1. Introduction

Energy management in microgrids (MGs) is a crucial aspect of power system studies. It encompasses various objectives, including cost reduction, emission reduction, enhanced reliability, and improved power quality. A microgrid typically comprises key components such as power sources, electrical storage, and loads. The DGs in a microgrid can be renewable, such as photovoltaic (PV) arrays and wind turbines (WTs), or nonrenewable sources as well as microturbines. Additionally, electrical energy storage can be achieved through battery storage banks or electric vehicle (EV) parking lots (PLs). Smart parking lots integrated into the microgrid provide various functionalities, including improvements in system power quality and also reliability, maintaining voltage stability, minimizing losses, and increasing profitability for EV owners [1]. Maximizing profitability and enhancing reliability are crucial aspects of smart parking utilities, particularly in their significance. To achieve these objectives, a comprehensive scheduling approach is required for EV charging and discharging programming. In recent years, a plethora of research investigations has been carried out in the domain of EMS, delving into diverse concepts and methodologies [2].

In [3], a novel approach is presented for coordinating the EV charging in the MG. The method aims to improve MG reliability by minimizing the charging costs of EVs. To achieve this, it considered the electric energy price uncertainty in the market and the charging time of EVs. In [4], a daily energy management model is introduced to enhance MG reliability in the context of a substantial number of electric vehicles (EVs) being present. The model allows vehicle owners to manage energy consumption during their travels through effective energy management techniques. In [5], a simulation technique utilizing probabilistic indices is employed to enhance the reliability of MGs with DG sources and EVs, particularly in island mode. In [6], an efficient objective function is put forth to diminish the operational costs of an MG with a significant number of EVs and DGs. In [7], the study focuses on the calculation details of MG reliability that incorporates both DG sources and EVs. [8] presents an economic-based optimization approach for EVs in the MG, specifically considering cogeneration, while also taking into account MG reliability indexes as operational constraints. In [9], the energy not supplied criterion (ENS) and the time of MG connection to the network are utilized to evaluate MG reliability. [10] investigates both economic and reliability aspects of the MG, using real-time pricing for power exchange transactions of the MG and parking lots (PLs) and employing a probabilistic method to calculate network reliability with and without DG sources and EVs. [11] proposes an energy management system for EV charging in the power system through a DRP, aiming to reduce operation costs and enhance MG reliability, with customer participation encouraged for effective energy management. [12] employs a DRP to improve distribution network characteristics, leveraging EV charging stations to enhance network reliability, with simulation results showing a significant reduction in ENS value through load response programs and scheduled EV charging. [13] introduces an intelligent algorithm based on neural networks for the microgrid EMS, highlighting the impact of DR on MG power exchange and EV charging/discharging. [14] proposes an optimal EMS approach for a MG incorporating PV panels, EVs, and responsive loads, considering load uncertainty and indicating a cost reduction of about 2.5% with the use of DR programs. [15] focuses on MG energy management with peak load management, aiming to reduce operating costs using time of use (TOU) pricing, incorporating an error function to calculate uncertainty in different scenarios. [16] defines demand response programs (DRPs) as changes in electricity consumption patterns in response to time-varying prices, including incentive payments to reduce consumption during high-price or reliability issue periods. [17] explores DRPs through pricing methods that incentivize consumers to shift their electricity demand away from peak times, highlighting the advantage of avoiding expensive peak-time power plant construction. In [18], a demand DRP is introduced for grid-connected EVs. The primary aim of this study is to conduct a comparative analysis of different approaches for managing EVs in the day-ahead scenario.

In [19], the study addresses the optimal scheduling of electric vehicle (EV) charge and discharge, taking into account uncertainty in electricity prices. The objective function is designed to maximize network profitability. [20] focuses on microgrid (MG) energy management with EVs and DG sources, aiming to improve MG reliability indices while considering uncertainties associated with DGs. [21] presents an optimal EV charge and discharge strategy considering uncertainties in EV and DG operations, with the objective function aimed at cost reduction and pollution mitigation based on probabilistic behaviors of EV and wind turbine charging and discharging. [22] introduces a scheduling method for optimizing the utilization of MG infrastructure during nonpeak times for EV charging, considering environmental and economic factors to effectively integrate a significant number of electric vehicles (EVs) into the network accounting for their uncertainties. In [23], a novel approach to microgrid EMS is proposed, considering the presence of electric vehicles (EVs), aiming to achieve maximum profitability in the standard 33-bus power system by reducing generation costs considering uncertainties in energy market prices and EV charging times. In [24], an energy management system is proposed that takes into account the uncertainties associated with electric vehicles and wind turbines.

