Nowadays, as the demand for plug-in electric vehicles in microgrids is growing, there are various challenges that the network must face, including providing adequate electricity, addressing environmental concerns, and rescheduling the microgrid. In order to overcome these challenges, this paper introduces a novel multiobjective optimization model where the first objective is to minimize the total operation cost of the microgrid and the second objective is to maximize the reliability index by reducing the amount of system energy not supplied. Because of these two compromising objectives, the evolutionary multiobjective seagull optimization algorithm is utilized to find the best local solutions. In this regard, integrated plug-in electric vehicles and demand response programs are used to smooth distribution locational marginal pricing. Furthermore, the effect of the system’s various configurations is analyzed in the suggested method to smooth the amount of distribution locational marginal prices in comparison to the initial case. Two case studies including modified IEEE 33-bus and 69-bus distribution networks are applied to evaluate the efficiency of the proposed approach.

1. Introduction

1.1. Background and Context

The widespread application of electric vehicles (EVs) in distribution networks led to an increase in electricity demand in the last decade, which caused several technical problems like the line overloading or congestion, an increase in electricity prices, a shortage of generation capacity, and an environmental pollution. Overloading of lines in the network causes incoordination between generation and consumption, defined as congestion in the distribution network. Congestion has some destructive effects on the network like a failure of equipment. Congestion in active distribution networks has been intensively examined [1], but less attention has been paid to it. High penetration of EVs and distributed energy resources like solar panels, wind turbines, and CHPs cause congestion in distribution networks, which is an enormous challenge to distribution system operators.

According to these explanations, the congestion or overloading of distribution system lines must be decreased and managed. Installing local distributed energy resources and installing flexible AC transmission systems encourage consumers to modify their consumption patterns through market-oriented approaches such as demand response (DR) programs, which are among the cases that distribution system operators can use to change the amount of active or reactive power at nodes [2]. The widespread use of diesel generators, traditional power plants, and PHEVs all contribute to increased air pollution. Recently, certain metropolitan regions have had trouble maintaining acceptable air quality levels, and high levels of key pollutants have sometimes surpassed allowable limits [3].

The scheduling of microgrids has attracted high attention, and various studies have been published in this context. So, this paper is going to investigate several related and updated articles in this subsection. A day-ahead microgrid operation including various renewable energy sources like wind turbines, solar panels, and PHEVs is discussed in [4]. Moreover, the uncertainties proposed in this paper are exactly formulated in the microgrid optimal management model utilizing the Monte Carlo simulation tool. A new stochastic nonlinear, nonconvex optimal operation of a microgrid equipped with compressed air energy storage and EVs is proposed in [5]. The information gap decision theory is utilized to overcome the probabilistic nature of the problem. Also, semidefinite programming is used to solve the problem. The author in [6] introduced optimal scheduling of smart microgrids equipped with distributed energy resources, DR programs, plug-in EVs, and diesel generators with the goal of total operating cost minimization while taking into account the benefits of emissions. Moreover, to investigate the risk related to the behaviors of EV owners, distributed energy resources, demand, and market electricity prices, the suggested model was developed as a two-stage stochastic programming problem.

1.2. Literature Review

The optimal operation of microgrids containing energy storage devices, plug-in hybrid EVs, and distributed energy resources is investigated [7]. The hybrid gravitational search and pattern search algorithm are applied to tackle the proposed problem. A multiobjective model has been formulated considering economic and environmental goals in the microgrid including EVs [8]. The linear weighting approach based on game theory was applied to coordinate the distributed energy unit consumption with the whole bearing of load and balance the two objectives better. In addition, an adaptive simulated annealing particle swarm optimization (PSO) algorithm was utilized to solve the proposed problem and obtain the optimum global solutions. The author proposes a new optimization problem that combines distributed energy resources and plug-in EVs by utilizing the probabilistic approaches to enhance the load supply and reduce microgrid dependence on the main grid [9]. Adaptive modified (AM)–PSO is applied for MG operation in the presence of MT/FC/battery hybrid power source with aim of reducing cost and emission [10]. A bilevel EV aggregator bidding strategy framework is discussed, in which the upper-level goal is the reduction of EV charging costs and the lower-level issue is the maximization of social welfare [11]. Network limitations are not taken into account, and it is also supposed that all resources like generation, EV aggregators, and loads are placed at a single bus.

