in reducing costs, boosting reliability, and optimizing operational schedules within HMGs. Furthermore, the power profile holds considerable importance in this study, significantly enhancing system reliability and stability. This study has achieved an impressive 6.147% improvement in cost-effectiveness compared to traditional methods. This has been put into practice and validated through implementation within a MATLAB (9.13.0 (R2022b))/Simulink framework.

1. Introduction

Microgrids (MGs) are small-scale, localized electrical grids that can work separately or in coordination with the main power grid. Hybrid microgrids are designed to provide reliable and efficient power to a designated zone or community, such as a university campus, military facility, or isolated village. These systems usually comprise an array of distributed energy sources like photovoltaic, wind turbines, battery storage systems, and auxiliary generators [1]. Moreover, they usually integrate advanced control mechanisms and energy management software tools to increase energy usage and minimize costs. This article presents the optimal planning and operation of a hydrogen-based microgrid incorporating renewable energy resources (RESs), including wind turbines, solar systems, and fuel cells and electrolyzers. Effectively managing these resources, principally fuel cells and electrolyzers, in line with their operational specifications presents an optimized design and energy management strategy. This approach anticipates the behavior of fuel cells and electrolyzers, ensuring compliance with each unit’s effective constraints [2].

In this research, hydrogen is generated using distinct methods to fulfill the requirements for fuel cells (FCs). The MG’s system design is heightened by reducing annual costs, decreasing fuel consumption, and increasing the deployment of RESs. The power produced by RESs is either employed to satisfy the MG’s demand or transformed into hydrogen through electrolysis processes. Any surplus power is then directed to the grid. To ensure a balance between production and demand, it’s essential to assess both the technical and economic constraints of HMGs.

As the energy sector evolves towards a more sustainable and distributed system, microgrids are becoming an accessible solution for integrating RESs, escalating energy efficiency and resiliency, and reducing carbon emissions [3]. However, effective management and control of MGs remains a significant challenge that requires the development of advanced strategies and technologies [4]. Numerous energy management and control strategies exist for microgrids, encompassing centralized and decentralized approaches [5].

Centralized approaches typically involve innovative control. Microgrid EMS plays a vital role in addressing the challenges of distributing and integrating distributed energy resources (DERs) into the electric grid [6]. The efficient use of RESs has become a significant priority in MGs energy management, which can help to enhance energy resilience by reducing carbon emissions, improving power quality and reliability [7]. Several energy management and control approaches that have been utilized to optimize the performance of microgrids include optimal power flow (OPF), demand response (DR), and energy storage systems (ESS). OPF optimally coordinates the production and consumption of electricity from DERs to reduce energy wastage and costs [8], whereas DR strategies help to match the demand for electricity with the available supply by providing incentives for consumers to decrease their demand during phases of high energy demand [9]. In this context, energy storage systems become essential to manage the imbalance between energy supply and demand [10]. Centralized approaches involve a central controller that manages the operation of the micro-grid system. “Here central control CC system controls” is considered by a high-performance figuring unit and a protected communication organization to accomplish various objects of the scheme (e.g., RESs and ESS). Meanwhile, LC is the local control system of the system (Figure 1).

Decentralized approaches, on the other hand, distribute control among various components of the system. All the entities are controlled at different levels, and there is no need for a high-performance computing unit in this approach (Figure 2), while hybrid approaches combine the features of both centralized and decentralized approaches. The integration of centralized and decentralized strategies generates an HMG environment that optimizes the advantages of both methods. This incorporation ensures a harmonious blend of grid-wide coordination and local autonomy, leading to resilient, efficient, and sustainable energy management. The hybrid system is illustrated in Figure 3.

A comprehensive review of the microgrid system’s control and energy management method has been conducted [9]. This offers valuable insights for improving the operation and management of MG systems and advancing the transition toward sustainable energy sources [10,11]. The multiphase stacked interleaved buck converter is a power electronic converter used for controlling the power flow in many applications, including green hydrogen production [12]. The converter consists of multiple interleaved buck converters stacked in parallel, which provides fault tolerance and high efficiency [13].

A fuzzy logic controller is employed to address the system’s nonlinear dynamic features, providing decision-based forecasts for power and voltage [11]. For the efficient planning and design of a hydrogen-based microgrid, numerous case studies have been conducted, exploring various types of DERs through the use of heuristic algorithms [12]. These studies aimed to reduce the cost and enhance the efficacy of the system. PSO and constraint methods were applied to reduce the cost and unmet load [13]. A comparison of several optimization techniques was conducted, with the inclusive findings authorizing that the PSO method emerged as the utmost effectual and practical optimization method for hydrogen-based MG system planning [14,15,16]. These assessments were based on criteria such as minimizing costs, maximizing consistency, and exhibiting more robust convergence attributes compared to other optimization methods. In this paper, a heuristic optimization approach, the PSO algorithm, is anticipated to determine the optimal capacity of RESs within an MG system [17].