2. Problem Formulations

For an MG study, there is an essential need to provide a suitable model of the MG to consider the uncertainties. Various goals such as cost reduction, improved voltage stability index, reliability, and power quality are desired and are considered for MG energy management. Ensuring the provision of electrical energy at the lowest cost while minimizing the occurrence of blackouts is of utmost importance [25]. In the subsequent sections, we present the formulation of objective functions for the EMS problem in a MG under uncertain conditions.

2.1. Proposed Objective Functions

The initial objective function pertains to the MG cost with the PL.

The proposed MG operation cost is a combination of the energy purchasing cost from the power system, DG power cost, EV parking cost, penalty cost for energy not supplied (ENS), and DRP cost. The first objective function can be formulated as follows:

$$ (1)

where $$, $$, $$, $$, and $$ represent the costs associated with purchasing energy from the power system, DGs, electric vehicle parking lots, energy not supplied (ENS) penalties, and DRP costs at time t, respectively. Also, π_h represents the selected scenario probability, Nh denotes the number of samples, N_PL signifies the number of PLs, and N_DG indicates the number of distributed generators. Finally, T is a period which is 24 hours. Also, in this paper, the time interval is considered one hour. The energy procurement cost from the power system is expressed as follows [26]:

$$ (2)

where $$ represents the quantity of exchanged electric power with the upstream power network and $$ denotes the market energy price. The operation cost of the distributed generator is computed according to the following equation [27]:

$$ (3)

where $$ represents the power generated by the i^th distributed generator at the h-level demand. Furthermore, α, β, and γ are specific cost values associated with each unit. The cost of the PL is determined using the following equation:

$$ (4)

where $$ and $$ represent the quantities of power used for charge and discharge in the j^th parking lot. $$ and $$ denote the electricity prices for EV charge and discharge in the parking lot [28]. The ENS penalty is determined using the following equation:

$$ (5)

where $$ and $$ represent the power shortage probability and the penalty for undesired power deficit. It is assumed that $$ accounts for 1% of the total load in the microgrid. The cost of the DRP is determined using the following equation:

$$ (6)

where $$ represents the reduction in power consumption by user participating in the demand response program, while $$ signifies the compensation provided to them for their reduced consumption [29].

The voltage stability index (VSI) of the power system is regarded as an additional optimization objective. Equation (7) is employed to calculate the VSI.

$$ (7)

where P_n and Q_n  are the load active power and load reactive power, respectively, V_m represents the m^th bus voltage, and Rn and Xn are the resistance and line impedance between the bus n and m. Figure 1 shows part of a radial distribution feeder.

3. Uncertainty Modeling

3.1. The Proposed Model Incorporates Uncertainties

Given the increasing trend of MG privatization and the dynamic nature of load and production, managing uncertainties is crucial for ensuring the power system’s reliability, operation, and control. The MG uncertainty emerges due to the absence of accurate data on the MG parameters. The primary sources of the MG uncertainty include variations in parameters over time, unanticipated dynamics, and measurement errors.

3.1.1. Electrical Demand Uncertainty

Electrical demand, being the primary source of uncertainty, significantly influences the performance of microgrids (MGs). Demand changes in MGs are primarily influenced by two factors: time and weather. The daily and weekly variations in demand are largely driven by the energy usage patterns of the user. The load changes are suitably characterized by a normal probability density function (PDF) as

$$ (16)

where P^Load is the electrical demand, $$ is the demand mean, and $$ is the demand variance [31].

3.1.2. Irradiation Uncertainty

The generation capacity of each photovoltaic array is influenced by deterministic factors such as solar radiation, panel surface temperature, panel surface area, and efficiency. Nevertheless, owing to the stochastic nature of solar irradiation, the power output of a photovoltaic array is subject to probabilistic variations. The behavior of PV units is described using the beta PDF, as shown in the following equation [32]:

$$ (17)

where si_t,  _h (kW/m²) is solar radiation intensity, Г is the gamma function, and also α and β represent the parameter of beta PDF. These parameters can be calculated by the following equations:

$$ (18)

Equation (19) is used to calculate the power generated by PV units in each hour.

$$ (19)

where η^pv represents the PV system efficiency and A^pv (m²) represents the photovoltaic surface area. The generation capacity of the photovoltaic system is formulated as

$$ (20)

where P^PV,rated is the photovoltaic array nominal capacity, f^PV is dirtiness factor, G_t,h and G^STC are the real-time irradiation and the array standard irradiation, λ^T is temperature parameter, and T_t,h and T^STC are the array real-time temperature and its standard temperature. It is worth mentioning that G^STC and T^STC are 1000 w/m² and 25°C [32].

