Introduction

Electricity is one of the most important forms of energy used in the world. Safety, power quality, the failures number, the control cost, and the natural problems associated with the use of energy are all issues that arise today. Most areas within a country are integrated into a large power grid that connects electricity producers and consumers via a network of transmission and distribution lines and supporting infrastructure. However, in some countries, certain areas, such as remote communities or isolated industrial facilities, are generally disconnected from the central grid and face their own challenges. These areas often rely heavily on expensive fossil fuels, such as diesel, to power their residential areas and factories. To reduce this dependence, renewable energy sources (RES) are increasingly being used in a variety of applications. As a consequence, microgrid-based RES can be used to power communities in inaccessible areas. The microgrid can include photovoltaic (PV) panels, wind turbines (WT), batteries as a capacity framework and diesel generators (DG). Managing these components is vital to providing a robust techno-economic microgrid. Many different strategies have been used to manage microgrids using multi-sector renewable energy sources. Belboul et al.1 described an optimized framework consisting of a PV/wind/battery/diesel generator based on a multi-objective salp swarm algorithm (MOSSA). The objective functions were the cost of energy (COE) and the loss probability of power supply (LPSP). Fathy et al.2 used the strategy of the Social Slope Optimiser (SSO) to decide on the ideal size of the sources making up a microgrid (MG). The goal was to decide on three planning factors: the number of PV panels, the number of WTs, and the number of days of battery autonomy. Zhu et al.3 identified the optimal size of a hybrid microgrid for an island made up of solar panels, wind generator, tidal current, batteries and fuel-powered generator. In this approach, an improved multi-objective grey wolf optimization technique (IMOGWO) was applied, to minimize the annual cost of the system (ACS) and the deficiency of power supply probability (DPSP). However, Jasim et al.4 used a hybrid algorithm based on the Cuckoo Search and Gray Wolf Optimization (GWO) algorithms to take advantage of the exploratory power of the former and the rapid convergence capability of the latter, in order to obtain lower annual electricity costs with the minimum number of units in the system. Whereas, Sami et al.5 optimized three potential hybrid structures to supply a remote rural area in Egypt using the firefly optimization algorithm (FA). The considered structures were PV/FC, PV/WT/FC and WT/FC. Ghenai et al.6 implemented hybrid renewable energy sources composed of PV, FC, and DG to meet the electrical energy requirements of a passenger ship in Sweden. Forootan Fard et al.7 applied the Homer software to find feasible approaches to investment to partially substitute the energy required by renewable energies when total emissions are limited to EPA standards. In8, Bukar and Tan explored power management strategies for a stand-alone photovoltaic, and wind power system combined with a fuel cell, to determine the formula of grid components achieving an efficient system at minimum cost. In references9, the authors proposed a control strategy for a hybrid microgrid system to maintain a continuous supply to the load in different operating modes. The combination of wind power, photovoltaics, a diesel generator, and battery storage with variable loads is considered for this purpose. The MOPSO (Multi-Objective Particle Swarm Optimization) method is applied to obtain the best system configuration. The cost of electricity (COE) and the probability of loss of power supply (LPSP) are defined as objective functions. Ghorbani et al.10 used a hybrid GA-PSO algorithm to determine the optimal off-grid size of a microgrid composed of a combination of photovoltaic panels, wind turbines, and batteries to power a house. In reference11, Ramli et al. used MATLAB and HOMER softwares to study the feasibility of a hybrid wind and solar energy system in the west coast region of Saudi Arabia. Focusing on wind turbines and photovoltaic panels, the study evaluates energy production and costs, taking into account factors such as surplus electricity and unmet electrical load. Bukar et al.12 used the grasshopper optimization algorithm (GOA) to determine the optimal size of an isolated microgrid located in Yobe State, Nigeria, consisting of PV, WT, battery and diesel generator powering five residential units, taking the cost of energy and the probability of power loss as minimization objectives. In13, the optimal technical and economic selection of the capacity of the different renewable energy sources of a hybrid microgrid based on a solar photovoltaic (PV), wind, biomass and vanadium oxide flow battery (VRFB) storage system, to meet the daily energy demand was carried out using HOMER simulation. Ren et al.14, developed an optimization model for the residential energy system based on photovoltaics, fuel cells and batteries. While ensuring reliable system operation, the model can identify optimal operating strategies with annual operating cost or annual CO2 emissions as the objective function to be minimized. Reference15 presented hybrid systems that combine fuel cell, wind turbine under turbulent wind, and energy storage system (ESS). The fuel cell is used as a backup power source to meet load demand and minimize the ESS size, particularly in the event of high WT power variability. Moghadam et al.16 presented a design for energy management of hybrid systems that combine PV, WT, and hydrogen storage (HS) based fuel cell to make the total net cost lower in the northwest region of Iran based on the flower pollination algorithm (FPA). In Ref17, the design of an optimal PV/wind/diesel hybrid microgrid with battery storage is carried out based on the Self-Adaptive Differential Evolution Multi-Objective algorithm for Yanbu city, Saudi Arabia, to minimize the loss probability of power supply (LPSP) and the cost of electricity (COE). Authors of reference18 analyzed the bi-objective optimization of the lifted cost of energy (LCOE) and the probability of loss of power supply (LPSP) of a grid-connected hybrid energy system comprising photovoltaic modules, a diesel generator, and a fuel cell (FC). For this, they used a multi-objective variant of the crow search algorithm. In19, a multi-objective design of a hybrid system consisting of a photovoltaic system, a fuel cell, and a diesel generator to provide electrical power to an off-grid community in Kerman, Iran, is presented in the context of operating reserve and load and sunlight variances. The total net cost and the probability of losing the power supply are considered to be the objectives to be minimized. Nadjemi et al.20 presented a review of sizing techniques for grid-connected hybrid systems, including PV/wind/ battery power devices. An improved discrete search algorithm (IDCS) was applied to simultaneously minimize total system cost and unserved load. In reference21, a hybrid energy storage system using a fuel cell and a supercapacitor is simulated to find the most economical design. The chosen configuration is based on reliability and cost-effectiveness. The simulation is carried out using HOMER Pro software for a commercial load in Cape Town, South Africa. Maleki et al.22 explored the execution of different variants of the particle swarm optimization (PSO) algorithm to design a hybrid (PV/wind/Batt) system providing high reliability and minimal total production costs over the system lifetime. Boujdaini et al.23 carried out the same study as in22 with the addition of fuel-powered generator. Maleki and Pourfayaz24 used the simulated annealing algorithm integrated with HOMER to optimize a hybrid system composed of PV, WG, and diesel generator, including two storage devices: a battery, and a fuel cell. In Ref25 a hybrid photovoltaic/wind turbine system has been submitted for the Lafarge cement plant in Al-Tafilah, Jordan. The system is designed to maximize the demand proportion served by the hybrid system at a lower cost of electricity (COE) than the grid tariff. The Hybrid Big Bang-Big Crunch (HBB-BC) algorithm is being introduced to optimally size a hybrid off-grid electricity system comprising a photovoltaic panel, a wind turbine, and a battery bank, to generate electricity for an isolated village in Qazvin, Iran. This is achieved by optimizing the system to constantly satisfy load demand while minimizing the total running cost of the system26. In Ref27, a method based on the clonal selection algorithm is proposed to obtain the optimal size of a solar/wind/battery hybrid power system. This latter is designed to satisfy the load demand with both low fluctuation rate and minimum cost. The study is carried out on a case study at Troyes Barbery Station - France. In28, the authors seek to find the best deal between devices, comprising photovoltaic panels, bio-generators, diesel generators, batteries, and the grid, while taking into account economic, environmental, and technical factors. The study is carried out using HOMER software, considering certain constraints, such as the insufficient space for installing photovoltaic panels and the CO2 penalties when diesel generators and the grid supply electricity. In the study of Mahmoud et al.29, the distribution grid is associated with PV/wind/hybrid fuel cells to meet demand, compensate for grid downtime, and minimize the energy bill of the load operation. For this, the Seagull Optimization Algorithm (SOA) and the Marine Predator Algorithm (MPA) were applied. The system was designed for an area in southern Egypt. Al Garni et al. studied the use of a combined dispatch strategy to optimize hybrid energy systems30. In a subsequent study31, they carried out an economic evaluation of off-grid renewable energy projects, using load data. Both studies were carried out at six isolated sites in Saudi Arabia. In several works32,33,34,35,36,37, A. R. Jordehi et al. attempt to propose very interesting models for the operational planning of microgrids with hydrogen refueling stations and for the optimal placement of hydrogen stations in power grids with a high penetration of renewable energies. In addition to optimal hydrogen pricing. In reference38, the authors focus on the frequency stabilization of various interconnected power systems with the integration of renewable energies and energy storage systems.

