# Decision-making solutions based artificial intelligence and hybrid software for optimal sizing and energy management in a smart grid system

Ferdaws Ben Naceur, Sana Toumi, Chokri Ben Salah, Mohamed Ali Mahjoub, Mehdi Tlija

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Ferdaws Ben Naceur, Sana Toumi, Chokri Ben Salah, Mohamed Ali Mahjoub, Mehdi Tlija. Decision-making solutions based artificial intelligence and hybrid software for optimal sizing and energy management in a smart grid system. Concurrent Engineering: Research and Applications, 2024, 32, pp.3 - 19. 10.1177/1063293x241266338. hal-05340635

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# Decision-making solutions based artificial intelligence and hybrid software for optimal sizing and energy management in a smart grid system

Concurrent Engineering: Research and Applications

2024, Vol. 32(1-4) 3-19

© The Author(s) 2024

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sagepub.com/journals-permissions

DOI: 10.1177/1063293X241266338

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Sage

Ferdaws Ben Naceur<fnref n="1" />, Sana Toumi<fnref n="2" />, Chokri Ben Salah<fnref n="3" />,<fnref n="4" />, Mohamed Ali Mahjoub<fnref n="1" /> and Mehdi Tlija<fnref n="5" />

## Abstract

This paper describes a decentralised smart grid system containing renewable energies, storage systems and distributed generation with human control and intervention. The importance of each element and the interaction between them leads to think about a decision-making strategy. In fact, the integration of a Photovoltaic Panel (PVP) is used due to its availability and its participation in the carbon emissions reduction. Also, a battery is required to fill a power gap or absorb extra generated energy. Moreover, an optimal sizing is needed to get an efficient system with minimum cost. Also, an energy management strategy (EMS) is essential to ensure the power resources scheduling in order to keep a continuous equilibrium supply-demand of electricity and avoid instabilities in the grid, with guaranteeing a minimum cost of electricity. In the first part, the proposed smart grid optimal sizing is determined under real weather data (solar radiation) of the city of Sousse, Tunisia, using the Hybrid Optimization of Multiple Energy Resources (HOMER) software technique. This approach is chosen thanks to its simplicity, effectiveness, and high precision compared to traditional techniques. In this paper, several configurations (Grid, (Grid-battery), (Grid-PVP), (Grid-PVP-battery)) are studied. The obtained results prove that the (Grid-PVP-battery) system configuration is the most efficient and economical solution. In the second part, a robust energy management strategy (EMS) is proposed for two smart grid configurations (grid-battery, grid-PVP-battery). This strategy is based on Fuzzy Logic Control (FLC) thanks to its non-linear modelling and its ability to make decisions relating to energy management. The primary goal of the suggested (EMS) is to ensure the energy resources scheduling in order to keep a continuous equilibrium among the production and consumption of electricity and avoid instabilities in the grid, with guaranteeing a minimum cost of electricity. As input data, (FLC) used time-varying price electricity (Price (t)) to solve an instant decision problem by choosing, at each instant, the optimal energy source (which provide electricity at the cheapest price possible). The obtained results, carrying out Matlab simulation, prove the efficacy of the proposed strategy, not only, in the energy resources scheduling to meet the load, but also, for the system cost reduction since the PVP has been used as much as possible since it is inexpensive relative to the costs of battery capacity and the grid.

## Keywords

smart grid, decision-making, sizing, photovoltaic panel, battery, hybrid optimization of multiple energy resources, switch, reliable, energy management strategy, artificial intelligence, fuzzy logic control

## Corresponding author:

Ferdaws Ben Naceur, National Engineering School of Sousse, LATIS - Laboratory of Advanced Technology and Intelligent Systems, BP 264 Sousse Erriadh 4023, University of Sousse, Tunisia.

Email: swadref87@hotmail.com

<footnote n="1">¹National Engineering School of Sousse, LATIS - Laboratory of Advanced Technology and Intelligent Systems, University of Sousse, Sousse, Tunisia</footnote>

<footnote n="2">²Institut de Recherche Dupuy de Lôme (UMR CNRS 60 27 IRDL), University of Brest, Brest, France</footnote>

<footnote n="3">³Laboratory of Automation, Electrical Systems and Environment (LASEE), University of Monastir, Monastir, Tunisia</footnote>

<footnote n="4">⁴ISSAT of Sousse, University of Sousse, Sousse, Tunisia</footnote>

<footnote n="5">⁵Department of Industrial Engineering, College of Engineering, King Saud University, Riyadh, Saudi Arabia</footnote>
Introduction