3.1.3. Wind Turbine Model

In this paper, a variable-speed turbine is utilized, and its generation power is directly influenced by the uncertainty in wind velocity [33]. The stochastic nature of wind velocity can be described by utilizing the Weibull PDF, as depicted in the following equation:

$$ (21)

where $$ is the Weibull PDF, υ_t,h(m/s) is the wind speed, and k and Ω represent the shaping parameter and scaling parameter, respectively, which can be calculated using the following equations:

$$ (22)

where μ^v is the mean of wind speed data and σ^v is the wind speed data variance. The power generation capability of the WT can be determined by utilizing the following equation:

$$ (23)

where $$ is the generated turbine power and P^r is the WT nominal capacity. Also, υ^cut-in is the cut-in velocity, υ^cut-out is the cut-off velocity, and υ^r is the rated velocity of a WT, respectively. The power generation curve as a function of wind speed variations is depicted in Figure 2.

3.1.4. The PL Uncertainties

The characterization of the input/output power of parking lots relies on multiple factors of uncertainty, such as the charging/discharging plan of EVs, the capacity and type of EV batteries, the proportion of EVs in parking lots, driver behavior, EV arrival/departure timings, and the SOC of the batteries. In this paper, the total capacity of PLs is assumed to be 500 EVs [34]. The scheduling of EV arrival and departure times is represented by the Weibull and Lognormal probability distribution functions, respectively. The parameters of the PDFs are listed in Table 1. The Weibull PDF and Lognormal PDF are represented by equations (24) and (25), respectively [35].

$$ (24)

$$ (25)

where $$ and $$ represent the Weibull PDF and Lognormal PDF for the EV’s arrival and departure, respectively.

Table 1. Parameters of the probability density functions for arrival and departure.

Arrival	K	Ω
	18.91	5.90
Departure	μ	σ
	2.21	0.30

Figure 3 illustrates the amount of EV arrivals and their departures, based on the parameters of the probability density functions (PDFs) [35].

The initial conditions of battery charging are influenced by several factors, such as distance traveled, kind of the EV battery, and its efficiency. Due to the variations in these parameters across EVs, the remaining energy in the batteries can be calculated probabilistically. This study encompasses three modes of charging and discharging ratio. The initial battery charge and the nominal charging and discharging ratios are selected based on the obtained scenario from Figure 4 PDFs. The scenario distribution curves presented in this approach are categorized into three zones for the initial SOC and five zones for the charge/discharge ratio.

It is worth mentioning that the PDF curve is estimated using the information provided in Table 2.

Table 2. The SOC and charging rate parameters [36].

	SOC		Maximum charge\discharge rate
	Discharge mode	Discharge mode
Mean	72	26	10
μ	2.6	1.7	1.1

It is assumed that the initial charge and charging and discharging ratio are considered independent of one another. Therefore, the scenarios are combined in order to generate a comprehensive scenario, based on equation (26). These scenarios are shown in Table 3.

$$ (26)

Table 3. The scenarios of initial SOC and charging/discharging ratio along with their associated probabilities.

	SOC	Charge and discharge ratio	(πs)
S1	μ1 − 2.5σ1	μ2 − 1.5σ2	0.0035
S2	μ1 − 1.5σ1	μ2 − 1.5σ2	0.0182
S3	μ1	μ2 − 1.5σ2	0.0966
S4	μ1 + 1.5σ1	μ2 − 1.5σ2	0.0182
S5	μ1 + 2.5σ1	μ2 − 1.5σ2	0.0035
S6	μ1 − 2.5σ1	μ2	0.018
S7	μ1 − 1.5σ1	μ2	0.0936
S8	μ1	μ2	0.4936
S9	μ1 + 1.5σ1	μ2	0.0936
S10	μ1 + 2.5σ1	μ2	0.018
S11	μ1 − 2.5σ1	μ2 + 1.5σ2	0.0035
S12	μ1 − 1.5σ1	μ2 + 1.5σ2	0.0182
S13	μ1	μ2 + 1.5σ2	0.0966
S14	μ1 + 1.5σ1	μ2 + 1.5σ2	0.0182
S15	μ1 + 2.5σ1	μ2 + 1.5σ2	0.0035

In this equation, π^EV represents the probabilities associated with the charging and discharging ratio. Additionally, π^SOC denotes the probability of the initial SOC in scenarios.