A market-oriented distribution system reconfiguration process is presented for the optimal configuration of the system and locational marginal pricing. Hybrid firework and a game-based algorithm are considered to minimize the cost-based objective function [12]. Applying the genetic algorithm (GA), a new procedure in finding the optimal reconfiguration in the distribution system using DLMP is offered [13].

An efficient operation of virtual energy storage systems (VESSs) within a multicarrier energy system is proposed in [14]. It addresses the pressing challenge of managing the power demand by proposing a congestion management system. The problem is cast as a bilevel model, where the upper level is overseen by the independent system operator to mitigate congestion issues, and the lower level is under the control of VESS to maximize its benefits. To simplify the problem and find the global optimum, a linearization technique has been employed to transform the bilevel problem into a single-level optimization problem. A smart grid system characterized by a significant presence of EVs engaged in bidirectional power exchange offers the potential to utilize EVs for addressing network congestion [15]. This research introduces a game-theoretical strategy to formulate an intelligent pricing framework and create a mechanism for alleviating congestion within the grid. The game attains a distinctive Nash equilibrium, effectively addressing power congestion issues while maximizing benefit for EVs.

An investigation was conducted to examine the effects of wind farms, EV charging stations, and DR on network line congestion in different scenarios using both analytical methods and structural decomposition [16]. Furthermore, several indices were introduced to assess the impact of each factor on congestion during periods of low and peak demand. In [17], a two-stage framework is introduced, which combines a reconfiguration strategy addressing technical and security constraints with a game-theoretic approach for day-ahead scheduling in microgrids to prevent market power issues. The first stage focuses on solving the distribution feeder reconfiguration problem to minimize losses and reduce distribution line overloading, while the second stage deals with the day-ahead scheduling problem for the disco and microgrids. This problem is approached using a multiobjective optimization technique rooted in game theory, considering the network’s topology.

1.3. Novelties and Contributions

The subject of congestion management has seen some excellent progress; however, there are numerous issues and shortcomings that need adequate attention. The following are, in brief, the drawbacks of prior references:

a.
They have mostly concentrated on reducing congestion through implementing an action such as FACTS units or rescheduling of generators, and the effect of overloading on the DLMPs, and, as a result, the social welfare of the system are not thoroughly examined.
b.
The congestion management of DERs has not been published on the multiobjective optimization of PHEVs charging and DR programs.
c.
In addition, a suitable tool should be used to include the uncertainty associated with the production of wind and solar electricity into the issue.

In order to investigate the shortcomings of prior articles, the suggested work tries to present the following novelties. The major novel contributions of the paper are given as follows:

1.
To solve the first shortcomings (a), an effective multiobjective optimization is developed in which minimize both operation costs and wind curtailment as well as maximize the amount of social welfare.
2.
To solve the second shortcomings (b), the effect of both EVs charging and discharging scheduling and DRPs implementation is simultaneously investigated to facilitate the optimal congestion management.
3.
To solve the third shortcomings (c), a coherent uncertainty management instrument based on Monte Carlo simulation has been employed.

Apart from the main novelties mentioned above, some incremental contributions have been proposed in this paper as given below:

1.
Optimal multiobjective scheduling of grid-connected microgrids by integrating hybrid EVs and DRP.
2.
Applying the distributed energy resources, various patterns of plug-in EVs arbitrage, and DR program to reduce the amount of congestion and smooth the DLMPs.
3.
Present a multiobjective framework to the suggested problem to minimize the operating cost of network and energy not supply.
4.
Using the Monte Carlo method to reduce the uncertainty of distributed energy resources and consumption load.

1.4. Paper Organization

This paper is organized as follows: The problem formulation is presented in Section 2. An overview of the evolutionary multiobjective seagull optimization algorithm (SOA) is provided in Section 3. Section 4 depicted simulations and numerical results. Finally, the conclusion is illustrated in Section 5.

2. Problem Formulation

A multiobjective problem is a type of optimization problem where multiple objectives need to be simultaneously optimized. In the defined problem, the two objectives are to minimize the total operating cost of the microgrid and to minimize the energy not supplied index, which is an indicator of the reliability of the system. The problem is further complicated by the fact that it is modeled as a mixed-integer, nonconvex, and nonlinear programming problems, which means that the decision variables involved are a combination of continuous and discrete variables, and the objective function is nonlinear and nonconvex. Solving such a problem requires specialized optimization techniques that can handle these complexities.