Over the last decade, the smart grid presents a promising
solution for improving the traditional grid reliability, in-
creasing its flexibility, maintaining its sustainability, and
minimizing the energy losses. Furthermore, one of the smart
grid objectives is to reduce the carbon emissions, thus, it
allows the involvement of renewable energy sources like
solar and wind power (Dan et al., 2020; Olfa and Mohamed,
2016). Besides, batteries, super capacitors, and other forms
of distributed energy storage are required to handle extra or
deficient electricity (Lu et al., 2021). Moreover, and
compared to the traditional grid, the smart grid can provide
electricity at the cheapest price possible. Indeed, the smart
grid consists on optimization techniques based on real time
data and dynamic energy prices to achieve the reciprocal
relation control between the energy demand and supply
(Khalid et al., 2019). In fact, customers can reduce their
consumption, store energy and reuse at a later time or
delayed some appliances operation according to a time-
varying price signal (Alam et al., 2014). Despite the ad-
vantage of the smart grid in meeting various electric needs
(ventilation, heating, air conditioning system, water heater
and pump), this type of grid requires a large advanced
information, communication, and devices. Also, the in-
corporation of sustainable power generators and systems
storage generates the addition of new technologies to power
systems operations. Therefore, an optimal sizing is needed
to get an efficient system with minimum cost. Also, an
energy management strategy (EMS) is essential to ensure
the power resources scheduling in order to keep a contin-
uous equilibrium supply-demand of electricity and avoid
instabilities in the grid, with guaranteeing a minimum cost
of electricity (Zeng and Berti, 2019). Furthermore, to
guarantee its optimization, smart grid dimension and price
need to be addressed. For the sizing issue, many approaches
have been proposed. In fact, authors in (Mohammadzadeh
and Gharehchopogh, 2020) have used the flower pollination
algorithm for a hybrid smart grid cost reduction, never-
theless, this algorithm presents an excess of time con-
sumption. In (Chokri et al., 2015), particle swarm
optimization algorithm (PSO) is the technique employed.
When faced with complicated scenarios, the PSO algorithm
may reach convergence too quickly and get stuck in a local
optimum. A mine blast algorithm has been adopted in
(Fathy, 2016) for a hybrid smart grid system in Egypt, the
disadvantage of this algorithm is its neglect of reliability
factors. In (Sufyan et al., 2019), a firefly optimization ge-
netic algorithm is used to determine a smart grid compo-
nents size. This technique is simple, but it was stuck in
local optima. To overcome these approaches shortcomings,
the Hybrid Optimization of Multiple Energy Resources
(HOMER) software technique is proposed thanks to its
simplicity, effectiveness, and high precision compared to
traditional techniques. It has been developed for both

off-grid and on-grid systems and it is known for their user-
friendliness (Tozzi and Jo, 2017). Indeed, in (Ramli et al.,
2018), the HOMER software has been adopted for a smart
grid optimal sizing in Algeria and in Saudi Arabia, re-
spectively. Its effectiveness has been proven in reducing the
cost when meeting the load. For the energy management
strategy issue, several approaches and tools have been
proposed to meet the challenges of integrating electricity
production from renewable sources as well as energy
storage. In (Kandaswamy et al., 2023), an EMS for a
photovoltaic panel (PVP)-gas turbine system and for an
Electric Vehicle Powered by a Hybrid Energy Storage
System, respectively has been presented. Load and power
forecasting, done a day ahead, have been taken into con-
sideration in order to ensure an optimal operation of the
system. In (Radhakrishnan and Srinivasan, 2016), authors
have proposed a multi-agent system based on distributed
energy management strategy for smart grids including re-
newable sources and distributed energy storage. Atheo-
retical algorithm, based on “Tit for Tat” game (GTFT), has
been adopted in (Reka and Ramesh, 2016) in order to give
for the customer an idea about his consumption cost.

The cuckoo search algorithm, known for its reduced
computation time (Nadjemi et al., 2017), has been applied to
a PV-wind-battery system. On the other hand, in (Singh
et al., 2022) a reinforcement learning method, based on the
“Q-learning” algorithm, has been adopted. It uses real data
of the smart grid environment. The grasshopper optimi-
zation algorithm, recently developed and inspired by the
food-seeking behavior of grasshopper swarms (Saremi
et al., 2017), has been applied to a hybrid system located
in Nigeria (Bukar et al., 2019). Furthermore, diverse al-
gorithms have been combined and used for the sizing
problem. In fact, in (Essa et al., 2019), a combination of
non-dominated sorting genetic algorithm (NSGA) and
multi-objective particle swarm optimization (MOPSO) was
adopted to simultaneously minimize carbon dioxide
emissions and system cost.

However, the most above-mentioned EMS need long
computing time and some essential data such as every node
measured power. Also, some EMS are centralized, which
leads to single point failure. Thus, the adopted EMS could
make undesirable decisions and generate instabilities in the
grid. Therefore, and to guarantee a continuous balance
between the supply and the demand of electricity, fuzzy
logic control (FLC) could be considered as a successful
solution thanks to its ability to make decisions relating to
energy management as suggested in (Singh et al., 2022).
Indeed, an energy management strategy, based on (FLC) has
been adopted to ensure the combination of energy storage
technologies with sustainable power sources. Based on the
average power generated, authors make decision about the
appropriate Solar Panel (SP) to use by taking into account
the various standards of the 11 SPs utilized as reference
panels (Justin Raj et al., 2022). In (Ben Naceur et al., 2022),
authors have introduced a neuro-fuzzy technique for the energy optimization and the production management. A multi-objective fuzzy stochastic programming approach, adopted by a Vietnamese electricity company in the residential sector, is presented in (Tsao et al., 2019) to reduce the expenses of the smart grid on the economical, ecological, and social scale under unpredictable situations. The purpose is to identify the ideal quantity, position, and performance of integrated sustainable energy resources among with their variable energy prices. The study, presented in (Derrouazin et al., 2017), focuses on designing an effective multi-input fuzzy logic control system for managing the flow of electricity of a smart grid based on PVP and a wind turbine with storage system.