Equations (27) and (28) can be used to calculate the needed time for full charging or full discharging of the EV battery depending on the initial SOC:

$$ (27)

$$ (28)

Equation (29) can be employed to compute the anticipated input and output power generated by the j^th parking lot within each Monte Carlo simulation. In this equation, SOC^max is the maximum charging level and SOC^min represents the minimum charging level of the EV battery. ES_n indicates the capacity of the battery, and P_v represents the maximum charging and discharging ratio of the EVs. Therefore, the anticipated input and output power of the j^th parking lot at the demand level h in each Monte Carlo test (e) can be calculated using the following equation [37]:

$$ (29)

where CP_j is the amount of parked electric vehicles in the PL, $$ is the percentage of the EVs present in the PL at the demand level h, and also SOC_s,n is the initial SOC of an electric vehicle. N_EVj is the amount of EVs in the PL. Also, SOC^min is 20% and SOC^max is 80%.

4. Proposed Optimization Algorithm

The proposed hMOPSO-HS algorithm is a combination of the MOPSO and HS algorithms. In the proposed algorithm, genetic mutations are applied to the MOPSO algorithm and subsequently, during each iteration of the algorithm, the parameters are effectively fine-tuned using the harmony search algorithm. The mechanism of the proposed algorithm is shown in Figure 5.

In the same way, all variables of a harmony are created and then the value of that harmony is calculated according to the objective function, and they are compared with the worst harmony in the matrix memory. If it is better than the worst harmony in the matrix memory, the new harmony is replaced with the previous one. The condition for stopping the algorithm is to achieve maximum iteration. The schematic diagram illustrating the MOPSO-HS algorithm is depicted in Figure 6.

The pseudocode of the proposed hMOPSO-HS algorithm is given in Algorithm 1.

5. The Understudy Microgrid

Figure 7 illustrates the test system employed as a microgrid (MG) in this study [41–43]. The understudy microgrid incorporates two 500 kW WTs located at bus 15 and bus 21, as well as two 500 kW PV arrays situated at buses 9 and 30. Furthermore, the MG includes six 500 kW parking lots positioned at buses 5, 12, 17, 19, 24, and 28. The wind velocity and irradiation data utilized in the analysis are obtained from the McHenry precinct of the North Dakota region [44]. Moreover, the load flow calculations are carried out using the forward-backward sweep (FBS) method.

An energy management period of 24 hours is carried out to facilitate the charging and discharging operations of EVs. The power exchange between PLs and the MG involves a total of 500 EVs. These EVs are assumed to be of the Chevrolet model, based on the technical specifications provided in [44]. Each EV has a battery capacity of 16 kWh, and the maximum charging and discharging power for each EV is set at 5 kW. The electricity prices procured from the upstream network for each hour are illustrated in Figure 8 [45].

6. Simulation Results Analysis

The simulations are performed in three parts. Firstly, the performance of the hMOPSO-HS algorithm is assessed by conducting optimization on several benchmarks. In the second part, the simulation is done regardless of the uncertainties and with the predicted definite data, and in the third part, the uncertainty is considered by selecting 15 scenarios from the MCS. To achieve the optimal energy management of MG in two cases, multiobjective particle swarm optimization (MOPSO) algorithm, nondominated sorting genetic algorithm (NSGAII), multiobjective differential evolution (MODE), multiobjective gray wolf optimization (MOGWO), and also the hMOPSO-HS algorithm is used.

6.1. First Section of the Simulation Results (Algorithm Performance Evaluation)

In this part, the hMOPSO-HS performance is assessed by conducting optimization on the CEC′09 benchmark functions [46]. The optimization process covers both unconstrained test functions UF1–UF10 and constrained test functions CF1–CF7 using the hMOPSO-HS algorithm. The acquired outcomes are subsequently contrasted with diverse multiobjective algorithms. The performance assessment is based on the calculation of the inverse generational distance (IGD). Smaller values of the IGD index indicate a smaller discrepancy between the values of the actual Pareto front and the Pareto front obtained through the optimization algorithm. After solving UF1-UF10, the corresponding IGD values were calculated and presented in Table 4.

Table 4. The IGD index values for the unconstrained benchmark functions.