However, the intermittent and unpredictable nature of renewable sources such as photovoltaic (PV) and wind pose a challenge for their integration into power grids [18]. One of the solutions proposed to address this challenge is incorporation of a hydrogen storage system to enable backup power supply for renewable hybrid energy systems (RHES) [19]. Combining these strategies can enable efficient and reliable energy management in RHES with hydrogen backup. It also identifies areas for future research, including developing more accurate and reliable models that can capture the dynamics of RHES and hydrogen storage systems. The optimization algorithm used in this approach can be based on various methods, such as linear programming, quadratic programming, or mixed-integer programming [20,21]. The significant advantage includes modest algorithm operation, less parameters tuning, and a reckless convergence rate. The primary contributions of this article are outlined below, derived from a thorough critical examination of prior research conducted by numerous scholars presented in

Table 1. Comprehensive overview of the existing literature.

Ref.	EMS Strategy	Contribution	Constraints
[22]	Moth-Flame Optimization (MFO)	An Integrated Management System (IMES) has been devised to oversee energy management. Achieved 1.287% reduction in the operational cost. Accomplished its objectives within an impressive time frame of under 150 min.	Taking power and cost under consideration while taking much time about to more than 150 min.
[23]	Amended Penguin Optimization Algorithm (APOA)	This research focuses on reducing steady-state error and improvement in power quality. Addressing Sag and Swell situations are discussed for enhancement of systems efficiency.	Power balancing only.
[24]	African Vulture’s Optimization Algorithm (AVO)	Techno-economic goals have been addressed comprehensively. Assessing daily operational expenses, including operational costs. BESS performance improved by using AVO.	Battery performance and operational cost.
[25]	Marine Predator Algorithm (MPA)	Introduces a centralized control system designed to manage large-scale distributed energy resources. To improve the microgrid performance, an adaptive dynamic voltage restorer (ADVR) with PID based on MPA has been utilized. This research includes a comparative analysis with two other distinct methods.	Power maintenance condition is under consideration.
[26]	SAC and XGBoost	A methodology has been devised that leverages the SAC algorithm as the decision-making tool for Home Energy Management Systems (HEMS). The comprehensive evaluation included an assessment of internal system factors as well as external environmental aspects.	Charging and discharging of electric vehicles, battery constraints and operational appliances limitations.
[27]	Quantum Teaching Learning-Based Optimization (QTLBO)	A daily optimal scheduling framework has been developed and implemented. Reduced the standard deviation in stochastic scenarios to a minimum value.	Power balancing and considering only global values for different sources.
[28]	Mixed Integer Linear Programming (MILP)	This study introduces an approach for storage systems, offering a new perspective on energy storage solutions. A techno-economic approach primarily focuses on future homes as self-sufficient entities.	Balancing of power and storage only.

.

• The proposed research design offers notable returns over traditional microgrid design approaches, including the following: Emphasizing the significance of proposed design and energy management optimization in MG systems involves developing a comprehensive cost-driven approach to optimize DERs. This approach considers the integration of hydrogen ($H_2$) storage and electrolyzer within a grid-tied operation mode.
• The problem formulation integrates economic and environmental considerations, particularly focusing on the utilization of an electrolyzer for hydrogen ($H_2$) production to FCs. The analysis explores the ideal scale for various resources in the energy system operation, emphasizing the potential for greater financial returns through increased integration of RESs.
• Rule-based fuzzy logic consistently outperforms traditional hydrogen-based microgrid design methods in terms of availability, present cost, power efficacy, and power quality enhancement.
• In the context of hydrogen-based microgrid context, the PSO method revolutionized the construction of MG architecture, streamlining the initial design phase and elevating system performance. Economic competence for the hydrogen-based microgrid is enhanced by proper energy management. PSO converges power within the constraints and improves the power quality, ultimately with the expected lowest cost.
• The obtained outcomes show that the proposed method is vigorous and beats the other traditional techniques in terms of faster performance, lowest costs, inferior level of harmonics, improved battery state of charge (SoC), more FC load power, and increased overall efficacy.

Further sections of this article include the System Model in Section 2, Energy Management System in Section 3, Simulation and Its Results in Section 4, and the Conclusion in Section 5.

2. System Model

The system explored in this paper is a hybrid microgrid that integrates a Proton Exchange Membrane Fuel Cell (PEMFC), an alkaline electrolyzer, hydrogen storage tanks, Battery Energy Storage System (BESS), and PV producers. The PEMFC and electrolyzer in this paper are based on the specifications of a Nexa 1.2 kW, 26 V, and 46 A PEMFC intended by Ballard [29] and $H_2$ Igen 300/1/25, 5 kW, 43 V, and 120 A alkaline electrolyzer [30]. A hydrogen-based microgrid introducing both RESs production and hydrogen storage can gain from a multi-stage power and energy management strategy to optimize its performance and ensure resource effectiveness [31]. The microgrid is modeled using the MATLAB/Simulink software [32].