One such technique is the evolutionary multiobjective SOA, which is a metaheuristic algorithm inspired by the behavior of seagulls in nature. This algorithm is designed to search for the optimal solution by iteratively generating a population of candidate solutions and using various selection and mutation operators to evolve the population towards the Pareto-optimal front, which represents the set of solutions that cannot be improved in one objective without worsening another. By using this algorithm, it is possible to find a set of Pareto-optimal solutions that strike a balance between the two competing objectives, taking into account the system’s reliability and operating costs.

2.1. First Objective Function (Total Operating Cost of Microgrid)

The proposed objective function identifies the minimum operating cost of microgrids. Equation (1) including some terms which the C^Upstream shows the trading power with the upstream grid, C^DER presents the amount of power generation by the DERs, the amount of power arbitrage in plug-in EVs has been shown by the third term of objective function C^ch/Dch, and the implementation cost of DRPs in the system is depicted as the C^DR. Moreover, the congestion of the distribution lines and the amount of active power losses are shown as the C^Cong and C^Loss in equation (1), respectively.

()

2.1.1. The Cost of Power With Upstream Grid

The amount of selling and buying power with the upstream like kinds of power plant for the operating time horizon is presented in equation (2). In this equation, the amount of transaction power

is multiplied to a coefficient

in order to change the power unit cost.

()

2.1.2. The Cost of DERs

To effectively manage DERs, it is important to develop cost function models that capture the operational and maintenance costs associated with each technology. The cost of WTs is modeled as a function of the rated power and the capacity factor. Similarly, the cost of PV panels is modeled as the efficiency of the panels and the expected lifetime of the system. CHP units, on the other hand, are modeled as a function of the fuel cost, the electricity and heat output, and the maintenance and repair costs. Once these cost function models are developed, they can be used to optimize the scheduling and dispatch of DERs, taking into account factors such as weather conditions, energy demand, and grid stability. This can help to minimize the overall cost of energy generation while ensuring that the power grid remains reliable. Overall, the development of accurate and reliable cost function models for DERs is crucial for effective optimization of renewable energy systems, ensuring that they are cost-effective and contribute to a sustainable energy future. The total cost of DERs is considered in equation (3), in which the total generation power of each DERS, including wind turbines, PV arrays, and CHP, is multiplied by its own coefficient to change its generation cost.

()

2.1.3. The Cost of Charge/Discharge of the Plug-In EVs

PEVs are a type of hybrid car that can be charged from an external power source, such as a charging station. The cost of charging and discharging a PEV is an important consideration for both vehicle owners and utilities, as it can have a significant impact on the overall cost and efficiency of the vehicle and the power grid. The cost of charging a PEV depends on several factors, including the cost of electricity, the charging time, and the battery capacity. Charging a PEV during off-peak hours when the demand for electricity is low can be more cost-effective than charging during peak hours when the demand is high. On the other hand, the cost of discharging a PEV and supplying power back to the grid is determined by the value of electricity at the time of discharge. This is typically performed through vehicle-to-grid (V–G) technology, which allows PEVs to discharge their batteries to the grid during peak demand periods when electricity is more expensive. PHEV owners can earn revenue by participating in V–G programs and selling the electricity stored in their vehicle’s battery back to the grid. The charge/discharge cost is given in equation (4).

()

2.1.4. The Implementation Cost of DR Program

One of the proper load profile management options that the system operator can provide is a DR program. In the paper, the incentive-based DR program is applied to consumers. The load profile is calculated using equation (6) after executing the DR program. The amount of shifted consumption power under the DR program is calculated by equations (7) and (8). In this article, load shedding should not occur in the system. Hence, all outages in the load profile at peak times must be compensated during the proposed time horizon (24 h), as shown in equation (9) [18, 19].

()

2.1.5. The Cost of Congestion

Overloading or congestion phenomena in distribution network lines can result in increased power losses, reduced system efficiency, and increased maintenance costs. To effectively manage these issues, it is important to develop accurate cost function models that can capture the operational and maintenance costs associated with these phenomena. The cost function model for overloading or congestion in distribution network lines typically includes several key parameters, such as the line capacity, the power flow, the voltage levels, and the cost of system losses. This cost can be modeled as a function of these parameters.