	UF1	UF2	UF3	UF4	UF5	UF6	UF7	UF8	UF9	UF10
hMOPSO-HS	0.005743	0.004373	0.048562	0.053022	0.071675	0.062543	0.05348	0.061612	0.057973	0.180345
MOPSO	0.006115	0.005784	0.043003	0.049105	1.930803	0.610471	0.008268	0.236419	0.175671	0.526617
MOABC [47]	0.00618	0.00484	0.0512	0.05801	0.077758	0.06537	0.05573	0.06726	0.0615	0.19499
MOEAD [47]	0.00435	0.00679	0.00742	0.06385	0.18071	0.00587	0.00444	0.0584	0.07896	0.47415
GDE3 [47]	0.00534	0.01195	0.10639	0.0265	0.03928	0.25091	0.02522	0.24855	0.08248	0.43326
MOEADGM [47]	0.0062	0.0064	0.0429	0.0476	1.7919	0.5563	0.0076	0.2446	0.1878	0.5646
MTS [47]	0.00646	0.00615	0.0531	0.02356	0.01489	0.05917	0.04079	0.11251	0.11442	0.15306
LiuLi algorithm [47]	0.00785	0.0123	0.01497	0.0435	0.16186	0.17555	0.0073	0.08235	0.09391	0.44691

The lower values of IGD indicate the superior performance of the proposed hMOPSO-HS algorithm in finding optimal solutions. Figure 9 displays the Pareto front for UF1 to UF3.

As depicted in Figure 9, the Pareto front obtained by the hMOPSO-HS algorithm exhibits minimal deviations from the actual Pareto front. Subsequently, the proposed MOGOA-BES algorithm was employed to optimize the constrained test functions (CF1-CF7), and the corresponding IGD index values are calculated and presented in Table 5.

Table 5. The IGD index values for the constrained benchmark functions.

	CF1	CF2	CF3	CF4	CF5	CF6	CF7
hMOPSO-HS	0.005743	0.004373	0.048562	0.053022	0.071675	0.062543	0.05348
MOPSO	0.006115	0.005784	0.043003	0.049105	1.930803	0.610471	0.008268
MOABC [47]	0.00992	0.01027	0.08621	0.00452	0.06781	0.00483	0.01692
GDE3 [47]	0.0294	0.01597	0.1275	0.00799	0.06799	0.06199	0.04169
MOEADGM [47]	0.0108	0.008	0.5134	0.0707	0.5446	0.2071	0.5356
MTS [47]	0.01918	0.02677	0.10446	0.01109	0.02077	0.01616	0.02469
LiuLi algorithm [47]	0.00085	0.0042	0.1829	0.01423	0.10973	0.01394	0.10446

The lower values of the IGD index in solving CF problems validate the higher accuracy and suitable dispersion of the solutions obtained by the proposed algorithm in comparison to other algorithms. Figure 10 illustrates the Pareto fronts of the proposed algorithm and the actual Pareto fronts for CF1, CF2, and CF3.

6.2. Second Section of the Simulation Results (Regardless of Uncertainty)

For the first part of the simulation, uncertainty is not considered, and definite data are used to perform the optimization. The predicted electrical demand by customers is shown in Figure 11.

The projected values of irradiation and wind speed are illustrated in Figure 12. The PV system unit has the capability to generate electricity between 8 am and 6 pm, while no power generation occurs during the remaining hours due to insufficient solar irradiation. The wind speed in the specified area fluctuates between 6 m/s and 11 m/s [47].

The Pareto fronts for the optimization algorithm are depicted in Figure 13.

To assess the optimization outcomes, the S-metric index is computed to gauge the dispersion of the dominating particles, and its representation can be observed in Figure 14. A smaller amount of the mean metric distance signifies that the Pareto particles are more scattered, and zero values of the S-metric distance mean that all the dominant particles are distributed at the same Pareto distance.

The best result is selected from the dominant particles. Also, the fuzzy mechanism is used for the best results selection. The optimal outcomes for the optimization algorithms are presented in Table 6.

Table 6. The optimal results in the first section.

	NSGAII	MOPSO	MODE	MOGWO	hMOPSO-HS
Cost ($)	6269	6235	6234	6230	6203
1/VSI (p.u.)	1.321	1.287	1.287	1.282	1.274

Based on the findings presented in Table 6, it can be observed that the hMOPSO-HS algorithm outperformed other metaheuristic algorithms in terms of performance. The final cost for the hMOPSO-HS is $6203 and the voltage stability index in the MG is 1.274 p.u. Figure 15 shows the operating cost of the MG separately.