The RESs considered in this study are photovoltaic panels and wind turbines. In addition, the microgrid has a battery storage system, supercapacitor, and hydrogen storage system. The objective of this step is to optimize the dispatch of RESs and energy storage components to minimize the cost of energy and carbon emissions. Where is a possible approach for such a strategy to design the complete model and its optimization with respect to the operational cost of the system? The convergence level of voltage is considered as well.

2.1. PV Power Management

In this stage, the PV panels generate electricity during daylight hours. This power is used to meet local demand and to charge the hydrogen storage system. Under consideration, the polycrystalline silicon PV panel is manufactured by Jinko Solar, and its model number is JKM215P-60B. The alphanumeric code “60B” indicates both the number of solar cells and their configuration. A significant amount of solar energy can be captured as photons and converted into electricity using thin-film semiconductors. By utilizing “direct band gap semiconductors” instead of “indirect band gap silicon material”, the cost of photo-absorbing materials can be reduced. Any surplus power is exported to the grid or used to power non-critical loads. The input for solar power management is defined by the solar Irradiation (I) and ambient temperature ($T_{amb}$) that is obtained from the National Solar Radiation Database NSRDB. At the beginning of solar power, the cell temperature ($T_C$) is calculated using (1) [33,34].

$${\mathrm{T}}_{\mathrm{C}}\left(\mathrm{t}\right)={\mathrm{T}}_{\mathrm{amb}}\left(\mathrm{t}\right)+\mathrm{I}\left(\mathrm{t}\right)({\displaystyle \frac{\mathrm{NOCT}-20}{0.8}})$$

(1)

Here, NOCT is the nominal operating cell temperature of the solar cells, and the output power of a solar panel is calculated using (2):

$$P_{PVunit}\left(\mathrm{t}\right)=\left(R_f\right)\left({\mathsf{\eta }}_{PV}\right)\left(A_{PV}\right)\left(\mathrm{I}\left(\mathrm{t}\right)\right)\left(1-{\displaystyle \frac{K_P}{100\left(T_C\left(t\right)-25\right)}}\right)$$

(2)

Here, $R_f$ is the reduction factor for dust accretion, whereas ${\mathsf{\eta }}_{PV}$ is the conversion efficiency of the solar cell, $A_{PV}$ denotes area of solar, and $K_P$ indicates the temperature coefficient. Consequently, (3) expresses the total power produced by a complete solar panel:

$$P_{PV}\left(\mathrm{t}\right)=\left(N_{PV}\right)\left(P_{PVunit}\left(\mathrm{t}\right)\right)$$

(3)

where $P_{PV}$(t) presents the output power of solar in watts and $N_{PV}$ is the number of cells for PV. The increase in temperature may sacrifice its efficiency. Figure 4 shows clearly the characteristics of voltage and power for the solar system.

A slight change in the temperature of solar panels can lead to a reduction in power output, affecting both current and voltage. In this proposed study, the optimized EMS considers the cost of solar power per kilowatt and enhances the quality of power delivered to the system.

2.2. Wind Power Management

Windmills generate power 24 h per day. The generated power is utilized to meet local energy demands and to charge the hydrogen storage system. Any excess power is either fed into the grid or used to supply non-essential loads. A total of 1.5 MW power is generated by a variable pitch wind model. To determine the output power of the wind farm, the calculated wind speed by anemometer height is transformed to match the wind turbine hub height by means of the power law Equation (4) [36].

$${\displaystyle \frac{V_b}{V_a}}={({\displaystyle \frac{h}{h_{reference}}})}^{\mathit{\partial }}$$

(4)

Here, $V_a$ and $V_b$ are the wind velocities in m/s at the wind turbine hub height and at reference height $h_{reference}$, respectively, whereas $\mathit{\partial }$ shows the exponential of power law, which is known as roughness factor. The roughness factor depends entirely upon the landscape, temperature, and wind speed at that specific time; either it’s the daytime only or its year time. Therefore, it would be different on plain land and in deeply woodland landscapes. So, the output of wind turbine $P_W$ can be stated by set of Equation (5):

$$P_W=\left\{\begin{array}{c}\begin{array}{c}\left(x{V}^3-y\right)P_{RW},V_{Cin}\le V\le V_{Ra}\hfill \\ P_{RW,}{V}_{Ra}\le V\le V_{CO}\hfill \end{array}\\ 0,Otherwise\end{array}\right.$$