Table 1 provides a summary of the reported approaches to hybrid microgrid design and deployment, identifying the advantages and shortcomings of each method.

In this paper, an autonomous hybrid energy system made up of a photovoltaic panel, a wind turbine, a battery, and a fuel-powered generator (diesel generator) is designed, taking into account the meteorological parameters of the region under study to estimate the power output of the wind turbines and photovoltaic panels. An energy management strategy (EMS) is suggested to coordinate the flow of energy between the various energy sources. This study aims to design an optimized autonomous hybrid energy system that meets load demand and ensures reliability, cost-effectiveness, and pollution reduction in a given area. The loss of power supply probability (LPSP) is taken into account to study the reliability of the standalone microgrid. To tackle the problem of optimal sizing of the proposed MG components, four multiobjective optimization algorithms namely the Multiobjective Particle Swarm Optimization (MOPSO)39, the Multiobjective Ant Lion Optimizer (MOALO)40, the Multiobjective Dragonfly Algorithm (MODA)41, and the Multiobjective Evolutionary Algorithm (MOGA)42 are used. These algorithms are characterized by their simplicity of construction and by the fact that they require fewer control parameters. Our study is based on real solar radiation, wind speed, and temperature data recorded for the remote area of Zaouiet Kounta, in the southwestern region of the province of Adrar in southern Algeria.

Table 1 Synopsis of indicated hybrid ser optimization methods.
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Mathematical model formulation

Methodology

In the present study, the microgrid is conceived to supply an electrical load in an isolated area of the Adrar region in southern Algeria. The proposed autonomous microgrid is composed of a load, two renewable energy sources namely a photovoltaic system and a wind turbine, a set of batteries as energy storage unit, a diesel generator as backup energy source, and an inverter. Figure 1 illustrates the overall configuration of the autonomous microgrid under study. The PV panels, WTs and batteries are connected to the DC bus, while the load and the DG are directly connected to the AC bus. The load is supplied mainly by the photovoltaic panels and wind turbines via a DC/AC inverter. The excess energy produced by these renewable energy sources is stored in the battery bank. The battery is used when the renewable energy sources are in a state of deficit, while the diesel generator operates and provides energy when the battery is in its minimum operating level. All the equipment in the microgrid is managed by an energy management system (EMS) to regulate the power flow and improve the useful life of the equipment.

Fig. 1
figure 1

An insulated microgrid layout.