In this work, an intelligent EMS, based on Fuzzy Logic controllers, is proposed to implement a control strategy for smart grids. (FLC) have been chosen due to their non-linear modelling and its ability to manage uncertain data and control and the scheduling of the energy resources. Moreover, the adopted Fuzzy systems are used to reduce the system cost with taking into account economic, social, and environmental factors.

In this paper, the HOMER is used for several configurations (Grid, (Grid-battery), (Grid-PVP), (Grid-PVP-battery)) in order to determine the most reliable and costless one. Then, the energy management strategy is studied for the (grid, battery) and (grid, PVP, battery) configurations. For both types, the FLC is proposed to solve an instant decision problem by choosing, at each instant, the optimal energy source (which provide electricity at the cheapest price possible) to supply the demand.

This paper is structured the following way: In Smart grid modelling section, the models of each smart grid components (grid, battery, PVP) are given. In the smart grid optimal sizing section, the smart grid sizing based on the HOMER technique is studied, its simulation results have been illustrated. In the energy management approaches section, the proposed energy management strategy is described for both configurations ((grid, battery) and (grid, PVP, battery)). The Fuzzy Logic Control algorithms, its modules and simulation results are developed in section 5. Section 6 gives the conclusion.

## Smart grid modelling

The adopted smart grid, presented in Figure 1, contains the electrical grid as the principal energy source, the PVP as the renewable energy source, the battery as the energy system storage, and the load.

### Electrical grid modelling

The electrical grid is given in Figure 2. Its modelling can be expressed as follows (Toumi et al., 2020)

$$ \begin{pmatrix} V_{g1} \\ V_{g2} \\ V_{g3} \end{pmatrix} = R_g \begin{pmatrix} I_{g1} \\ I_{g2} \\ I_{g3} \end{pmatrix} + L_{gdt} \begin{pmatrix} I_{g1} \\ I_{g2} \\ I_{g3} \end{pmatrix} \quad (1) $$

Where

* $V_{g123}$: the grid line voltages.

* $I_{g123}$: the grid line currents.

<figure><img src="image_3.png" /><figcaption>Figure 1. The studied smart grid.</figcaption></figure>
* $(R_g, L_g)$: the grid filter.

## Battery modelling

The battery is adopted as an energy system storage to fill the consumption gap created when the PVP's energy generation is lacking. Its modelling can be given as follows (Amara et al., 2022; Chokri et al., 2015):

$$V_{Bat} = E_L - R_{Bat}I_{Bat} \quad (2)$$

$$C_{Bat} = (E_D * D_{aut}) / (DOD_{max} * \eta_{Bat}) \quad (3)$$

Where

* $C_{Bat}$: the battery capacity (Ah).

* $E_L$: the energy load.

* $V_{Bat}, I_{Bat}, R_{Bat}$: the battery voltage (V), current (A), and resistor (Ω), respectively.

* $D_{aut}$: the number of autonomy days.

* $E_D$: the electricity consumption per day (Wh).

* $\eta_{Bat}$: the energy efficiency of the battery.

* $DOD_{max}$: the maximum depth of discharge of the battery (80%).

## Photovoltaic panel modelling

The modelling of a photovoltaic panel is given by the following equation (Amara et al., 2021; Geleta et al., 2020).

$$I_{pv} = N_p I_{ph} - N_p I_s \left( \exp \left( \frac{q \left( \frac{V_{pv}}{N_s} + \frac{I_{pv} R_s}{N_p} \right)}{KTA} \right) - 1 \right) - \frac{\left( \frac{N_p V_{pv}}{N_s} + I_{pv} R_s \right)}{R_{sh}} \quad (4)$$

Where

* $I_{pv}, V_{pv}$: the PVP Current and voltage, respectively.

* $I_s$: the saturation current.

* $I_{ph}$: the photo-current.

* $K$: the Boltzmann constant.

* $q$: the electron charge.

* $N_p, N_s$: the number of cells in parallel and in series, respectively

* $R_s, R_{sh}$: the series resistance and the shunt resistance, respectively.

## Smart grid optimisation

Smart grid optimization steps are summarized in Figure 3.

The optimization process can be described according to two important steps:

* Before setting up the system, a sizing step is necessary: This is the first step where the design and size of the system are established according to the precise objectives and established constraints. Modeling, simulation, and analysis of potential system performance are typically required during this step. The objective is to define the optimal parameters of the system before implementing it.

* Stage of management and verification of the proper functioning of the system after its implementation: After installation of the system, this stage involves monitoring its operation in real time, collecting information on its real performance and adjusting the parameters if necessary in order to improve its effectiveness. Methods such as closed-loop control, real-time data analysis and continuous optimization can be used to ensure optimal system operation under varying conditions.

<figure><img src="image_4.png" /><figcaption>Figure 2. Grid topology.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 3. Different steps of optimisation.</figcaption></figure>
In the combination of these two steps, it is possible to ensure that the system is optimally designed from the start and that it continues to function efficiently throughout its operation.

## Smart grid optimal sizing

The proposed technique to optimal dimension is centralized on the HOMER software thanks to its simplicity, effectiveness, and high precision. The main objective is to study the two configurations already mentioned in order to determine the most cost-effective one.

## HOMER software description

The HOMER (Hybrid Optimization of Multiple Energy Resources) software tool is used to improve the design of microgrids. The different steps of sizing a renewable energy installation are summarized in Figure 4:

The HOMER software function is based on five steps as follow (Jayachandran and Ravi, 2019):

* Step 1 (Load study): Consists of examining the energy demand or load that the system is expected to meet. Total energy requirements over a period of time can be measured using load analysis, which is typically expressed in kW hours (kWh) or MW hours (MWh).