(5)

where the output of WT is dependent upon two significant features: the rated power $P_W$ of the turbine and airstream speed V. Moreover, other vital wind velocity standards are used to control the turbine’s action. The cut-in velocity showed by $V_{Cin}$, the rated velocity of turbine denoted by $V_{Ra}$, and finally, the cut-off speed, can be measure by $V_{CO}$. Now the remaining constant values $x$ and $y$ can be calculated by some expressions:

$$x={\displaystyle \frac{1}{{V_{Ra}}^3-{V_{Cin}}^3}}$$

(6)

$$y={\displaystyle \frac{{V_{Cin}}^3}{{V_{Ra}}^3-{V_{Cin}}^3}}$$

(7)

Typically, the $V_{Cin}$ has the choice in the values of 2.5–3.5 m/s while the $V_{CO}$ has the range of 20–25 m/s. Figure 5 depicts the wind turbine characteristics with respect to power.

When the wind speed exceeds the specified threshold values, the output power must be limited to these thresholds to prevent damage to the generator and its associated power electronics. If the wind speed exceeds the cut-off limit, the system needs to be shut down and removed from the circuit to safeguard its components. Thus, the proposed optimized EMS enhances the efficiency and reduces the cost of energy produced from wind.

2.3. Hydrogen Power Management

During the photovoltaic and wind power generation phase, excess power is used to produce hydrogen through electrolysis. The produced hydrogen is stored in a hydrogen tank to be used later when there is no sunlight or less power production from the wind source and cannot meet any type of demand, either residential or industrial. The most common method of producing hydrogen is through electrolysis, which involves splitting water into hydrogen and oxygen using electricity. The hydrogen produced can then be stored in tanks or in underground salt caverns. The storage and transportation of hydrogen require careful consideration due to its highly flammable nature [39].

The hydrogen-production rate should be optimized based on the current and future demand for electricity. The power output from the hydrogen fuel cell is optimized to meet the current load demand while not overloading the system. So, the hydrogen and oxygen parts are to be considered as lossless. The volume of hydrogen and oxygen can be measured by (8) and (9) [40].

$$V_{H,n}=V_{H,n-1}+n_{H,n}{t}_{opt}$$

(8)

$$V_{O,n}=V_{O,n-1}+n_{O,n}{t}_{opt}$$

(9)

Volume of tank level disparity depends on the primary level, i.e., $V_{H,n}$ and $V_{O,n}$. Flow rate is described in $n_{H,n}{t}_{opt}$ and $n_{O,n}{t}_{opt}$, correspondingly. In this regard, flow rates can be considered in the optimization problem with first-order polynomial expressions. MATLAB polyfitZero function can give these expressions. The final flow rate values of hydrogen and oxygen can be found by (10) and (11):

$$n_{H,n}=n_{HEl,n}+n_{HFC,n}$$

(10)

$$n_{O,n}=n_{OEl,n}+n_{OFC,n}$$

(11)

where $n_{HEl,n}$ and $n_{HFC,n}$ are the hydrogen-based electrolyzer and fuel cell flow rates, respectively, and $n_{OEl,n}$ and $n_{OFC,n}$ are the electrolyzer and fuel cell flow rates of oxygen, respectively. Power and current of the electrolyzer and fuel cell are at the mercy of the polarization curve. The constraints of power are to be defined as in-between 20 to 80 percent of the determined power of fuel cell at any time. The stored hydrogen energy in the hydrogen tank (HT) must also satisfy specific constraints, and it can be measured by (12):

$$V{H}_2^{min}\le V{H}_2\left(\mathrm{t}\right)\le V{H}_2^{max}$$

(12)

where $V{H}_2^{min}$ and $V{H}_2^{max}$ are the minimum and maximum hydrogen energy stored in a tank. $V{H}_2$(t) is the total energy stored in a tank at time (t). Meanwhile, the electrolyzer power is well-thought-out in the ohmic zone of operation. Currents were found on the basis of pre-determined power and curve, respectively.

2.4. Grid Integration

If the hydrogen storage is depleted, or if there is a rise in local load demand, power can be imported from the grid. Conversely, if excess power is generated by the PV panels or the hydrogen fuel cell, it can be exported to the grid. Meanwhile, focus on the voltage fluctuation and cost of the system during this part. In the proposed study, uncertainty in RESs generation and electrical load is typically modeled using probabilistic techniques such as Monte Carlo simulations and optimization methods. These approaches for variability and randomness are inherent in RESs and load patterns. Load fluctuations and weather conditions can significantly affect the simulated results. In the short term, this can lead to fluctuations in the available power. This factor may have an influence on operation planning and increase the requirement for backup power sources. Over the long term, this may affect the cost-related decisions and planning of system infrastructure. Thus, effectively managing the uncertainty associated with load profiles and weather conditions is essential for establishing a successful operation and EMS. This article elaborates on robust strategies for managing RESs and ensuring grid stability. The proposed solution to address these challenges is the incorporation of a hydrogen storage system to enable backup power supply for the renewable hybrid energy systems (RHES).