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PV array modeling

PV arrays are made up of an appropriate number of series/parallel connections of solar cells. Cells connected in series are required to achieve the voltage level specified for a given photovoltaic panel. Whereas to get more output current from a panel, similar strings are usually connected in parallel. The rated output power is determined by multiplying the output current by the output voltage. Several models have been developed to calculate the photovoltaic panel’s output power. Figure 2 presents the model which is used in this study, which is the double diode model43.

The PV panel current can be computed using the formula below:

$$\:I={N}_{p}{I}_{ph}-{N}_{p}{I}_{o1}\left(\text{exp}\left(\frac{\left(\frac{V}{{N}_{s}}+\frac{I}{{N}_{p}}\right)}{{\alpha\:}_{1}{V}_{T1}}\right)-1\right)\:-{N}_{p}{I}_{o2}\left(\text{exp}\left(\frac{\left(\frac{V}{{N}_{s}}+\frac{I}{{N}_{p}}\right)}{{\alpha\:}_{2}{V}_{T2}}\right)-1\right)-\left(\frac{\frac{{N}_{p}}{{N}_{s}}V+I\cdot\:{R}_{s}}{{R}_{p}}\right)$$
(1)

where \(\:{I}_{ph}\) represents the photon current, \(\:{N}_{s}\) and \(\:{N}_{p}\) define the series and parallel configurations of the cells with \(\:{I}_{o1}\) and \(\:{I}_{o2}\) giving way to reverse saturation of current from diodes; I and V specify the terminal current and voltage corresponding pv – panels; whereas \(\:{\alpha\:}_{1}\) and \(\:{\alpha\:}_{2}\)are the ideality factors of each diode, \(\:{V}_{T1}\) and \(\:{V}_{T2}\) denote the thermal voltages of the diodes and \(\:{R}_{s}\) and \(\:{R}_{p}\)are shorthand notations for series resistances of cells.

Fig. 2
figure 2

Two diodes PV panel model.

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The total output energy of an array of photovoltaic panels is determined as follows:

$$\:{P}_{PV}\left(t\right)={N}_{PV}\times\:I\left(t\right)\times\:V\left(t\right)$$
(2)

where NPV is the number of photovoltaic modules.

Wind turbine modeling

The output power of the wind turbine is a function of the wind speed, which depends on the height at the same point. The speed of wind measured must therefore be adapted to the height of the fan rotor. The wind speed at rotor height is determined as follows44,45:

$$\:{\text{V}}_{2}={\text{V}}_{1}{\left(\frac{{\text{H}}_{2}}{{\text{H}}_{1}}\right)}^{{\beta\:}_{\text{W}\text{T}}}$$
(3)

V1 and V2 are the speed of wind at the altitude of the reference point (H1) and at the altitude of the rotor (H2). The constant βWT represents the coefficient of friction with a designated value of 0.14344,45.

The output power generated by wind turbines (WTs) is estimated using the following equation44:

$$\:{\text{P}}_{\text{W}}\left(\text{t}\right)=\left\{\begin{array}{cc}{\text{n}}_{\text{w}}{\eta\:}_{\text{w}}{\text{P}}_{{\text{r}}_{-}\text{w}}*\frac{\left({\text{V}}^{2}\left(\text{t}\right)-{{\text{V}}^{2}}_{{\text{c}}_{\text{in\:}}}\right)}{\left({{\text{V}}^{2}}_{r}-{\text{V}}^{2}{\text{c}}_{\text{in\:}}\right)}&\:{\text{V}}_{{\text{c}}_{-}\text{in\:}}<\text{V}\left(\text{t}\right)<{\text{V}}_{\text{r}}\\\:{\text{n}}_{\text{w}}{\eta\:}_{\text{w}}{\text{P}}_{{\text{w}}_{\text{r}}}&\:{\text{V}}_{\text{r}}<\text{V}\left(\text{t}\right)<{\text{V}}_{{\text{c}}_{-}\text{off\:}}\\\:\text{O}&\:\text{V}\left(\text{t}\right)<{\text{V}}_{{\text{c}}_{-}\text{in\:}}\text{\:or\:}\text{V}\left(\text{t}\right)<{\text{V}}_{{\text{c}}_{-}\text{off\:}}\end{array}\right\}$$
(4)

where Pw(t) is the WTs output power, \(\:{\text{n}}_{\text{w}}\), \(\:{{\upeta\:}}_{\text{w}}\), and\(\:{\:\:\text{P}}_{{\text{r}}_{-}\text{w}}\) are respectively the WTs number, the WTs efficiency, and the maximum power of the WTs.

The total power generated by a set of wind turbines (NW turbine) is determined using the following expression:

$$\:{\text{P}}_{\text{t}\text{o}\text{t}-\text{w}}={\text{N}}_{\text{w}}\times\:{\text{P}}_{\text{w}}\left(\text{t}\right)$$
(5)

Battery modeling

The battery device is an essential part of the autonomous microgrid, responsible for supplying the load in the case of deficiency in the energy produced from renewable sources. The battery capacity is determined as follows46:

$$\:{C}_{\text{Batt\:}}=\frac{AD\times\:{P}_{\text{load\:}}}{{\eta\:}_{\text{Inv\:}}\times\:{\eta\:}_{\text{Batt\:}}\times\:BDL}$$
(6)

where \(\:{P}_{\text{load\:}}\)is the load power demand, ŋInv and ŋBatt are respectively the inverter and battery efficiency, AD is the number of days of autonomy, i.e. the number of days during which the battery can meet the load power demand without any failure, and BDL is the battery discharge level.

