Energy Management in the Microgrid and Its Optimal Planning for Supplying Wireless Charging Electric Vehicle

Sraidi, Salma; Maaroufi, Mohamed

doi:https://doi.org/10.1155/2022/5923568

Journal of Electrical and Computer Engineering

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Evolutionary, Neural and Fuzzy Systems for Smart and Micro Grids

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Research Article | Open Access

Volume 2022 | Article ID 5923568 | https://doi.org/10.1155/2022/5923568

Energy Management in the Microgrid and Its Optimal Planning for Supplying Wireless Charging Electric Vehicle

Salma Sraidi¹and Mohamed Maaroufi¹

Academic Editor: Mohamed Louzazni

Received30 Sept 2021

Revised29 Dec 2021

Accepted20 Jan 2022

Published27 Feb 2022

Abstract

The ongoing research work on electric vehicles (EVs) as well as the growing concern around the world to ensure a pollution-free environment is sure to lead to a significant increase in the number of EVs in the near future. The electrification of automobiles is an inevitable trend of future development. However, the growth of EVs relies on several elements: autonomy, the charging practice and infrastructure, the price, and the high amount of energy needed for supplying EV. This tendency impacts several points in transportation such as the road infrastructure and electrical power network. The aim of this article is the integration of new energy power sources as a part of the microgrid (MG) to supply EV with dynamic wireless charging. The main goal is to establish an energy management strategy reducing the running cost. The purpose is suggested for two kinds of operation mode: relying only on the MG (island mode) or relying on the MG and the large grid (grid-connected). The optimization problem is solved on the basis of the particle swarm optimization (PSO) algorithm. We could note that the stability of the microgrid in the off-grid mode is better, when the load is close to the output power of the distributed power supply. Through the coordination and cooperation of the battery output and the other two distributed power generation units, the microgrid can achieve its autonomy and maximize the economy of the system operation. Thanks to our methodology, a better revenue and an enhanced flexible dispatching of the system were met in the grid-connected mode as well.

1. Introduction

In recent years, EVs have been seen as a significant alternative to ensure faster energy transition and low-carbon footprint. It drew the attention of many researchers and manufactures. The electrification of automobiles is an expected movement for future development. However, EVs’ autonomy and charging have always been an issue limiting their development. In a recent report [1], MIT states that the major challenge is to acquire an infrastructure for a nationwide charging of EVs rather than manufacturing batteries with affordable cost. Hence, in order to increase the penetration rate of EVs, countries are building large numbers of charging facilities connecting EVs to electric power system [2]. There are 57 charging stations in Morocco counting more than 92 connectors [3]. Currently, EV could be charged either by a regular cable or by a magnetic field as wireless charging. Wired charging stations are the most commonly used for EV energy supply from the grid [4]. These types of stations have many disadvantages. The battery charging requires plugging and unplugging under artificial inert conditions, which poses a safety hazard. On the other hand, the entire charging process requires manual operation with low automation. The wireless power transfer WPT technology [5, 6] uses a noncontact method for power transmission, which makes up for the shortcomings of the traditional direct contact power supply method and has many advantages.

The wireless charging could be static or dynamic; the static mode is proceeded when the vehicle is stopped, while in the other mode the EV is charged during the motion. The technic of dynamic wireless power transfer DWPT could be the sustainable solution needed for EV’s integration on transportation systems. However, taking into account the randomness of EV charging behaviour and assuming high penetration rate of EV, this solution represents some difficulties, with impacts on the infrastructures capacity and electrical network [7].

There have been numerous researches about the impact of EV charging on the grid in order to set an optimal recharging method, either by dimensioning an electrical charging station based on renewable energy [8] or by an integrated storage system as supercapacitor or batteries to reduce the peak demand [9]. The literature [10, 11] presented the conception of fast charging station based on renewable energies and storage systems would decrease the impact on the electrical network.

Renewable energy sources, such as solar, hydropower, and wind, have gradually evolved into the most developing fields in modern electrical engineering and technology [12]. However, the intermittent nature of photovoltaic (PV) and wind turbine (WT) power has brought some challenges with their integration into the local/large grid [13]. In addition, we may need to think about how to maximize the power generation efficiency of renewable energy and reduce the impact on the large power grid within the scope of affordable investment.