Additionally, the cost function model can be used to optimize the scheduling and DERs dispatch and DRPs to alleviate congestion. By incorporating the cost function model into the optimization algorithm, it is possible to identify the most cost-effective solutions for congestion management in distribution network lines, such as load shedding. Overall, the development of accurate and reliable cost function models for congestion in distribution network lines is essential for effective management and optimization of power systems. These models can help to identify the most cost-effective solutions for mitigating congestion, supporting the integration of DERs, and ensuring the reliability and efficiency of the power grid.

Equation (10) shows the amount of congestion created in the microgrid. The purpose of this function is to manage the congestion of distribution lines and, as a result, to smooth out the nodal price of buses in order to increase customer satisfaction.

()

2.1.6. The Cost of Power Losses

The power losses of different microgrids can be calculated as the product of the losses with the square of the current of each line (between two nodes in the network) according to equation (11)

()

2.2. Second Objective Function (ENS)

The amount of customer energy not supplied plays a very important role in the issue of short-term rescheduling of microgrids. In this paper, plug-in EV batteries are used as a storage device in the microgrids. The parameters that show the consequences of blackouts in microgrids are considered as follows:

()

The reliability load point factors like failure rate, repair rate, and the amount of outages are calculated as equations (14)–(16)

()

The determination of load point indices involves individual calculations for each load point, while reliability system indices are derived from these load point indexes (17) and (18). This segment outlines fundamental equations for diverse reliability indices. Although the actual reliability evaluation involves more intricate calculation methods, the subsequent definitions rely on specific parameters

()

The above-mentioned equations are utilized to calculate the main reliability indices including system average interruption frequency index (SAIFI) (19), system average interruption duration index (SAIDI) (20), and customer average interruption duration index (CAIDI) (21)

()

2.3. Constraints

2.3.1. Equality Constraints

Equation (22) shows that the left and right sides of this equation must always be equal. The left side of the equation gives the amount of power consumption, PEV charging, and power loss of the system. In return, the right-hand side of the equation presents the amount of power production by upstream, PEV discharging, and DER generation

()

The DERs include several distributed generations in the distribution network as equation (23).

()

2.3.2. Inequality Constrains

The inequality constraint (24) shows the apparent power limitation. The voltage magnitude limitation is defined as a constraint (25). Due to this limitation, the amount of voltage magnitude must not exceed the permissible limit (between 0.92 and 1.02 pu). Constraints (26)–(28) present the DER’s generation limits.

()

2.4. DER Modeling

2.4.1. Wind Turbine

The speed and wind power are the main factors that affect WT generation. In order to forecast the speed of wind, the Weibull probability density function (PDF) has been utilized [20].

()

The Weibull PDF is defined by equation (29). By considering the wind power speed, the produced power by WT at tth time is presented by equation (30).

()

2.4.2. Solar Cell

The PV systems are the immediate transformation of sunlight to electric power without generating any CO₂ emissions. Both the angle and sunlight intensity are the main factor in the amount of solar cells generation [21].

()

The beta PDF is defined by equation (31). The generated power of PV modules can be kept in a standalone system, can be stored in BES units, or can feed a greater electricity power grid. Moreover, the PV power production is determined based on the environment temperature and sunlight intensity that could be computed as follows:

()

The amount of power generated by PV units through the mth PV at tth time is shown in equation (32). Also, the cell temperature can be presented in equation (33).

()

The standard operational PV temperature is described as the cell temperature when the photovoltaic units drop under 0.8 kW/m² sunshine and 20 degree C of ambient temperature.

2.4.3. Combined Heat and Power Units

The CHP units are defined as a mix of power and heat that produce both of them simultaneously. The mathematical formulation of CHP units is expressed in equation (34) [22].

()

2.4.4. Consumption Load

The probability nature of the consumption load is formulated by the standard PDF that is given in equation (35).