Multi-objective development of an (MG) system considering renewable energy, hydrogen storage systems, and demand response involves optimizing multiple objectives simultaneously. These objectives typically include maximizing renewable energy utilization, minimizing energy costs, and enhancing grid reliability [41]. So, how can these optimization algorithms be applied in the context of hydrogen-based microgrids? Objective function of the cost is given in (13).

$$Objective{}_{fcn}=\mathit{[}{P}_{\mathsf{\eta }},Cost\_effectivenss]$$

(13)

To calculate the current price of all system expenses counting capital, maintenance, fuel consumption, trade-off power with the grid, and CO₂ emissions consequence, the Net Present Cost (NP-Cost) methodology is utilized. The objective of curtailing the total system cost can be calculated by (14).

$$\mathrm{NP}-\mathrm{Cos}\mathrm{t}=\mathrm{NP}-P{V}_{COST}+\mathrm{NP}-W_{COST}+\mathrm{NP}-F{C}_{COST}+\mathrm{NP}-Carbon\_emissio{m}_{COST}$$

(14)

The precise carbon emission is measured in (kg/kWh), and to calculate the NP -$Carbon\_emissio{m}_{COST}$ where ${\lambda }_{emission}$ ($/kg) is the emission penalty calculated in (15) and (16):

Carbon_emission = [(kg/kWh) × Fuel_Cost]

(15)

$$\mathrm{NP}-Carbon\_emissio{m}_{COST}={\sum }_{t=1}^{8760}[{\mathrm{Carbon}}_{\mathrm{emission}}\times {\lambda }_{emission}]\times {\displaystyle \frac{1}{CR\left(IR,R\right)}}$$

(16)

where NP-$P{V}_{COST}$, NP-$W_{COST}$, NP-$F{C}_{COST}$, NP-$Carbon\_emissio{m}_{COST}$ are the total net current cost of solar, wind, fuel cell, and carbon emission.

3. Energy Management System

The EMS for hydrogen-based microgrids comprises three main components: the power system, the hydrogen storage system, and the control system. The power system includes an energy source, such as a solar panel or wind generator, while the hydrogen storage system includes hydrogen production, storage, and utilization components. The control system coordinates these components to ensure a constant supply of renewable energy to the microgrid [5]. One of the challenges of hydrogen technologies-based microgrids is the low energy density of hydrogen. It requires a large volume of hydrogen to store the same amount of energy compared to other conventional energy sources. Therefore, hydrogen storage systems need to be optimized to reduce the space requirement. Meanwhile, centralized EMS may be used for island microgrids [42].

The challenge could be overcome with a fuzzy control system to control the battery, super-capacitor, and hydrogen storage. It will increase the complexity of this study, but with the optimization technique, it will be less costly [43]. However, in this study the PSO technique is used. To calculate all the values of the system, all costs sum up in a PSO [12]. Moreover, complexity of this system could be vanished simply by offline energy supervision methods for different combinations of energy storage systems according to different kinds of applications like MGs and EVs. Optimization techniques enable microgrid EMS to make informed decisions regarding resource allocation, demand response, energy trading, grid stability, and cost minimization. By leveraging these techniques, microgrids can improve their operational efficacy, reduce costs, integrate renewable energy resources effectively, and enhance the overall system reliability and resilience [44]. So, in this research the lack of standardization of hydrogen storage, distribution, and consumption technologies is addressed with an optimization technique. This lack of standardization makes it difficult for hydrogen-based microgrids to become a mainstream energy source.

The MG system includes a hydrogen storage reservoir to store the produced hydrogen. The amount of stored hydrogen can be calculated at any time using the mathematical equations outlined in Section 2. It depends on the variables of the electrolyzer and fuel cell flow rates. Meanwhile, the efficiency of the fuel cell could be estimated per the requirements of the system [15]. The EMS can manage one variable at each time. In modern MG systems, it’s becoming more common to employ two energy management techniques simultaneously to enhance system efficiency and reduce operational costs but to sacrifice on the one-time cost. After the system cost has been determined using optimization techniques, the next milestone to address is improving the power quality. The improvement in power quality can be demonstrated by the voltage convergence across the entire system achieved through PSO.