Compared with the traditional power grid, the MG integrates Distributed Power Sources (DPS) (as photovoltaic, wind, micro gas turbine, etc.), load, energy storage system, and control device to form an independent system. It could be independent or connected to the traditional power grid. Thus, the emergence of MGs related to RE could alleviate the conflict between large power grids and DPS. This minimizes the possibility of large power grids being damaged by DPS, as well as EV’s large demand [14]. At present, there are three configurations to optimize energy storage: best index, optimal energy storage capacity, and system lowest cost [15]. Literature [16] proposes a model for the optimal operation of MGs, with the optimization goal of minimizing the total cost of the system, while meeting customer needs and system security. An efficient algorithm based on particle swarm optimization minimizes the total energy consumption and operating cost of the MG by optimizing the adjustment of control variables [17]. The integration of Bayesian network theory’s advantage and particle swarm algorithm provides a new strategy for MG optimization operation based on Bayesian-particle swarm algorithm [18]. Literature [19] introduces an energy management strategy that is used in an independent solar-powered diesel-storage MG system and uses the enhanced Pareto evolutionary algorithm to calculate the optimal configuration of the capacity of each distributed unit. The energy management system (EMS) has an important role and benefit for the optimal management of MG [20]. Optimization, scheduling structures, and load shifting are the main EMS’s challenges to deal with. Reference [21] presented a control method of demand response on smart grids and emphasized its utility and benefit for the smart grid. Based on a heuristic algorithm, an optimization and smart energy system for an MG related to EV permits reducing the cost of electricity for a population [22]. An investigation on the contribution of MG and EVs as key enablers for sustainable development shows that the integration of RE and management of EVs charging station all contribute to affordable and reliable energy system [23].

Microgrids can be a suitable energy supply for EV, with benefits on both the economic and environmental levels of the energy systems [24]. As a matter of fact, they can effectively mitigate the possible risks on the power grid that could be caused by large-scale charging of EVs [25]. MGs enable also the local consumption of energy which contributes actively in achieving “zero emission” objective [26]. To be environmentally friendly, the EVs should rely on a green energy supply in order to operate. Implementing wireless charging of EV and the new power generation into MGs will surely be beneficial for increasing EV popularity. Hence, the development of microgrids as a control strategy for EV wireless charging is crucial. Wider deployment of EV wireless charging along with new energy sources will certainly drive a higher capacity of new energy consumption.

On the basis of the previous discussions (role of MG, emergence of EV, and its impact on the electrical grid), this paper explores the necessity of MG energy management system for an efficient and stable operation. This MG intends to supply an electrified road dedicated to the DWPT. The paper also establishes an optimized dispatch suitable for a complementary wind-solar-storage system and puts forward the corresponding energy management strategy. To solve the optimization model, the PSO algorithm is used. In fact, the effectiveness and the accuracy of the optimization model and energy management strategy proposed in this paper are verified through calculation examples. Dynamic learning factors and inertia weights are applied to resolve the optimization problem with PSO algorithm. The strategy of EMS with the lowest running cost possible is carried out for two kinds of operation modes (island mode and grid-connected mode). Finally, the simulation analysis is achieved with two different load requirements by EV. The core of this paper is organized as follows: Section 2 presents the description of the studied system. Economic operation dispatch model of MG for both modes is detailed in Section 3. Section 4 covers the energy management strategy of the system and the choice of optimization model. The efficiency of the optimal scheduling model proposed was proved in Section 5 through a case study.

2. System Description

In view of the sustainable development and the turning point of energy generation, RE production is a crucial factor in the electricity generation system [27]. In addition, the massive integration of EV in the future would not only disturb the electrical network but also contribute to the pollution since it is supplied by the traditional thermal power plant [28]. Wind power and solar power are combined to form a wind-solar complementary system presenting a good solution [29]. Compared with solar or wind energy independent power supply systems, this complementarity is greatly enhanced. It effectively compensates for the utilization defects of wind or solar independent systems in terms of resources. The combination of solar-wind systems can achieve all-weather power generation functions; also, it is equipped with energy storage devices to guarantee uninterrupted power supply [30].

Many researchers have developed diverse optimization models to deal with the EMS problem in MG especially linked to supplying a population [31], a smart home [32], or charging EV with regular cable in a traditional recharge station [33]. However, none of them have covered the subject of EV’s dynamic wireless charging. Supplying the vehicle in-motion by DWPT offers the option of spreading the load along the road and therefore reducing the load power. The DWPT consists in directly feeding the engine; no physical linking is required between the grid and EV. The vehicle could be supplied any time on the day by passing across the electrified road without the necessity for stopping to recharge. This technic seems to be a sustainable solution to be combined in transportation systems to reduce carbon dioxide emissions in long distance rides.