It is recognized that the intermittency of solar radiation and wind speed affects the generation of electricity from renewable sources such as PV and WT. Therefore, it is important to consider the number of days of autonomy when determining the size of the battery bank to compensate for any power deficits from these sources. When there is a surplus of energy produced, the additional energy is used to recharge the batteries. The power supplied by the batteries is determined as follows47:

$$\:\begin{array}{c}{P}_{\text{Batt\:}}\left(t\right)=\left({P}_{wt}\left(t\right)+{P}_{pv}\left(t\right)\right)-\frac{{P}_{\text{load\:}}\left(t\right)}{{\eta\:}_{\text{Inv\:}}}\end{array}$$
(7)

where \(\:{P}_{wt}\left(t\right),{\:P}_{pv}\left(t\right)\), and \(\:{P}_{\text{load\:}}\left(t\right)\) are respectively the power generated by the WT, the PV and the power demand of the load, and ŋInv is the efficiency of the inverter.

There are three possible scenarios. The first is when the battery is in the charging phase, indicating that the energy produced by the renewable sources exceeds the power demand, PBatt(t) > 0. The second is when the battery is delivering power to the load, indicating that there is a deficit in energy production, PBatt(t) < 0. The third is when the power produced by the renewable sources is equal to the power demand of the load, PBatt(t) = 0.

To check the battery status, an important parameter that influences the battery performance is the state of charge (SOC(t)), which depends on the surplus or shortfall of energy produced by renewable sources compared to the demand. SOC can be expressed as follows48:

  • Charging mode, if; \(\:\left({{P}_{wt}\left(t\right)\:\:+P}_{pv}\left(t\right)\right)\)> \(\:{P}_{\text{load\:}}(t\))

$$\:\text{SOC}\left(t\right)=\text{SOC}\left(t-1\right)\times\:\left(1-\sigma\:\right)+ \left(\left({P}_{wt}\left(t\right)+{P}_{pv}\left(t\right)\right)-\frac{{P}_{\text{load\:}}\left(t\right)}{{\eta\:}_{\text{Inv\:}}}\right)\times\:{\eta\:}_{\text{Batt\:}}$$
(8)

  • Discharging mode, if; \(\:\left({{P}_{wt}\left(t\right)\:\:+P}_{pv}\left(t\right)\right)\)< \(\:{\text{P}}_{\text{load\:}}(\text{t}\))

$$\:\text{SOC}\left(t\right)=\text{SOC}\left(t-1\right)\times\:\left(1-\sigma\:\right)+\left(\frac{{P}_{\text{load\:}}\left(t\right)}{{\eta\:}_{\text{Inv\:}}}-\left({P}_{pv}\left(t\right)+{P}_{wt}\left(t\right)\right)\right)\times\:{\varvec{\eta\:}}_{\text{Batt\:}}$$
(9)

Diesel generator modeling

The diesel fuel-powered generator is used in the microgrid as a secondary power source (backup) and plays an important role in keeping the system stable, particularly when the load fluctuates and there is a rapid increase in energy demand. The fuel requirement for the diesel generator is estimated as follows49,50:

$$\:F\left(t\right)=0.246\text{*}{P}_{\text{diesel\:}}\left(t\right)+0.08415{*P}_{\text{diesel\:}}^{\text{rated\:}}$$
(10)

where \(\:{P}_{\text{diesel\:}}\) (t) and \(\:{{P}_{\text{diesel}}^{rated}}_{\text{\:}}\)represent the diesel fuel-powered generator power at instant t, and its rated power.

The overall efficiency of the diesel-powered generator is evaluated as follows51:

$$\:{\eta\:}_{\text{overall\:}}={\eta\:}_{\text{brake\_thermal\:}}\times\:{\eta\:}_{\text{generator\:}}$$
(11)

where \(\:{\eta\:}_{\text{brake\_thermal\:}}\)is the brake thermal efficiency, and \(\:{\eta\:}_{\text{generator\:}}\) is the efficiency of the diesel generator.

Inverter modelling

The inverter is a device that converts the direct current generated by renewable energy sources (RES) into alternating current to power the load. The efficiency of the inverter can be calculated as follows52:

$$\:{\eta\:}_{\text{Inv\:}}=\frac{P}{P+{P}_{0}+k{P}^{2}}$$
(12)
$$\:P={P}_{\text{out\:}\:\:}/{P}_{\text{n\:}\:\:},{P}_{0}=1-99{\left(10/{\eta\:}_{10}-1/{\eta\:}_{100}-9\right)}^{2}$$
(13)

and\(\:\text{\:}k=1/{\eta\:}_{100}-{P}_{0}\)

where \(\:{P}_{\text{n\:}\:\:}\) represents the rated power of the inverter, \(\:{\eta\:}_{10}\) and \(\:{\eta\:}_{100}\) are respectively the inverter efficiencies at 10% and 100% of its nominal power, both of which are defined by the manufacturer.

Description of the target site and system specifications

Target region and meteorological data

The planned microgrid will be installed in a remote area of Zaouiet Kounta, in the southwestern region of the province of Adrar in southern Algeria53,54,55,56,57,58,59,60. The province of Adrar is located between longitudes of 1 degree east and 3 degrees west, and latitudes of 20 degrees north and 30 degrees north. The region has relatively hot summers and cold winters, with persistent strong winds throughout the year. Autumn is generally associated with an increase in wind speed. Figure 3 shows the location of the study site. Table 2 provides key information and the period during which data were measured.

The meteorological data used in this study, especially wind speed, solar radiation, and ambient temperature at Zaouiet Kounta (Adrar), come from NASA (National Aeronautics and Space Administration)61. The data are collected during the period from 01/06/2022 to 01/06/2023, the average solar radiation is 252.8682 W/m2, the average wind speed is 4.636981 m/s, and the average ambient temperature is 298.007 K. Figures 4, 5 and 6 illustrate the hourly profiles over a year (8784 h) for solar radiation, wind speed measured at 10 m above ground, and ambient temperature.