The constraints of the optimization problem include factors such as the output power generated by each type of DER, maintaining power balance within the MG system, and managing the energy exchange between its components. The power generation constraints for each type of DER include both the minimum and maximum limits of power output at given time t, and it can be calculated in (17):

$$P_{minimum}\le P_{output}\le P_{maximum}$$

(17)

where $P_{minimum}$ and $P_{maximum}$ are the limits of output power measured in watts, and $P_{output}$ is the acceptable output power. At each time t, the total electrical load within the hybrid microgrid system must be equal to the power generated by all DERs and the total amount of energy exchanged with the grid, and it can be measured by using (18):

$$P_{solar}\left(t\right)\times {\mathsf{\eta }}_{DC/Dc}+P_{wind}\left(t\right)\times {\mathsf{\eta }}_{AC/DC}+P_{fuelcell}\left(t\right)\times {\mathsf{\eta }}_{DC/AC}=P_{sell\_grid}\left(t\right)\times E_{sell}\left(t\right)-P_{buy\_grid}\left(t\right)\times E_{buy}\left(t\right)+P_{Load}\left(t\right)$$

(18)

where $P_{solar}\left(t\right),$ $P_{wind}\left(t\right)$ and $P_{fuelcell}\left(t\right)$ are power generated from each DER while ${\mathsf{\eta }}_{DC/Dc}$, ${\mathsf{\eta }}_{AC/DC}$ and ${\mathsf{\eta }}_{DC/AC}$ are the efficiencies of corresponding inverters. $P_{Load}\left(t\right)$ shows the total power consumed by the load. $P_{sell\_grid}\left(t\right)$ and $P_{buy\_grid}\left(t\right)$ are power sold to and bought from the main grid, which are determined based on predefined exchange rates at specific time intervals.

The optimization problem for energy management needs to incorporate the maximum allowable exchanged energy, as dictated by the technical constraints of the system such as capacities of transformers, circuit breakers, and the distribution network. Therefore, it must be ensured that the exchanged energy remains within the limits set by the maximum allowable selling and buying energy in the hybrid microgrid and can be measured by (19) and (20):

$$P_{buying}\left(t\right)\le P_{buy\_maximum}$$

(19)

$$P_{selling}\left(t\right)\le P_{sell\_maximum}$$

(20)

where $P_{buying}$ and $P_{selling}$ represent the buying and selling powers, respectively, and $P_{buy\_maximum}$ and $P_{sell\_maximum}$ denote the maximum allowable power that can be bought or sold at time t. The constraint of the hydrogen generation strategy is that each hybrid MG is limited to utilizing only its renewable energy resources for hydrogen production, and it can be measured in (21):

$$P_{solar}\left(t\right)+P_{wind}\left(t\right)\ge P_{EL}\left(t\right)$$

(21)

At this point, it is necessary to define the limits of the hydrogen storage system. During regular operating hours, hydrogen gas is generated by the electrolyzers using available power that can be measured in (22). The upper and lower limits of power consumption by the electrolyzers are detailed in (23) and (24):

$$H_{2\_EL}={\displaystyle \frac{{\mathsf{\eta }}_{EL}{P}_{EL}}{LH{V}_{H_2}}}$$

(22)

$$P_{EL}\le P_{EL\_max}\times U_{EL}$$

(23)

$$P_{EL}\le P_{EL\_min}\times U_{EL}$$

(24)

where $H_{2\_EL}$ is the hydrogen produced by the electrolyzer and ${\mathsf{\eta }}_{EL}$ shows the efficiency of the electrolyzer at which the power is consumed to produce the hydrogen in off-peak hours. $P_{EL}$ is the actual power consumed in watts W. The maximum hydrogen produced by the electrolyzer can be expressed in (25).

$$H_{2\_EL}\le H_{2\_E{L}_{\_}max}\times U_{EL}$$

(25)

Likewise, fuel cells utilized the produced hydrogen, and its constraints are expressed in (26). Meanwhile during the peak hours of the system, the electrical power can be expressed (27) and (28), which is produced by fuel cells:

$$H_{2\_FC}\le P_{FC\_max}\times U_{FC}$$

(26)

$$P_{FC}\ge P_{FC\_min}\times U_{FC}$$

(27)

$$P_{FC}\le P_{FC\_max}\times U_{FC}$$

(28)

where $H_{2\_FC}$ is the hydrogen produced by the fuel cells. Other quantities of power produced by the fuel’s cells are already expressed in the above section.

Multiple objectives are considered in the designing of the EMS, like technical and economic aspects. Technically, the EMS should maximize the equipment life and minimize the power loss during supply to load. The second half is an economic aspect; in this part, obviously, it should be cost-effective. The proposed flow chart of the EMS is presented in Figure 6. Expected solar and wind radiation on a daily basis are elaborated in Figure 7 and Figure 8. Variations of these curves depend on the weather conditions. The dotted line shows the average of both solar radiation and wind speed on a daily basis.

The EMS includes various constraints, such as those pertaining to hydrogen energy storage, handling excess power generated during hydrogen storage, scenarios where power is required from the utility, and time constraints, all of which are detailed in Section 2 and Section 3.