Our system, as seen in Figure 1, proposes the integration of RE (solar and wind) to supply an electrified road destined to the wireless charging of EV. In addition, a storage device based on a battery is implemented in order to deal with the problem of solar and wind energies’ intermittence. This system offers a reliable combination of MG technology and wireless power transmission technology for EV charging. Two modes would be studied:(i)First mode: it consists of an isolated MG based on renewable energy sources along with a storage system, called island mode(ii)Second mode: the same configuration of MG as the first mode is adopted; the only difference resides in its connection to the large grid, instead of being isolated

3. Economic Operation Dispatch Model of Microgrid

When the MG is operating on islands, it does not interact with the large grid. The total energy generated by the distributed power sources in the isolated MG is used for the operation of its own load within the MG. In this mode, wind power and PV power generation in the wind-solar hybrid MG is not dispatchable. At the same time, the MG is not connected to the electric energy of the large power grid, so the dispatching variables only exist in the storage system: the battery.

In grid-connected operation, the microgrid is connected to the external grid through a quick switch. Energy exchange between the larger grid and the MG is possible: selling and buying energy can be done in both directions, thus realizing the interaction between the MG and the grid. Both modes need to consider the coordination of the DPS’s power output with the EV’s demand. Nevertheless, the difference between the two operation modes is that the grid-connected one focuses on the interaction with the larger grid. The model proposed in this paper considers both off-grid and grid-connected modes and adopts a time-of-use tariff model in grid-connected mode, so that the system can have better revenue and more flexible dispatching methods.

3.1. Optimal Scheduling Model in the Island Operation Mode

3.1.1. Objective Function

This paper aims to establish an economic optimization model for the MG with the lowest operating cost 24 hours a day. In the island mode, the transaction of electric energy is stopped, and the MG is isolated from the large power grid. The optimization goal is shown in the following formula:

Here, represents the operating cost of the MG in one day of operation, represents the operating cost of photovoltaic power generation equipment at the i^th hour, represents the operating cost of wind power equipment in the i^th hour, represents the operating cost of the battery storage system at the i^th hour, is the operation and maintenance coefficient of each DPS where according to [34], and according to [35]. represents the penalty fee when there is a power shortage, is the load power shortage, and , , and represent the output of photovoltaic power, wind energy, and battery at the i^th hour. k is the penalty coefficient; its value is related to the unit price of electricity.

3.1.2. Constraints

(1)Distributed power output constraints: Here, , , and are the output power of PV power generation, WT power generation, and battery, respectively, and , , , , , and are the upper and lower limits of PV power generation, WT power generation, and battery output power.(2)Power balance constraints:Here, is the load demand for charging EV by WPT at the i^th period.

3.2. Optimal Scheduling Model in the Grid-Connected Operation Mode

3.2.1. Objective Function

The fundamental factor that differentiates the MG connection from the isolated islands is the existence of electricity transactions. In addition, the amount of energy transactions is nonlinear. The minimum operating cost is taken as the optimization goal, as shown in the following equation:

Here, means the cost of purchasing electricity from the grid at a given period i. is the electricity purchased at that same period, and d is the electricity price, using the Time-of-Use (TOU) price model [36], as shown in Table 1. represents the income from electricity sales in the i^th period; is the electricity sold in the i^th period; h is the price coefficient of electricity sold, and the value in this paper is 0.29 $/kwh [37]; is the power exchanged with the large grid in the i^th period.

3.2.2. Constraints

(1)Distributed power output constraints: Here, and , respectively, represent the minimum power and maximum power interacting with the large power grid.(2)Power balance constraints:

Here, is the power value exchanged between the MG at the i^th period and the large grid, which is positive when purchasing electricity and negative when selling electricity.

4. Wind-Solar Complementary Microgrid Energy Dispatch Strategy

The core issue of energy management for MG is to optimize the output among power generation units. Therefore, this paper proposes an ideal dispatch strategy based on battery charge and discharge status to meet the requirements. Changing the charging and discharging state of the battery allows an optimal use of the released electric energy and at the same time ensures a proper operation of the system. In MG operation, there are two modes of operation: off-grid and grid-connected.