* Step 2 (Resource Assessment): This step involves analyzing the various renewable energy resources available at the site, such as solar radiation, wind speed, and so on.

<figure><img src="image_6.png" /><figcaption>Figure 4. Different steps of sizing.</figcaption></figure>

It is essential to take this information into account in order to define the potential renewable energy production capacity of the system.

* Step 3 (Calculation of system sources): Based on the load analysis and resource assessment, the system elements (such as solar panels, wind turbines, batteries, etc.) are set up in a manner reliable to meet energy demand.

* Step 4 (Optimization): Optimization methods are frequently employed to determine the most cost-effective configuration of system elements while satisfying energy demand and taking into consideration other constraints such as system reliability, available space, budget, etc.

* Step 5 (Simulation and sensitivity analysis): Once a system configuration is established, it is essential to simulate its performance over time to assess its quality and resilience in various situations. The sensitivity study provides an understanding of the impact of variations in input parameters (such as energy prices, component costs, etc.) on system economics and performance.

## HOMER software economic criteria

As economic criteria, the Net Present Cost (NPC) and the Cost of Energy (COE) are used.

### Net present cost

The NPC, expressed as follows, is defined by the component overall expenses during its entire lifespan (Lau et al., 2018)

$$ NPC = \frac{C_{tot, ann}}{CRF(i, T_p)} \quad (5) $$

Where: $C_{tot, ann}$: the total annualized cost (DT/year); $i$: the actual interest rate; $T_p$: the project lifetime (years); $C?F$: the capital recovery factor, given by:

$$ CRF(i, n) = \frac{i(1 + i)^n}{(1 + i)^n - 1}, \quad n: \text{years} \quad (6) $$

### Cost of energy

The COE, given as follows, is defined by the estimated price per kW hour (kWh) of the system produced electricity (Lau et al., 2018).

$$ COE = \frac{C_{tot, ann}}{E_{tot, ann}} \quad (7) $$

Where

* $E_{tot, ann}$: the annual quantity of electricity transported to the grid (kWh/year).
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Tunisia solar radiation (Rekik and El Alimi, 2023).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 6.** Sousse's monthly solar radiation and clearness index.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>**Figure 7.** (a) Daily load demand, (b) monthly load demand.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Battery state of charge.</figcaption></figure>

## Sizing simulation results

The studied smart grid simulation is carried out using real weather data of the city of Sousse in Tunisia. Indeed, Sousse is a sizeable city of around 173,000 inhabitants, about 140 km south of Tunisia's capital city, Tunis. It is located on the coast in the central east of the country. As shown in Figure 5, Sousse is positioned at longitude 10°6.0'E (East) and latitude 35°82.4' (North). Figure 6 presents the monthly solar radiation and clearness index of the city of Sousse. In fact, the highest value of the solar radiation is observed on July with 7000 kWh/m²/day. The daily and the load demand is illustrated in Figure 7. It proves that the consumption of energy is highest during working hours (between 6:00 and 18:00). Also, August is the month with the highest consumption (3.169 kW).

The proposed system components (grid, PVP, and battery) parameters are mentioned in the Appendix. The HOMER software is used for the system sizing. Figures 8 and 9 and Table 1 present all the possible configurations sizing. It is clearly seen that (Grid-PVP-battery (case (1))) is the most cost-effective configuration (NPC = 10,640.65 MDT, EC = 0.1357 DT). In contrast, without integrating the PVP, the NPC is high (14,479.91 in case (3) and 14,868.76 in case (4)). Furthermore, HOMER software allows the pollution reduction by minimizing the CO2 emissions (1319.73 kg/year in case (1)). Thus, the HOMER not only allows effective in optimal sizing but only in reducing environment pollution.

## Energy management approaches

Electricity consumption has been increased as a result of population explosion in the majority of the world's countries, and the great diversity of residential and industrial development. All around the world, there are several power stations and a vast network of transmission lines that serve numerous clients, but the scenario has become too large especially after the addition of photovoltaic and wind power supplies. Therefore, it is become important to increase the responsibility of users to stay current with load control
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Monthly grid power and PVP power.</figcaption></figure>

<table><caption>**Table 1.** System optimal sizing.</caption><thead><tr><th>Case</th><th>PVP (kW)</th><th>Battery (kWh)</th><th>Grid (kW)</th><th>NPC (MDT)</th><th>COE (DT)</th><th>CO<sub>2</sub> (kg/year)</th></tr></thead><tbody><tr><td>(1)</td><td>2.981</td><td>1</td><td>999,999</td><td>10,640.65</td><td>0.1357</td><td>1319.731</td></tr><tr><td>(2)</td><td>2.926</td><td>0</td><td>999,999</td><td>10,680.34</td><td>0.1357</td><td>1460.805</td></tr><tr><td>(3)</td><td>0</td><td>1</td><td>999,999</td><td>14,479.91</td><td>0.2756</td><td>2596.96</td></tr><tr><td>(4)</td><td>0</td><td>0</td><td>999,999</td><td>14,868.76</td><td>0.2830</td><td>2596.53</td></tr></tbody></table>

trends thanks to the integration of a digital control enhancing the electric network.