4. Simulation and Results

The main objective of this article is to find the optimal solution to improve the power profile and cost-effectiveness. Fuzzy logic utilizes sets and reasoning, offering user-friendly comprehension. It excels at solving complex problems that pose challenges for an alternative system. Fuzzy logic delivers precise outputs, particularly when handling imprecise or inaccurate data. In this research, the above stages should be implemented using a power and an EMS that continuously monitors the system’s status and controls the power flows. The Yalmip toolbox [45] is utilized to resolve the optimization problem, whereas the PSO technique is implemented in this article. The primary advantage encompasses more straightforward algorithm implementation, reduced parameters adjustment, and rapid convergence speed [46]. The optimization technique has been developed using a MATLAB/Simulink model. PSO exhibits numerous benefits over traditional optimization techniques, notably its fast convergence [47].

In this paper, input given in the simulation process comprises the financial facts, daily solar radiations, wind speed in m/s, and the load. The made-up peak load of consumers on the MG is about 2 MW. The average solar radiation, wind velocity/speed, and load of each consumer (p.u.) are revealed in

Table 2. Average input data for different sources.

$\mathbf{Solar}\mathbf{Radiation}\mathbf{(}\mathbf{W}\mathbf{/}{\mathbf{m}}^{\mathbf{2}}\mathbf{)}$	Wind Speed (m/s)	Electrical Load (p.u.)
422	6.45	0.6211

. The capital costs of each DER unit are derived from [48,49,50], and a summary of these costs is provided in

Table 3. Capital cost for each unit.

Unit Type	Solar Panel ($/kW)	Wind System ($/kW)	FCs ($/kW)	Electrolyzer ($/kW)
Capital Cost	1000	950	600	150

. Optimum size for each unit is given in

Table 4. Total cost and optimum size for each unit.

Solar Panel (kW)	Wind System (kW)	FCs (kW)	Electrolyzer (kW)	Cost (T $)
700	670	900	440	25

.

The methodology, based on fuzzy rules and PSO, is implemented for optimizing MG systems. It involves integrating various inputs into an algorithm, considering technical system constraints, and assessing both economic and technical outcomes. The rule-based fuzzy system operates with two inputs: the system’s voltage and the power produced by the system. Prior to evaluating the outcomes, specific rules are established. These rules include defining upper and lower limits for the inputs, ensuring that the system’s outcomes remain within these predefined limits. The fuzzy controller’s parameters include membership functions that are triangular, range of power of about −20 to 20 units, range of voltage in the proposed system of −10 to 10, proposed distribution that is medium, 25-rule base, and a defined output range of −20 to 20. These parameters were meticulously chosen based on various considerations, and were specifically designed to improve power quality by regulating power and voltage, ensuring optimal system performance. Moreover, PSO have been employed during the parameter-selection process to strike a balance between complexity and effectiveness. Figure 9 illustrates the rule-based surface area with distinct colors for identification. The bluish areas indicate the most feasible outcomes achieved by the system, while the reddish areas represent less favorable scenarios, which may suggest faults or non-convergent values within the system. The optimization process follows a detailed, step-by-step algorithm, as depicted in Figure 10. The PSO convergence characteristics with respect to the cost obtained in the optimal strategy of the MG system is exposed in Figure 11. The optimal solution is found just after a hundred iterations.

The latter half of the research focused on voltage convergence within the hydrogen-based microgrid. PSO is utilized to optimize the power at each level. Figure 12 presents the optimized output characteristics of RESs. Voltage level of each RES has significant value to serve the demand with less instabilities, as the power profile is a crucial consideration in the research. Once the power quality is well-established at the main source of generation, the entire energy storage system can reap benefits.

The FCs consistently provided a reliable current to meet consumer demand during periods of power scarcity in RESs production. The optimized features of FCs are detailed in Figure 13. Moreover, the fuel consumption during FC energy management is a noteworthy aspect, and its details are presented in its characteristics. Figure 14 depicts the characteristics of the battery system during simulation. This illustration emphasizes the significant role of SoC in the battery storage system. SoC depends entirely on two factors: voltage and current level of battery. When the current level of battery lags behind the voltage level, the battery’s state of charge should be high. Meanwhile, when the current level starts to rise, more current is drawn from the battery to meet the load requirements. So, SoC in batteries plays a vital role within hydrogen-based microgrids. Through precise energy management, the state of charge for the battery stabilizes at approximately 65% and maintains this level through continuous system optimization.

Ultimately, the voltage convergence is determined and displayed in Figure 15. Each phase of voltage reaches its specific convergence point. Three phases are dealt separately with color discriminates like red, yellow, and blue. All convergences are found within the 30 iterations as prescribed for the entire system. The converged voltage complies with a predefined constraint, ensuring it falls within the range of −2 to 2 for the respective phase. The convergence criterion was established using the PSO technique. Complete convergence was achieved within 30 iterations. In this context, voltage represents the local best quantity, while the output power of the hydrogen-based microgrid serves as the global convergence value. An optimized voltage profile has been developed for the system. By improving the voltage quality, the output power is optimized, leading to increased system reliability.