4.1. Off-Grid Operation Mode

According to the power generation data of PV and WT detected in the MG energy management system, the output of the battery is adjusted in a timely manner. The decision variable in this mode is the charge and discharge power of the battery. The sum of wind and solar outputs and the demand for the load of charging EVs have the three following situations:(1)Wind and solar combined output cannot reach the EVs’ load demand(2)Wind and solar combined output equals the EVs’ load demand(3)Wind and solar combined output exceeds the EVs’ load demand

When the first situation occurs, the battery is in discharge state, and the discharge amount is determined according to the electric energy shortage value. If the storage battery releases all the stored electric energy and still cannot meet the requirements, the power electronic devices inside the MG will act to reduce the power supply to EVs or give priority to EVs in need. As for the second situation, this is the most ideal state, the battery does not need to be charged or discharged. Meanwhile, in the third state, the battery stores electricity and could be used by the system in the first situation. If there is excess power after the battery is fully charged, this part of the energy is released into the Earth through the unloader, or it could be used in the road lightening.

4.2. Grid-Connected Operation Mode

There are also three situations for the magnitude of the combined wind and solar output and the demand on the load side:(i); the excess power charges the battery or can be sold directly to the large power grid. Due to the difference in electricity prices, we can choose to give priority to large grids when electricity prices are high in order to earn more revenue.(ii); neither charging or discharging the battery nor trading energy with the large power grid is possible.(iii); we choose either to discharge the battery or purchase electricity from the large grid. If the electricity price is high at this time, priority is given to using battery discharge to make up for the shortfall; otherwise, priority is given to purchasing electricity, and the electricity from the battery is reserved until the electricity price is high. The energy stored in the battery could be sold to the large grid in order to improve the economic benefits of the entire MG operation [34].

4.3. Application of PSO in Energy Management

Considering the problem and its size, we have adopted an optimization based on a heuristic algorithm. We assume that the PSO is suitable to verify and resolve the objective functions mentioned above.

The algorithm is an emerging optimization technology whose ideas are derived from artificial life and evolutionary computing theory. PSO completes the optimization by following the best solution found by the particles and the best solution of the entire group. It has been successfully used in function optimization such as system identification [38], neural network training [39], and other application fields.

The steps to apply PSO to the energy management of the MG start by searching a space identification and initializing PSO parameters, such as population size N, total number of iterations , inertia weighting factors and , and learning factors C1 and C2. The number of current iterations t is initialized at 0 t = 0. After that, we generate N random particle swarms. The initial position of each particle will be randomly set between the maximum and minimum of the control variable. Objective functions (1) and (4) are used to evaluate each particle in the initial population. For each particle swarm, is satisfied. Search for the optimal value of the objective function, and set the particles associated with the optimal value to the global optimal value . Set the initial value of the inertia weight to ω (0); the minimum and maximum values of the inertia weight factor are usually 0.4 and 0.9. All the steps are shown in Figure 2.

5. Case Study and Simulation

In order to evaluate if the suggested methodology is effective for enabling the integration of DPS on MG for charging electric vehicle with WPT, we opted for a load configuration taking into consideration real predictions of traffic on an hourly basis. This prediction used data collection of traffic flow of four-month span (January to April 2019), available on the Open Data Portal of Transport Infrastructure of Ireland [40].

The output power curve of the wind-solar hybrid unit derives from a biprobability-interval optimization model for wind-solar power day-ahead scheduling under uncertainties.

5.1. Load Profile

A lot of research has been done to predict the number of vehicles passing on a highway during a day. For our study, we were based on the curve given by the literature [40], which made a study of the traffic flow forecast hour-by-hour based on real data on the traffic in Dublin’s metropolitan circle on seven highways.

It assumed a percentage of 1% of the vehicles which will be electrified and need to be recharged. The aim of the said study was to reestablish a pricing methodology for charging stations in areas rich in renewable energy. The curve of number of vehicles to be charged on highways hour-by-hour is given by Figure 3.

Different projects have tested the efficiency of WPT with different power transmission levels [41–43]. To evaluate the methodology and the optimization used in this paper, we consider 2 scenarios: the first one relies on an average power demand for each vehicle of 5 kW, while in the second one the average power demand is 15 kW as shown in Figure 4.

Figure 5 presents the demand of a single vehicle following the NEDC driving cycle [11]. As shown in this figure and from a microscopic standing point, EV load can create disturbance due to its inherently random load profile.