Fig. 3
figure 3

Geographical map of the study area.

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Table 2 Displays geographical data for the study area.
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Load evaluation

Defining an accurate load profile is critical to design an efficient microgrid. In other words, by carefully defining the load profile, it is possible to design a microgrid that efficiently meets the site’s energy needs, effectively integrates renewable energy sources, and ensures reliability and sustainability. A load profile describes the variations in electrical demand over time for a specific site. Therefore, this work assumes that the microgrid under consideration serves a specific load (a small village). Figure 7 shows the load profile for the study area for an entire year.

Specifications of hybrid microgrid system components

To ensure the reliability of the system, components should be selected with an appropriate power rating to avoid blackouts or even the collapse of the microgrid due to equipment failure. The technical and economic parameters of the main components are shown in Table 3.

Table 3 System components techno-economic characteristics.
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Fig. 4
figure 4

Profile of solar radiation for the study site. (a) Annuel (b) month of January.

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Fig. 5
figure 5

Profile of wind speed for the study site. (a) Annuel (b) month of January.

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Fig. 6
figure 6

Profile of ambient temperature for the study site. (a) Annuel (b) month of January.

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Fig. 7
figure 7

Residential units load profile. (a) Annuel (b) month of January.

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Hybrid microgrid system energy management strategy

Energy management strategies cover a wide range of activities and technologies designed to optimize energy consumption, improve efficiency and reduce costs in various sectors, including residential, commercial and industrial. In fact, it’s important to incorporate an energy management strategy (EMS) into the process of sizing a microgrid integrated with hybrid renewable energy. In the context of this study, its main task is to allow an optimal distribution and management of the energy flow among the different devices included in the autonomous microgrid system under study. Figure 8 illustrates the used EMS layout.

The main objectives of the proposed EMS can be outlined as follows:

  1. a.

    By implementing system efficiency procedures, significant cost reductions and energy savings can be achieved, resulting in improved overall energy efficiency.

  2. b.

    Increasing the use of renewable energies.

  3. c.

    Minimizing fossil fuel consumption for both cost savings and environmental sustainability.

  4. d.

    Preserve the battery pack to minimize degradation and extend its lifespan.

The proposed Energy Management Strategy (EMS) outlined in this study operates on the basis of on four modes, as follow:

  • Mode 1: As soon as the renewable energy sources (PV and WT) output power exceeds the demand, the excess energy is fed back into the battery. This operating mode is activated when the SOC at time “t” is greater than the maximum SOC threshold value (SOCmax).

  • Mode 2: Whenever the power generated by the RES exceeds demand requirements and the battery is totally charged (SOC(t) equals SOCmax), the surplus power is routed to a discharge load for dissipation.

  • Mode 3: In this mode, the power produced by the SER is less than that required by the load and the battery is fully charged (SOC(t) greater than SOCmin). In this case, the battery is used as an energy source to provide electrical power and satisfy the load.

  • Mode 4: When the RES doesn’t produce enough energy to meet the load requirements and the battery is simultaneously depleted. The diesel generator is started to produce electricity to supply the load and recharge the battery. This regime is deactivated once electricity generation from renewable energy sources (RES) has been initiated.

Fig. 8
figure 8

Proposed rules for energy management strategy.

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Problem formulation

In addition to outlining the objective functions considered, this section also describes the energy management strategy and the various steps involved in the proposed response technique.

Objective function

In order to evaluate the performance of the proposed hybrid PV/wind/diesel/battery microgrid, the cost of energy (COE) and the loss probability of power supply (LPSP) are taken as objective functions. The goal is to minimize both functions while achieving the highest reliability and lowest cost for the hybrid off-grid microgrid under study.

Cost of energy (COE)

The COE is a function of the total net present costs (NPC), which includes the system investment cost, the cost of operation and maintenance, and the replacement charge, and fuel consumption cost. It can be computed for each element of the microgrid on the basis of the equations below62,63:

$$\:{C}_{t}^{PV}={N}_{PV}\left({C}_{C}^{PV}+{C}_{O\&M}^{PV}\times\:\left(\frac{(1+i{)}^{n}-1}{i(1+i{)}^{n}}\right)\right)$$
(14)
$$\:{C}_{t}^{WT}={N}_{WT}\left({C}_{C}^{WT}+{C}_{O\&M}^{WT}\times\:\left(\frac{(1+i{)}^{n}-1}{i(1+i{)}^{n}}\right)\right)$$
(15)
$$\:{C}_{t}^{\text{Batt\:}}={C}_{C}^{\text{Batt\:}}+{C}_{O\&M}^{\text{Batt\:}}\:\times\:\left(\frac{(1+i{)}^{n}-1}{i(1+i{)}^{n}}\right)+{C}_{R}^{\text{Batt\:}}\times\:\:\:\:\:\:\:\:\:\:\:\:\:\sum\:_{j=1}^{\left(\frac{n}{{n}_{\text{Batt\:}}}-1\right)}\:\left(1+\frac{1}{(1+i{)}^{j{n}_{\text{Batt\:}}}}\right)$$
(16)
$$\:{C}_{t}^{DG}={C}_{C}^{DG}+{C}_{O\&M}^{DG}\times\:\left(\frac{(1+i{)}^{n}-1}{i(1+i{)}^{n}}\right)+{C}_{R}^{DG}\times\:\sum\:_{j=1}^{\left(\frac{n}{{n}_{\text{Batt\:}}}-1\right)}\:\left(1+\frac{1}{(1+i{)}^{j{n}_{DG}}}\right)$$
(17)