The power variations have been mitigated by enhancing the system’s power quality. As the system’s voltage converges, the overall power quality of the entire system is improved. This aligns with the second objective of the paper. Figure 16 illustrates the variation in electrical generation throughout the day, specifically from solar and wind sources. It also indicates any surplus power generated and presents the combined output of both sources. Figure 17 illustrates the hourly voltage profile over a typical day, describing the voltage for the load, solar, and wind sources.

The comparison of this research with different studies is described in

Table 5. Comparison of cost estimation and voltage convergence with traditional techniques.

	Solar Panel ($/kW)	Wind System ($/kW)	FCs ($/kW)	Electrolyzer ($/kW)	Total Cost after Assessment $	Time or Total Number of Iterations	Voltage Convergence	Power Quality Improvement
Ref. [8]	360	200	150	-	-	3500 s	No	No
Ref. [51]	5	5	5	30	-	1408 s	No	No
Ref. [52]	60	-	2	45	-	-	No	No
Ref. [12]	770	900	907	439	$2.44\times {10}^7$ to $2.33\times {10}^7$	200 iterations	No	No
In this research	700	670	900	440	$2.29\times {10}^7$ to $2.17\times {10}^7$	100 iterations	Yes	Yes

, with a graphical representation provided in Figure 18. The representation of results has been significantly improved, and voltage convergence has been ensured in the research.

The results, however, highlight the effectiveness of our approach, which surpasses previous methods in terms of voltage convergence and enhancing power quality. The generation mix for 1 day totals approximately 4.2 MW, while the voltage profile for a typical day illustrates the load coverage with the ease of hydrogen storage with 100 kW. The system is optimized through efficient optimization techniques, ensuring the fulfillment of load requirements at reduced costs in the long run. All the results are much better than the aforementioned studies and advanced conferring to power profile improvement as well. As depicted in Table 5 above, the proposed model outperforms the previous studies in terms of both convergence speed and accuracy. When the power quality is enhanced to meet demand, the convergence and accuracy occur sooner, as detailed in this article. However, in the face of increased load unpredictability, both the microgrid’s current cost and energy efficiency decline. Table 5 clearly illustrates that the applied methodology reduces the cost for an MG system from 24.4 to 22.9 million dollars while simultaneously enhancing power quality with 100 iterations. This study has achieved a remarkable 6.147% improvement in cost-effectiveness compared to traditional methods. However, electrolyzer technology is anticipated to significantly reduce cost consumption within the hybrid MG system, as indicated by Figure 18.

The objective function is computed when the entire power production is adequate to meet the essential load in the HMG system. It will help to design the MG system in an optimum way, and it will assist for the next studies as well, according to the convergence level of cost by the fuzzy rule based and PSO method.

5. Conclusions

This article proposes a method and algorithm to simultaneously optimize the costs of different DERs in a hydrogen-based MGs system, considering various technical and economic limitations. This study encompasses progress in hydrogen production, storage, transportation, and utilization technologies, all aimed at fully realizing its potential as a sustainable energy carrier, especially through utilizing RESs. This research has proven to be considerably more valuable than traditional studies, particularly in terms of the cost per kW for solar, wind, fuel cells, and electrolyzers. The core goal involves reducing costs and enhancing the overall power quality of the entire MG system. The suggested objective function is reduced throughout the project’s lifespan through the utilization of the fuzzy rule based and PSO method. Overall, this method, with the improvement in voltage profile, power quality, and energy management strategy, can help to maximize the utilization of RESs, reduce reliance on the grid, and optimize the system’s performance and efficiency. The battery’s state of charge stabilizes at around 65%, maintained through continuous system optimization, with the characteristics of the fuel cells and overall system comprehensively illustrated. The total generation mix is approximately 4.2 MW, ensuring optimal load converged for a typical day with the aid of 100 kW for hydrogen storage, enhancing HMG efficacy. This study manages to save approximately 6.147% of the total cost by employing optimization techniques. Considering power quality as well, this study has achieved a remarkable 93.853% enhancement in cost-effectiveness compared to prior methods. In real-world applications, every energy management solution has its own set of pros and cons. However, the most appropriate energy management scheme can be chosen based on the optimization goal.

Future research will center on leveraging artificial intelligence tools and optimization techniques to improve current and power delivery in hydrogen-based microgrids. Additionally, exploring the power quality of these systems will be a key area for future investigation. There is also potential to further reduce costs by implementing more advanced AI methods, which will contribute to the advancement of electrical systems.