The proposed control relies on fuzzy logic to create two energy management strategies in a house. The first one is founded on the installation of power storing elements and the second one by integrating a photovoltaic source. To determine an adequate management strategy, it is important to understand the system's behavior according to the input data. Indeed, for a smart grid system, the real-time electricity price environment presents the most important data. The produced electricity can supply the consumer according to his requested amount of energy or also can be stored in the battery and reused later. In fact, the total cost of electricity can be reduced by recharging the battery from the electricity grid when the electricity price is low and using it during the period when the electricity price is high.

The two configurations of a smart grid have been given by Grid-Battery-Load and Grid-PVP-Battery-Load.

### Grid-battery system

This combination is completed in a generic system design model for users with power storage services shown in Figure 10, which is constituted by an energy management system, a load, the electrical network and a battery. The energy management system operates like the brain of the framework and controls the electrical power supply needed for the load. In this energy management system, the cost controller and data collection unit based on fuzzy logic are important elements.

<figure><img src="image_12.png" /><figcaption>**Figure 10.** Grid-battery system.</figcaption></figure>

The information collector periodically gathers energy price data, the battery state of charge (SOC) and the power demanded by the load, while the cost control unit makes the decision to supply the load with the suitable energy source based on the price of electricity from the network and the state of charge of the battery. For the grid-battery system, the energy management strategy includes:

a. The information collector: it collects, at each instant, the battery state of charge (SOC (t)), the electricity price (Price (t)), and the load power (LP).

b. The cost control unit: it is based on the Fuzzy Logic Control (FLC). It makes the optimal decision to supply the load with the appropriate energy source (grid or battery).

c. The decision bloc: the decision will be given by the three switches C1, C2 and C3, as follows:
* 'C1' closed: The grid supplies the load.

* 'C2' closed: The battery supplies the load.

* 'C3' closed: The grid recharges the battery.

## Grid-PVP-battery system

The total cost of electricity can be reduced by adding the photovoltaic panel to the first defined system. As its cost is considered zero, it is recommended to exploit it as much as possible to keep the load supplied. In this case, the produced energy can be stored by the battery then used when the photovoltaic power is not available and when the electricity price is high. Figure 11 shows the Grid PVP-Battery-Load system. As in the first energy management system functions as the principal component and manages the power supply for the load. The PVP is used as a renewable energy source thanks to its reducing cost and its participation in decreasing the carbon emissions (Toumi et al., 2020).

In this case, the information collector consists of periodically collecting the battery state of charge (SOC (t)), the photovoltaic panel power (PPVP (t)), the electricity price (Price (t)), and the load power (LP). The cost control unit makes the optimal decision to supply the load with the adequate energy source (grid, PVP, or battery). The decision bloc, based on the four switches C1, C2, C3, and C4, generates the following decisions:

* 'C1' closed: The PVP supplies the load.

* 'C2' closed: The grid supplies the load.

* 'C3' closed: The PVP recharges the battery.

* 'C4' closed: The battery supplies the load.

## Energy management approaches details

This work proposes two energy management approaches in a lighting system with variable grid electricity prices.

The first approach consists of integrating a storage element into the systems connected to the grid.

<figure><img src="image_13.png" /><figcaption>Figure 11. Grid-PVP-battery system.</figcaption></figure>

In the second, the first system has been improved by integrating a priority renewable source for powering the system and charging the battery.

For both configurations, if the Price (t) exceeds 0.25€/ kWh, it will be considered high.

**Energy management of grid-battery system.** The Fuzzy logic algorithm, proposed for a grid-battery system, is shown in Figure 12. As input data, SOC (t) and Price (t) are used. The following steps can describe the algorithm.

* Read (Price (t)) and battery (SOC (t)) at each instant.

$$ \text{if Price} > 0.25 \quad \begin{cases} \text{if SOC}(t) > SOC_{min} \\ \text{Run load with Battery} \\ \text{if SOC}(t) < SOC_{min} \\ \text{Run load with Grid} \end{cases} $$

<figure><img src="image_14.png" /><figcaption>Figure 12. (a). Energy management strategy of grid-battery system main flowchart. (b). Battery charging operation. (c). Battery discharge operation.</figcaption></figure>
■ if Price

$$ \le 0.25 \begin{cases} \text{if SOC}(t) < \text{SOC}_{\text{max}} \\ \text{Run load with Grid And recharge the battery} \\ \text{if SOC}(t) > \text{SOC}_{\text{max}} \\ \text{Run load with Grid And the battery is isolated} \end{cases} $$

Energy management of grid-PVP-battery system. For the grid-PVP-battery system, the Fuzzy logic algorithm is given by Figure 13(a)–(c).

It mainly consists of controlling the PVP power as follows:

$$ \text{P}_{\text{PVP}} \ge P_L \begin{cases} \text{if } P_{\text{PVP}} = P_L \\ \text{Run load with PVP} \\ \text{if } P_{\text{PVP}} > P_L \\ \text{Run load and charge the battery} \end{cases} $$

<figure><img src="image_15.png" /><figcaption>Figure 13. (a). Energy management strategy of grid-PVP-battery system main flowchart. (b). Battery charging operation. (c). Battery discharge operation.</figcaption></figure>

$$ \text{P}_{\text{PVP}} < P_L \begin{cases} \text{if Price} < 0.25 \\ \text{Run load with PVP + Grid} \\ \text{if Price} > 0.25 \\ \text{Run load with PVP + Battery} \\ \text{if SOC}(t) > \text{SOC}_{\text{min}} \\ \text{Run load with Grid} \\ \text{if SOC}(t) < \text{SOC}_{\text{min}} \\ \text{Run load with Grid} \end{cases} $$

## Discussion

The role of energy storage has a significant impact in grid-connected systems where the price of electricity is variable: The first approach in this work shows that a storage element plays a very important role in minimizing the cost of consumption when the price of grid electricity increases.