The four sources and the inverter total net cost can be computed as follows:

$$\:NPC={C}_{t}^{PV}+{C}_{t}^{WT}+{C}_{t}^{Batt}+{C}_{t}^{DG}+{C}_{t}^{Inv}$$
(18)

where \(\:{N}_{WT}\) and \(\:{N}_{PV}\)are WT and PV number respectively, \(\:{{C}_{C}^{WT},\:\:C}_{C}^{PV}\), \(\:{C}_{C}^{Batt}\), \(\:{C}_{C}^{disel}\), and \(\:{C}_{C}^{Inv}\) are respectively the costs investment of WT, PV, battery, DG, and inverter, \(\:{{C}_{(O\&M)}^{WT},\:\:\:C}_{(O\&M)}^{PV}\), \(\:{C}_{(O\&M)}^{Batt}\), and \(\:{C}_{(O\&M)}^{diesel}\) are respectively the O&M costs of WT, PV, battery, and DG, \(\:{C}_{R}^{Batt}\) and \(\:{C}_{R}^{diesl}\)are the battery and diesel generator replacement costs, \(\:{N}_{batt}\) and \(\:{N}_{diesel}\) are the lifetimes of the battery and diesel generator respectively, i is the annual interest, n is the system lifetime.

The COE is computed as the annual cost of the useful electric energy produced by all the elements of a hybrid system, divided by the total energy produced during the corresponding year, as follows63,64,65,66,67:

$$\:COE=\frac{NPC}{{\sum\:}_{h=1}^{8760}{P}_{load}}\times\:CRF$$
(19)

where \(\:{P}_{load}\) is the power consumed per hour by the load, and CRF represents the capital recovery factor, calculated as follows:

$$\:CRF=\frac{{i(1+i)}^{n}}{{(1+i)}^{n}-1}$$
(20)

Loss of power supply probability (LPSP)

Once the optimal sizes of the hybrid renewable energy systems (RESs) have been determined, it is important to assess the reliability of the microgrid in question. It is done by calculating the Probability of Power Supply Loss (LPSP) index, which is calculated by:

$$\:LPSP=\frac{\sum\:({P}_{load}-{P}_{WT}-{P}_{PV}+{P}_{SOC,min}+{P}_{diesel})}{{P}_{load}}$$
(21)

The LPSP value falls within the range of [0, 1]. When the total output power produced by optimized hybrid SERs matches the load demand, it confirms the system’s reliability. However, the most economical suitable scenario is when the total power generated matches the total demand, resulting in an LPSP value close to zero. In order to minimize the COE while ensuring system reliability, the variables to be optimized are \(\:{\text{N}}_{\text{P}\text{V}}\), \(\:{\text{N}}_{\text{W}\text{T}}\), and \(\:{\text{N}}_{\text{A}\text{D}}\), with respect of the following constraints:

$$\:{N}_{PV}^{min}\le\:{N}_{PV}\le\:{N}_{PV}^{max}$$
$$\:{N}_{WT}^{min}\le\:{N}_{WT}\le\:{N}_{WT}^{max}$$
$$\:{N}_{AD}^{min}\le\:{N}_{AD}\le\:{N}_{AD}^{max}$$

where \(\:{N}_{PV}^{min}\), \(\:{N}_{WT}^{min}\), and min\(\:{N}_{AD}^{min}\) represent respectively the minimum number of PV, WT, and AD, while \(\:{N}_{PV}^{max}\), \(\:{N}_{WT}^{max}\), and \(\:{N}_{AD}^{max}\) represent respectively the maximum number of PV, WT, and AD.

Multiobjective optimization

In this study, the optimization problem for the given hybrid microgrid system (HMGS) is defined as a multi-objective optimization problem. Such optimization is the task of simultaneously optimizing two or more conflicting objectives, described as follows:

$$Minimize:f\left( x \right) = \left[ {\begin{array}{*{20}c} {f_{1} \left( x \right)} \\ {f_{2} \left( x \right)} \\ \vdots \\ {f_{n} \left( x \right)} \\ \end{array} } \right]$$
$$\:Subjected\:to\left\{\begin{array}{c}H\left(x\right)=0\\\:G\left(x\right)\le\:0\end{array}\right.$$

where the vector f(x)= [\(\:{f}_{1}\) (x), \(\:{f}_{2}\)(x)………, \(\:{f}_{n}\)(x)] is the set of n objective functions to be optimized simultaneously, x= [x1, x2, ………, xn] is the vector of the variables, \(\:H\left(x\right)\) and \(\:G\left(x\right)\) are respectively the set of equality and inequality constraints.

Results and discussion

This paper describes the proposed microgrid configuration for a stand-alone hybrid renewable energy system based on photovoltaic panels/wind turbines as the main sources, a set of energy storage batteries, and a diesel generator as a backup source to eliminate the negative impact of energy shortage. These facilities are responsible for providing sufficient energy to this small, isolated agglomeration in the Algerian desert that is not connected to the main electrical grid. The optimization task is performed using MATLAB version R2023a. implemented on a PC i5-1135G7 Intel Core i5-1135G7 with 1 TB RAM and i5-1135G7 Intel Core i5-1135G7 running on the Windows 11 Pro (64-bit) platform (10.0, build 22631).

This study involves the use of four multi-objective optimization algorithms to tackle the design optimization problem presented in this paper:

  1. 1.

    Multiobjective Particule Swarm Optimization (MOPSO);

  2. 2.

    Multiobjective Dragonfly Algorithm (MODA);

  3. 3.

    Multiobjective Ant Lion Optimizer (MOALO);

  4. 4.

    Multiobjective Evolutionary Algorithm (MOGA).