From a macroscopic point of view, if we consider the grid as the unique source of energy, as seen in Figure 4, the mobility energy needs peak coinciding with existing periods of grid loads peak. This situation is very detrimental to the electrical grid as it overloads it.

For these reasons, supplying the electrified road for WPT of EV by an MG based on RE would not only help with the zero emission but also help to avoid the impact on the electrical grid.

Subsequently, we would present the details of the charging EV by the isolated and grid-connected MG for different level of charge.

5.2. Island Mode

For our case, to study the electrification of road for the wireless power transfer of EV, we assume an output power curve of the wind-solar hybrid unit as shown in Figure 6 according to [44]; it was based on a biprobability-interval optimization model for wind-solar power day-ahead scheduling under uncertainties.

The upper limit of battery charging and discharging power is 150 kW, and the lower limit is 100 kW; we consider the power range of the interaction between the system and the grid as [−250 kW, 250 kW].

5.2.1. Charge 1: 5 kW

In the island particle swarm optimization algorithm, the maximum number of iterations is 300, and the number of particles is 600.

The optimized scheduling results show that the operating cost per day is 194.5 $/day. If we consider that the electrified road was supplied directly from the grid, and using the TOU price shown in Table 1, the operating cost per day would be 360.8 $/day, which gives us a daily gain of 166.3 $ per day with the use of MG.

The output of each device is shown in Figure 7 and Figure 8.

Figure 6 presents the curve of the load considering that the average power demand of each vehicle is 5 kW and presents the power output of the renewable energy installed in the microgrid as shown in the following equation:

Figure 7 presents the shortage power or the power needed after feeding the demand by wind/solar power and the battery power output. As seen in this figure, the battery fills in the lack of power in the microgrid.

When there is little difference between wind/solar combined output and load demand, the optimized result is ideal. The effectiveness of optimization is explained by selecting two typical moments. When the wind and solar output is smaller than the required amount, it is sufficient to meet the demand of the load by discharging the battery. It can be clearly seen in Figure 9 that, at around 18 : 00 in the evening, the peak power demand of this day is ushered in. The combined solar and wind output can no longer meet the demand of the electrified road, and the difference is about 125 kW. Since the maximum discharge power of the battery selected in the MG system is 150 kW, it can completely make up for this part of the shortfall. Therefore, even in the evening when the load demand is large, there is no need to remove the load; thus the power supply reliability of the entire system is maintained. Similarly, at 5 o’clock in the morning, the combined solar and wind output at this time is greater than the required amount of electricity, with a difference of 29 kW. Since the upper limit power of the battery for charging has reached 100 kW, the extra energy can be absorbed by the battery itself, and the excess energy will not be wasted by leaking into the ground. The rest of the moments are also in the same situation as the above two moments. The battery can always discharge or store the power. From the definition in the objective function (1), it can be seen that the penalty fee for the last item is reduced to the lowest.

Under the premise of ensuring the reliability of power supply, the operating economy of the wind-solar complementary MG system is ensured.

5.2.2. Charge 2: 15 kW

The operating cost of the system is $/day. In the event of an important load demand of EVs or due to a huge power need in an electrified road destinated to the heavy-duty vehicles, the load profile may undergo a considerable change as shown in Figure 10. In short, the huge change in load will make the gap between it and the combined wind/solar output and load become larger and larger. By comparing Figure 11 and Figure 12, it can be clearly seen that the optimized result is not ideal due to the limitation of battery capacity, and the shortfall value after optimized scheduling is still relatively large. In this case, we could also select a typical moment to analyze the optimization results. At 8 o'clock in the morning, the difference reached as much as 483 kW. The maximum discharge power of the battery is only 100 kW, which is far insufficient to make up for the shortfall. At this time, the MG can adopt load shedding measures by assuming a methodology that requires feeding EVs with a state of charge in battery lower than 50% or reducing the average power to 10 kW or 5 kW, for example. However, the penalty cost for load shedding is quite expensive, and the operating cost has risen from 194.5 to 3099.7 $. Under this circumstance, not only is the reliability of electricity usage not guaranteed, but also it brings huge losses to the entire power grid.