The 2nd approach shows that the integration of renewable energy sources such as solar panels in the first system (the first approach) gives greater efficiency to the connected systems, especially in the northern regions of Africa, which are characterized by high solar radiation that lasts throughout the year. The use of these sources also reduces the cost of consumption, not forgetting the advantages of solar panels in terms of cleanliness and reduced CO₂ emissions.

### Fuzzy logic control modules

Two fuzzy algorithms have been developed to an optimal operation control of the Grid-battery and Grid-PVP-battery systems.

<figure><img src="image_16.png" /><figcaption>Figure 14. Input functions modules (a) price, (b) SOC.</figcaption></figure>
## Grid-battery system

The fuzzy logic control is based on input and output modules. The input functions modules, presented in Figure 14, are the battery state of charge (SOC (t)) and the

electricity price (Price (t)). The output functions module, presented in Figure 15, allows to take the right decision (choose the grid or the battery to supply the load). Table 2 gives all the possible decisions.

<figure><img src="image_17.png" /><figcaption>Figure 15. Output function module (Ci).</figcaption></figure>

<table><caption>Table 2. Possible outputs for the grid-battery system.</caption><thead><tr><th rowspan="2">Price</th><th colspan="3">SOC</th></tr><tr><th>SOC<sub>min</sub></th><th>SOC<sub>moy</sub></th><th>SOC<sub>max</sub></th></tr></thead><tbody><tr><td rowspan="3">Low</td><td>C1 closed</td><td>C1 closed</td><td>C1 closed</td></tr><tr><td>C2 opened</td><td>C2 opened</td><td>C2 opened</td></tr><tr><td>C3 closed</td><td>C3 closed</td><td>C3 opened</td></tr><tr><td rowspan="3">High</td><td>C1 closed</td><td>C1 opened</td><td>C1 opened</td></tr><tr><td>C2 opened</td><td>C2 closed</td><td>C2 closed</td></tr><tr><td>C3 opened</td><td>C3 opened</td><td>C3 opened</td></tr></tbody></table>

<figure><img src="image_18.png" /><figcaption>Figure 16. Input function module ($P_{PVP} - P_L$).</figcaption></figure>

<table><caption>Table 3. Possible outputs for the grid-PVP-battery system.</caption><thead><tr><th rowspan="3">Price</th><th colspan="6">SOC</th></tr><tr><th colspan="2">SOC<sub>min</sub></th><th colspan="2">SOC<sub>moy</sub></th><th colspan="2">SOC<sub>max</sub></th></tr><tr><th>DP >0</th><th>DP <0</th><th>DP >0</th><th>DP <0</th><th>DP >0</th><th>DP <0</th></tr></thead><tbody><tr><td rowspan="4">Low</td><td>C1 closed</td><td>C1 opened</td><td>C1 closed</td><td>C1 opened</td><td>C1 closed</td><td>C1 opened</td></tr><tr><td>C2 opened</td><td>C2 closed</td><td>C2 opened</td><td>C2 closed</td><td>C2 opened</td><td>C2 closed</td></tr><tr><td>C3 closed</td><td>C3 opened</td><td>C3 closed</td><td>C3 opened</td><td>C3 opened</td><td>C3 opened</td></tr><tr><td>C4 opened</td><td>C4 opened</td><td>C4 opened</td><td>C4 opened</td><td>C4 opened</td><td>C4 opened</td></tr><tr><td rowspan="4">High</td><td>C1 closed</td><td>C1 opened</td><td>C1 closed</td><td>C1 opened</td><td>C1 closed</td><td>C1 opened</td></tr><tr><td>C2 opened</td><td>C2 closed</td><td>C2 opened</td><td>C2 closed</td><td>C2 opened</td><td>C2 closed</td></tr><tr><td>C3 closed</td><td>C3 opened</td><td>C3 closed</td><td>C3 opened</td><td>C3 opened</td><td>C3 opened</td></tr><tr><td>C4 opened</td><td>C4 opened</td><td>C4 opened</td><td>C4 opened</td><td>C4 opened</td><td>C4 opened</td></tr></tbody></table>

## Grid-PVP-battery system

The fuzzy logic control is based on input and output modules. The input functions modules are the battery state of charge (SOC (t)) and the electricity price (Price (t)) (presented in Figure 14) and the normalized difference power index, DP, between the PVP power, $P_{PVP}$, and load power, $P_L$, (Figure 16).

Where DP is the normalized difference power index.

$$ DP = \frac{P_{PVP} - P_L}{P_{PVP} + P_L} \quad (8) $$

The output functions module is the same as in the previous case, it gives the appropriate decision (choose the grid, the PVP or the battery to supply the load). Table 3 gives all the possible decisions.

## Simulation results and discussion

The input-output fuzzification phase is generated based on an annual database collected from a measurement station. Which consists of an acquisition chain connected to two wind speed and sunlight sensors of an hybrid PV/wind turbine system located in the Department of Energy of the Higher Institute of Applied Sciences and Technology in Sousse, Tunisia and catches for each 15 min (Figure 17).