To better analyze the performance of the hMOPSO-HS optimization algorithm on MG operation costs, the share of each component in the final cost is shown as a percentage in Figure 16. About 48% of the MG operation cost is allocated to the purchase of electricity from the upstream network, while the share of distributed generation and parking lots from the final cost of operation is 16% and 22%, respectively. The DR share is equal to 8%, and the ENS fine share is about 6% of the final cost.

Figure 17 shows the generation capacity of each part of the MG components for 24 hours after optimization by the proposed hMOPSO-HS algorithm.

In this case, the MG voltage profile in 24 hours is shown in Figure 18. The voltage amplitude in all buses for 24 hours is more than 0.94 p.u.

6.3. Third Section of the Simulation Results (considering Uncertainty)

In the second section of the simulations, demand and generation uncertainties as well as parking lot uncertainties are considered. Fifteen scenarios are chosen by the MCS, and the per-unit values of wind power, PVs and charge in these scenarios are shown in Figure 19.

The Pareto fronts for the optimization algorithms in the second part are shown in Figure 20.

Similar to the first section, for better evaluation, the S-metric index is calculated for the algorithms which is shown in Figure 21.

Considering the uncertainty, the S-metric index results reveal an increase in the dispersion of the outcomes compared to the first section. A lower mean value of the S-metric index means scattering with a uniform distribution of dominant particles of the proposed hMOPSO-HS. The MG cost and the voltage stability function for the selected particles are given in Table 7.

Table 7. The optimal results in the second section.

	NSGAII	MOPSO	MODE	MOGWO	hMOPSO-HS
Cost ($)	6684	6673	6623	6646	6605
1/VSI (p.u.)	1.412	1.388	1.391	1.371	1.367

In this section, the MG operation cost and 1/VSI index are the lowest when the proposed hMOPSO-HS is used for MG energy management. The operation cost is $6605, and 1/VSI is 1.367 p.u. for the MG optimized by the hMOPSO-HS. In Figure 22, the MG component cost is shown as a separate bar chart. The results show that considering the uncertainty in MG, it increases the purchasing energy cost from the power grid and the penalty for not supplying energy. Also, the demand response program has played an important role in reducing operation costs.

In Figure 23, the share of each part in the final cost is shown by percentage.

In this part of the simulation, the percentage of the cost from a power system is about 50% and it has increased by 2% compared to conditions without considering uncertainty. Also, the share of ENS and DR has increased. The DR share of total cost is 12%, and the ENS share is 9% for this section. But, the share of PL costs and DG production costs has decreased to 18% and 11%, respectively. The MG voltage is shown in Figure 24.

The voltage profile shows that in the case of uncertainties, the voltage amplitude has decreased compared to the conditions of the previous section. The minimum voltage amplitude is 0.93 p.u.

7. Conclusion

In this paper, a novel energy management system based on uncertainty for MG energy management is proposed. The MG selected for the simulation consists of PV and wind sources along with EV parking lots. The renewable source generation powers, PL, and load consumption uncertainties are considered in the simulation and other sources of uncertainty are omitted. The operation cost and voltage stability index (VSI) are considered objective functions, and an innovative hybrid algorithm called hMOPSO-HS is proposed for solving the optimization problem. The hMOPSO-HS algorithm is a combination of the mutant version of MOPSO and harmony search (HS) algorithms. Simulations are done in two different cases. In the first case, the uncertainty is neglected and, in the second part of the simulation, the uncertainty is considered. The optimization results of the proposed hMOPSO-HS algorithms are compared with several multiobjective algorithms for two cases of simulations and also the S-metric index is calculated for all of them. The simulation results indicate better performance of the hMOPSO-HS algorithm than all other algorithms. The simulation results also showed that if uncertainty is considered, the cost of the demand response program and the cost of purchasing energy from the upstream network will increase to reduce the impact of uncertainty on the sources of distributed generation and parking of EVs. For future studies, new electrical energy storage technologies such as compressed air storage (CAS) or power to gas (PtG) can be added to the microgrid and the impact of the presence of these storages can be investigated. Indeed, the studies presented in this paper can be replicated and applied to real-world systems. By conducting similar experiments on real systems, researchers can verify the effectiveness and applicability of the proposed approaches in practical scenarios.

Conflicts of Interest

The authors declare that they have no conflicts of interest.