In the literature, some studies1,9, treat the Hybrid Microgrid System (HMS) problem as a single objective function problem using the weighted sum approach, by multiplying each of the objective functions by a user-assigned weight. However, this method has the disadvantage of finding only one solution, depending on the weights already provided. In this section, the performance of the microgrid with different design options will be investigated using multi-objective optimization to achieve the set of possible Pareto optimal solutions, commonly called Pareto fronts.

For all algorithms MOPSO, MOALO, MODA, and MOGA, the maximum number of iterations and the size of the population are set to 200 and 100, respectively. The archive size is set to 100. In addition, the sensitivity analysis of the algorithms, which involves testing each model with different parameter combinations, is carried out. The comparison reveals that the models with manageable parameters, listed in Table 4, are the most effective optimizers in this study.

Table 4 Algorithms parameters.
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The set of Pareto optimal solutions of the autonomous microgrid obtained by each algorithm based on the COE and LPSP functions is shown in Fig. 9. This figure shows that all four algorithms spread the solutions well over the non-dominated front. The COE decreases as the LPSP increases and vice versa. Multiple executions of the four algorithms (MOPSO, MOALO, MODA, and MOGA) for optimizing the autonomous microgrid design generate very stable Pareto bounds for each algorithm, as shown in Fig. 9.

It is well known that multi-objective algorithms generate a large number of solutions, usually very different ones. The most representative solutions are kept, while the others are rejected (Parito set). The larger the difference between the representative solutions, the more difficult it is for the decision-maker to choose the best solution19,43,44. Such drawbacks are not faced in this study because the values obtained for the LPSP function are very low, below 10%, so the best solution is selected by taking the minimum value of the COE function.

The optimal outcomes achieved by the four proposed algorithms (MOPSO, MOALO, MODA, and MOGA) are summarized in Tables 5 and 6, highlighting their performance in cost-effectiveness and reliability optimization of hybrid renewable energy systems. MOPSO delivers the most cost-effective configuration, achieving the lowest Cost of Energy (COE) at 0.267272 million dollars, with a standard electricity cost of 0.252 $/kWh and a Loss of Power Supply Probability (LPSP) of 9.16%. The optimized system involves 984.080 kW of solar energy, utilizing 135 photovoltaic (PV) panels, 264.539 kW of wind energy, powered by 53 wind turbines (WTs), 637.352 kW of battery storage, distributed across 16 battery units, and 73.891 kW of diesel energy, supported by 1 diesel generator. This layout balances the use of renewable energies with cost-effectiveness while maintaining reliable power supply parameters.

MOGA ranked second, it achieves a COE of 0.270516 million dollars with a slightly higher standard electricity cost of 0.1577 $/kWh and an LPSP of 10%. he optimized system integrates 249.864 kW of solar energy, using 35 PV panels, 340.711 kW of wind energy, employing 69 WTs, 222.853 kW of battery storage, across 9 battery units, and 52.791 kW of diesel energy, generated by 1 diesel generator. MOGA favors wind power over solar power, offering an alternative configuration with modest costs and reliability.

The third-ranked algorithm, MOALO, yields a COE of 0.274362 million dollars, a standard electricity cost of 0.16250 $/kWh, and an LPSP of 8.49%. The optimized setup consists of 442.209 kW of solar energy, implemented with 61 PV panels, 271.338 kW of wind energy, driven by 55 WTs, 220.082 kW of battery storage, provided by 6 battery units, and 62.601 kW of diesel energy, produced by 1 diesel generator. MOALO puts a little more emphasis on solar power than MOGA, but with better operating costs and greater reliability.

MODA ranks fourth, with a COE of 0.286988 million dollars, a standard electricity cost of 0.02425 $/kWh and the lowest LPSP of 7.87% among the algorithms.This configuration includes 920.343 kW of solar energy, employing 127 PV panels, 285.096 kW of wind energy, utilizing 58 WTs, 549.911 kW of battery storage, across 14 battery units, and 100 kW of diesel energy, supported by 2 diesel generators. MODA focuses on greater solar capacity and diesel generation, prioritizing system reliability over cost efficiency.

Table 5 The optimum results of sizing and cost optimization.
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Table 6 Results for the optimized variables: NPV, NWT, Nbattery, NDG.
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Fig. 9
figure 9

Best pareto optimal solution set of the COE and LPSP objective functions according to (a) MOPSO; (b) MOALO; (c) MODA; (d) MOGA.

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Fig. 10
figure 10

Diagram of COE, LPSP and CO2 emissions according to the different optimization approaches.

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Fig. 11
figure 11

Load variation and generated powers from different components for one week according to (a) MOPSO; (b) MOALO; (c) MODA; (d) MOGA.

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Figure 10 provides a comprehensive comparison of the COE, LPSP, and CO2 emissions generated by the applied optimization approaches. It is is worth noting that the LPSP values achieved by the all four algorithms are consistently low and present minimal variation. Among these, the MODA method stands out with the lowest LPSP value of 7.86%, reflecting superior reliability, while the MOGA method produces the highest value of 10%. The use of a diesel generator as a backup power source is a major factor in increasing operating costs, mainly due to fuel consumption, and in substantially increasing CO2 emissions, which underlines its impact on the environment. The MOPSO method demonstrates its effectiveness by achieving the lowest CO2 emission value of 0.000484 tonnes, underlining its potential for sustainable operation. In contrast, the MOGA method achieves the highest emission level, at 0.0535 tonnes, indicating a considerable shortfall in environmental performance. This comparison highlights the trade-offs between cost, reliability, and environmental impact inherent in these optimization approaches.