In this section, the grid-battery and the grid-PVP-battery systems will be studied and discussed.

### Grid-battery system

As input data of the first system grid-battery, the electricity price (Price (t)), varies from 0 to 0.5€/kW, is illustrated in
<figure><img src="image_19.png" /><figcaption>**Figure 17.** Measurement station located at ISSAT of Sousse Tunisia (a): hybrid PVP/WT system; (b): solar radiation sensor; (c): wind sensor.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 18.** Electricity price (t).</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Figure 19.** State of charge of the battery SOC (t).</figcaption></figure>
**Figure 18.** Figure 19 presents the battery state of charge (SOC(t)) variation from 0 to 90%.

The energy management strategy in the grid-battery system pursue the following approach, if the grid electricity price is less than 0.25€/KWh then the grid is the source of power for the load and research of the battery if its state of charge is not maximum so C1 and C3 are closed and C2 open. And if the grid electricity price is greater than 0.25€/KWh then the battery is the power source for the load if its SOC is greater than 0.5 (50%), if not (SOC <0.5) then the load is powered by the grid to increase battery life.

<figure><img src="image_22.png" /><figcaption>**Figure 20.** Switcher 1 (C1) evolution.</figcaption></figure>

The states of switches C1 (grid-load), C2 (battery-load) and C3 (grid-battery) are given by Figs 20–22, respectively. Unlike C1, C2 and C3 are opened and closed simultaneously. These results confirm our objective (choose, at each instant, either the grid or the battery to supply the load).

Indeed, in T1, when Price (t) is low, the grid is chosen (C1 is closed), the battery is recharged (C3 is closed). In T2, when price is high and SOC is high (>0.5 c.a.d. 50%) then the battery is chosen for the load supply (C2 is closed, C1 and C3 are opened). When the SOC is low (<0.5), the load is always powered by the network whatever the electricity price (Only C1 is closed (see Figure 20)).

<figure><img src="image_23.png" /><figcaption>**Figure 23.** Photovoltaic panel power $P_{PVP}$ (t).</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>**Figure 21.** Switcher 2 (C2) evolution.</figcaption></figure>

<figure><img src="image_25.png" /><figcaption>**Figure 24.** Load power evolution $P_L$ (t).</figcaption></figure>

<figure><img src="image_26.png" /><figcaption>**Figure 22.** Switcher 3 (C3) evolution.</figcaption></figure>

<figure><img src="image_27.png" /><figcaption>**Figure 25.** The power difference $P_{PVP}(t) - P_L(t)$.</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>Figure 26. Switcher 1 (C1) evolution.</figcaption></figure>

<figure><img src="image_29.png" /><figcaption>Figure 27. Switcher 2 (C2) evolution.</figcaption></figure>

<figure><img src="image_30.png" /><figcaption>Figure 28. Switcher 3 (C3) evolution.</figcaption></figure>

## Grid-PVP-battery system

The use of a multi-source system is not only to compensate grid electricity prices during peak hours but also to exploit green and free photovoltaic energy. The priority is always to exploit photovoltaic energy when available to power the load and recharge the battery. Second is to use the battery if its state of charge is sufficient, and lastly is to use grid.

The PVP power and the load power have been shown in Figures 23 and 24, respectively.

As input data of the second system grid-PVP-battery, the electricity price (Price (t)), varies from 0 to 0.5€/kW (Figure 18), the battery state of charge (SOC(t)) variation from 0 to 90% (Figure 19), as well as the normalized difference power index DP (Figure 25).

<figure><img src="image_31.png" /><figcaption>Figure 29. Switcher 4 (C4) evolution.</figcaption></figure>

Figs. 26–29 show the states of switches C1 (PVP-load), C2 (grid-load), C3 (PVP-battery), and C4 (battery-load), respectively.

The energy management strategy in the grid-battery system pursue the following approach, if the PPVP is low, the SOC of the battery is low (<0.5) and the price is low then C1, C3 and C4 are opened and only C2 is closed. It's clear that C2 is opened except during the interval T'4. Thus, the use of the grid to supply the load is done for a very short period (0.1 h = 6 mn). Therefore, the main objectives were been achieved. Firstly, the load is still powered.

Second, the PVP has been used as much as possible (C1 is closed), which can lead to system cost reduction since the PVP has a very low cost, example the slots time T'1 and T'2. Moreover, C1 and C3 evolutions are identical (we can cite the slot time T'3), indeed, while supplying the load, the PVP is the only source used to recharge the battery. Also, C1 and C4 curves evolve in an opposite way. Therefore, when the PVP is not available or when there is bad weather, such as days with cloudy skies, the battery is also utilized to sustain the demands if SOC is high (>0.5). Finally, the proposed strategy is effective, not only, in the energy resources scheduling to meet the load, but also, for the system cost reduction.

## Conclusion

This paper dealt with a smart grid system containing the traditional grid, the PVP, and the battery. The main objectives were to propose an optimal sizing, based on the HOMER software technique in order to get an efficient system with minimum cost. Second, Also, an energy management strategy, based on the Fuzzy logic flow, has been adopted to ensure the power resources scheduling in order to keep a continuous equilibrium supply-demand of electricity and avoid instabilities in the grid, with guaranteeing a minimum cost of electricity. The simulation results prove that the HOMER software technique is effective to determinate that the (grid-PVP-battery) configuration is the most reliable and costless one. Also, results confirm the efficiency of the proposed energy management strategy by studying two smart grid
configurations (grid-battery, grid-PVP-battery) using
time-varying price electricity to solve the instant decision
problem.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with re-
spect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors acknowledge “Researchers Supporting Project number (RSPD2024R685),” King Saud University, Riyadh, Saudi Arabia.”