From the above analysis and research, it can be seen that when the load demand is close to the output power of the distributed power supply, the stability of the MG is better. Through the coordination and cooperation of the battery’s output and the other two distributed power generation units, the self-sufficiency of the MG can be achieved. When there is a huge difference between the load demand and the output of DPS, the stability of the entire MG operation and the reliability of the power supply will become worse. Relying only on the supply and storage of batteries could not be useful under different load changes or to ensure the safety of the system, in addition to the economic impact. Therefore, in order to reduce a series of impacts brought by load changes, the next step will be to analyze the optimal scheduling of grid-connected operation modes.

5.3. Grid-Connected Mode

5.3.1. Charge 1: 5 kW

In the grid-connected operation model, there are two optimized variables: one is the charging and discharging power of the battery, and the other is the power interacting with the large grid. Therefore, the dimensions of the particle swarm optimization algorithm have become 48. The first 24 unknowns represent the magnitude of the interaction with the electric energy of the large power grid at each time in 24 hours, and the last 24 unknowns are allocated to the battery charging or discharging for each hour.

When the electricity price is changed, that is, when the TOU electricity price is adopted, the optimized results are shown in Figure 13 and Figure 14. It can be seen that, in this mode, it can still have good power supply reliability, but the charging and discharging of the battery and the transaction with the large power grid have undergone certain changes, which are caused by changes in electricity prices. At 10 o'clock, on the basis of ensuring the power consumption of the load, more power is sold to the large power grid through the battery discharge at 10 o'clock, and the load in the large power grid is relieved from the power supply pressure during the peak power consumption. More electricity is purchased in the parity stage from 23 to 7 hours and it is stored in batteries for use during peak electricity consumption. After the particle swarm optimization algorithm runs for one day, the income is about 253.4 $, which has better returns and a more flexible scheduling method than the model that does not use the Time-of-Use electricity price method.

5.3.2. Charge 2: 15 kW

When the super-large load shown in Figure 3 appears, the optimized results are shown in Figure 15 and Figure 16. When the electricity price is low, such as from 23 : 00 in the evening to 7 : 00 in the morning, it would be better to purchase electricity and store it in the battery power generation unit. In the time period from 16 : 00 to 19 : 00 and 8 : 00 in Figure 13, in order to give priority to ensuring the reliability of power supply, the battery discharge and power purchase have reached the upper limit, but the load demand is still not met, and penalty fees are incurred during this period. Despite the adoption of the Time-of-Use electricity price model, the operating cost on the last day reached 8372.9 $.

6. Discussion

Table 2 summarizes our results. In fact, if the electrified road was only powered by the electrical network, there will certainly be no power shortage. The network will be able to meet the need perfectly, but the price will be high. In addition, as previously discussed, such a demand would have a negative impact on the electricity network.

The suggested methodology would therefore make it possible to reduce the huge demand on the network. An example is shown in Table 2, in which two selected hours (8 a.m. and 7 p.m.) illustrate the importance of adopting an MG equipped with a suitable EMS in order to reduce the harmful impact of wireless charging on the electrical grid. We could see the power shortage, which is significant in the case of the huge load (15Kw per EV) in the off-grid mode.

Besides, when the load is close to the DPS’s output power of the MG, there is no need to connect to the grid. The stability and autonomy of MG are ensured through the storage device.

Finally, thanks to the energy management system, the cost of the system is more viable in the case where the MG is implemented than when the grid presents the unique source supply.

7. Conclusions

Starting from the economic functioning of the MG and the necessity of feeding EVs, this paper has studied the optimal distribution model of the complementary wind-solar MG. Given the fact that this MG is supplying an electrified road for the dynamic wireless charging of EV under the modes of operation connected to the grid and isolated, the current paper proposes a corresponding energy management strategy. On this basis, an improved particle swarm optimization algorithm with dynamic weights and dynamic learning factors is proposed to give it better self-learning ability and better social cognitive ability. The actual calculation example shows that, in off-grid mode, when the load demanded by the vehicles is close to the output power of the distributed power supply, the stability of the MG is better. Through the coordination and cooperation of the battery output and the other two distributed power generation units, the MG can realize its self-sufficiency and maximize the economy of system operation. In the grid-connected mode, the Time-of-Use electricity price model is used to improve the system’s revenue and dispatching methods flexibility.

Finally, this study could be further completed by an economic comparison of the various system’s costs incurred due to a different choice of the optimization model (other than PSO).

Data Availability

All data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that there are no conflicts of interest.

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Copyright © 2022 Salma Sraidi and Mohamed Maaroufi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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