Figure 11 provides a comprehensive illustration of the variation in load and energy production between the various microgrid components over a one-week period, as analyzed by four distinct optimization algorithms: MOPSO, MOALO, MODA, and MOGA. This figure provides a clear and insightful comparison of the energy production capacities of the microgrid components under each optimization strategy. In particular, the results highlight that energy production from solar panels is predominantly higher in the MPSO and MODA cases, underscoring the important role of solar power in these optimization scenarios. The figure provides a valuable tool for understanding the impact of different strategies on energy distribution and overall system performance.

Figure 12 illustrates the load profile and power generation from photovoltaic (PV) panels, wind turbines (WT), batteries, and battery state of charge (SOC) using the multi-objective particle swarm optimization (MOPSO) algorithm for specific hours.

Figure 13 shows the battery state of charge (SOC) obtained using the MOPSO algorithm for specific hours. The state of charge remains within the specified limits, confirming the accuracy of the proposed approach.

Figures 14 and 15 illustrate the contribution of the diesel generator (DG) to annual energy production within the microgrid. Figure 14 shows that the microgrid optimized using the MOPSO algorithm is much less dependent on the diesel generator. This reduction reflects the efficient integration and use of renewable energy sources to satisfy a substantial part of the load demand. In contrast, Fig. 15 provides a comparative analysis of diesel generator use among the microgrids optimized by the four algorithms: MOPSO, MOALO, MODA, and MOGA. Notably, the microgrid derived from the MOPSO algorithm stands out as the most environmentally and economically favorable option, producing the lowest carbon dioxide emissions. These results underline the potential of the MOPSO algorithm to promote sustainable energy solutions while minimizing environmental impacts.

While all methods effectively satisfy load requirements, designers remain focused on developing cost-effective and environmentally sustainable solutions. The aim is to design microgrid architectures that satisfy load demands using the highest possible proportion of renewable energy, thereby improving the safety, reliability, and economic performance of the microgrid.

Fig. 12
figure 12

Load variation and generated powers from different components obtained using the MOPSO algorithm for specific hours.

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Fig. 13
figure 13

Battery state of charge for specific hours.

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Fig. 14
figure 14

Power generated by diesel generator according to MOPSO over a full year.

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Fig. 15
figure 15

Power generated by diesel generator according to (a) MOPSO; (b) MOALO; (c) MODA; (d) MOGA.

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Figure 16 shows a detailed breakdown of the contribution of each energy source to covering the annual load determined by the proposed optimization methods. The results highlight significant differences in the use of energy sources between the methods.

  1. 1.

    MOPSO: The photovoltaic (PV) system dominates with the largest contribution, accounting for 50.21% of the load, followed by batteries at 32.52%. Wind turbines provide 13.50%, while diesel generators account for just 3.77%, reflecting a strong preference for renewable energies.

  2. 2.

    MODA: As with MOPSO, the photovoltaic system leads the way with a 49.60% share, while batteries account for 29.64%. Wind turbines contribute a little more with 15.37%, and the diesel generator plays a minimal role with 5.39%.

  3. 3.

    MOGA: In contrast, wind turbines take first place with 39.33%, followed by the photovoltaic system with 28.85% and batteries with 25.73%. The share of diesel generators remains minimal at 6.09%.

  4. 4.

    MOALO: The photovoltaic system is again in the lead with a 44.39% share, followed by wind turbines with 27.24% and batteries with 22.09%. The diesel generator contributes only 6.28%.

This analysis highlights the different power generation strategies employed by the optimization methods, with MOPSO having the greatest reliance on solar power and MOGA emphasizing wind power.

It is important to ensure that the system meets load requirements efficiently. The primary objective is to design a system that minimizes costs while maximizing longevity. Figure 17 shows a detailed cost breakdown for each system component, as well as the total system cost.

Of the algorithms analyzed, the MOPSO-based system emerged as the most cost-effective option, with a total annual cost of $437,880. This cost is spread over five main components, with renewable energy sources accounting for the largest share: $106,892 for the solar equipment and $100,258 for the wind system. The inverter and batteries contribute $112,166 and $107,911, respectively, while the fossil-fuel generator generates the lowest annual cost at just $10,653.

Fig. 16
figure 16

The annual energy contribution of photovoltaic, wind, battery and diesel generator for different optimization approaches.

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Fig. 17
figure 17

Optimum system cost breakdown using MOPSO.

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Conclusion

This work proposes an innovative solution to meet the energy needs of remote areas in southern Algeria, particularly in the Adrar region. Given the high cost of extending power lines to these remote locations, the installation of a mini-grid equipped with renewable energy sources seems to be the most realistic option for providing electricity to these villages. The proposed microgrid integrates photovoltaic (PV) panels, wind turbines (WT), battery storage, a diesel generator (DG), and an inverter to provide an alternating load. Four recent meta-heuristic algorithms, combined with the management strategy to efficiently manage the flow of energy between the different parts of the system, are used to determine the optimal size of the microgrid components that minimize the cost of energy (COE). The reliability of the microgrid is evaluated using the Loss of Power Supply Probability (LPSP) metric. The study considers three design variables: the number of photovoltaic panels, the number of wind turbines, and the number of days of battery autonomy. Compared to other optimization algorithms, the MOPSO method stands out as the most effective approach for designing an optimal and compact microgrid utilizing hybrid renewable energy sources. In an energy system optimized using the MOPSO method, the photovoltaic system contributes the largest share, covering 50.21% of the load. Batteries account for 32.52%, providing energy storage and ensuring load balancing. Wind turbines supply 13.50%, while the diesel generator contributes only 3.77%, functioning primarily as a backup source. This design achieves a remarkably low cost of energy (COE) of 0.2520 $/kWh and an LPSP value of 9.164%, demonstrating exceptional cost-efficiency and reliability.