ORCID iD

Ferdaws Ben Naceur https://orcid.org/0009-0003-5949-6055

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## Author biographies

<figure><img src="image_32.png" /></figure>

Dr. Ferdaws Ben Naceur is researcher teacher in the Computer Science Department at the Higher Institute of Applied Sciences and Technology of Sousse, Tunisia. Dr. Ben NACEUR holds L.CS., Eng., and Ph.D. degrees in Computer Science from the University of Sousse, Tunisia. Her expertise spans various areas of computer science, including Data-Analysis Algorithms, Artificial Intelligence applications, IoT, optimization techniques, Smart Grids.

<figure><img src="image_33.png" /></figure>

Dr. Sana Toumi received her B.Sc. and the M.Sc. degrees in electrical engineering from Ecole Nationale d'Ingénieurs de Monastir (ENIM), Monastir, Tunisia in 2012 and 2013, respectively. She received a Ph.D. degree in electrical engineering from l'Université de Bretagne Occidentale (UBO), Brest, France in 2017. Currently, she is working with the Institut de Recherche Dupuy de Lôme, IRDL (UMR CNRS 6027), University of Brest, Brest, France. His current research interests include marine current turbine systems, power electronics, faulty conditions and fault-tolerant control.

<figure><img src="image_34.png" /></figure>

Pr. Chokri Ben Salah is Associate Professor of Electrical Engineering at the Higher Institute of Applied Sciences and Technology of Sousse, Tunisia, received his Ph.D in Electrical Engineering from the Higher School of Electrical Engineering at Sfax (ENIS), Tunisia since 2011. His specific research interests are in the renewable energy, Electric Systems and Control, Sizing, Management of Hybrid Systems, Smart grid, micro-grid and Electric and hybrid vehicles. He is member of Laboratory of Automation, Electrical Systems and Environment (LASEE) at National School of Engineers of Monastir/University of Monastir, Tunisia.
<figure><img src="image_35.png" /></figure>

Pr. Mohamed Ali Mahjoub received the BSc and MSc degrees in computer science from the National School of Computer Science of Tunis, Tunisia and National School of Engineers of Tunis, in 1990 and 1993, respectively, and the PhD and HDR degrees in electrical engineering and signal processing from the National School of Engineers of Tunis, Tunisia, in 1999 and 2013, respectively. From 1990 to 1999, he was a computer science engineer with the National School of Engineers of Tunis. In September 1999, he joined the Preparatory Institute of Engineering of Monastir as an assistant professor in computer science. In December 2013, he joined the Electronics Engineering Department, National School of Engineers of Sousse (ENISo) as a full professor. He is a founding member of the Laboratory of Advanced Technology and Intelligent Systems (LATIS), ENISo. His research interests include predictive intelligence, probabilistic graphical models and computer vision.

<figure><img src="image_36.png" /></figure>

Dr. Mehdi Tlija is an Associate Professor in the Industrial Engineering Department at the College of Engineering, King Saud University. He brings experience from previous roles at the University of Sousse and the University of Monastir. Dr. Tlija holds B.S., M.Sc., and Ph.D. degrees in Mechanical Engineering from the University of Monastir, Tunisia. He was a master fellow at UQTR, Canada, and a doctoral fellow at SUPMECA, France. His expertise spans various areas of industrial engineering, including Decision-Support Systems, optimization techniques, Geometric Modeling, Sustainable Engineering, Smart Design and Manufacturing, Renewable Energy, Biomechanical Engineering, Robotics, Inspection and Quality, and Industry 4.0 systems.

## Appendix

<table><caption>**Appendix A1.** Smart grid parameters values.</caption><thead><tr><th></th><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td rowspan="5">Grid</td><td>Resistance</td><td>0.1 mΩ</td></tr><tr><td>Inductance</td><td>1.5 mH</td></tr><tr><td>Frequency</td><td>50 Hz</td></tr><tr><td>Cost of selling the grid</td><td>0.081 DT/kWh</td></tr><tr><td>Cost of grid purchase</td><td>0.242 DT/kWh</td></tr><tr><td rowspan="7">Battery</td><td>Capacity</td><td>800 Ah</td></tr><tr><td>Battery status</td><td>40%</td></tr><tr><td>Efficiency</td><td>0.85</td></tr><tr><td>DOD</td><td>0.8</td></tr><tr><td>Voltage of flow</td><td>12 V</td></tr><tr><td>Cost of switching</td><td>300 DT/kW</td></tr><tr><td>Investment cost</td><td>350 DT/kW</td></tr><tr><td rowspan="5">PVP</td><td>Maintenance and operating costs</td><td>10 DT/year</td></tr><tr><td>Rated power (kW)</td><td>50 kW</td></tr><tr><td>Cost of switching</td><td>1000 DT/kW</td></tr><tr><td>Cost of funding</td><td>1000 DT/kW</td></tr><tr><td>Cost of the service maintenance</td><td>11 DT/year</td></tr><tr><td></td><td>Lifetime</td><td>20 years</td></tr></tbody></table>