()

2.5. Radiality Constraint

Due to its reduced cost and simple system operation, the radial configuration of the system is typical. It should be noted, nonetheless, that distribution networks typically consist of different trees, in which scenario the system will be equipped with many substations. Determining the distribution system’s radial configuration is consequently difficult. This study introduces a novel technique for assessing network radiality using the Laplacian matrix of the bus incidence matrix (A). The recommended method uses a part of graph theory called the minimal spanning tree (MST), which is the optimal feeder routing problem. The MST algorithm can be used to solve the optimal feeder routing problem, which is a subgraph of the graph and includes the system in which each node has the least weight of the whole branch. We consider the system to be a graph represented by G(V(G)V(G), E(G)), wherein V(G) denotes a collection of vertices and E(G) denotes a collection of edges. The connection matrix is a form A(G) matrix of dimension n_n × n_n, where n_n is the entire number of buses. Furthermore, d_i(G) represents the degree of vertex i (i = 1, 2, 3, …, n_n) and D(G) is the diagonal matrix with the ith diagonal ingress of d_i(G). Thereby, L(G) is the Laplacian matrix of A(G) that is denoted in (34). Equations (36) and (39) must be satisfied concurrently, in this case, to use the radiality conditions of the distribution network as a tight restriction [23]. Here, n_s and n_b are the entire number of substations and branches, respectively.

()

2.6. PHEVs Modeling

Different kinds of rechargeable batteries are installed on the PHEVs that can be recharged by connecting to the distribution network. Moreover, utilizing fossil fuel sources over long distances instead of battery energy is one of the abilities of these machines. To suitably model PHEVs behavior, some essential parameters that specify the charging behavior must be taken into account. Kind of charger, state of charge (SoC), PHEV number, capacity of the battery, time of charging, and charging length are the important parameters [24]. Generally, there are some uncertainties regarding the PHEV charging demand in both private and general parking lots. To manage the uncertainties driven by PHEVs, three different charging patterns are discussed in this section as follows: (i) uncoordinated charging pattern; (ii) coordinated charging pattern; and (iii) smart charging pattern; in the second approach, PHEVs are charged at any moment when linked to the charging point [25].

Due to the gathered information about the PHEV’s movement in the grid, PHEVs face two main travel routes in a day. One of these trips takes place when leaving home in the morning, and the other takes place when returning home in the evening. Also, short-term trips are considered during the day. PHEVs are linked to the electrical network at 6:00 p.m. when they get home. Therefore, the time of charging can be formulated utilizing a probability distribution function with a narrow interval near 6:00 p.m. [26].

()

In the second pattern, the PHEV owner prefers to charge their vehicle’s battery during off-peak periods because the price of electricity is very high during peak periods. The high cost of electricity during peak hours forces PHEVs to charge after 9:00 p.m. Thus, the charging scheme of the second pattern is modeled as equation (41)

()

Ultimately, in the smart charging scheme, the charging of PHEVs is performed at a time when the power generation amount is higher than the power consumption and the electricity price is at the minimum level. Between all the smart charging schemes, the presented idea is one of the most typical. A normal probability distribution function is suggested to specify the charging start time [27].

()

Among the plug-in time, the value of SoC can be calculated as (43).

()

2.7. Distribution Locational Marginal Pricing Concept and Calculation

Distribution locational marginal pricing is one of the famous market pricing approaches employed to control the distribution network in an efficient manner while overloading happens on the large-scale grid. The congestion in the electricity network is raised when one or more limitations on the distribution network prevent the lowest cost of energy for the customer [28]. An exact and market-based method of energy pricing, containing congestion costs, is provided in this paper to deal with the expensive electricity supply at the high electricity price nodes. Marginal congestion prices, marginal loss costs, and marginal energy prices are the three items of the DLMP. The DLMP supplies a precise and real electricity price signal for market players at any node of the distribution network. The DLMP is the set of Lagrangian multipliers that are associated with the active power equation of every node [29]. The DLMP at each bus in the network is the dual variable for the equality limitation at that bus. Due to the above explanations, DLMP is described as (44)–(47).

()

3. Providing an Overview of Evolutionary Multiobjective SOA (EMoSOA)

The optimization method may solve any metaheuristic optimization issue by finding the best global answers when exploration and usage characteristics are balanced properly. In order to maintain optimum convergence, the exploration process depicts variation in the search for novel answers on a global scale [30]. The primary idea behind the suggested algorithm is inspired by the seagulls’ typical activities. An adaptation of the seagull optimization technique for multiobjective optimization has been created using the four components [31]. The grid and archive controller are the two most important integrals since they hold the best nondominated Pareto answers. The later integrals use the pioneer selection method and evolutionary operators to choose the best option from the archive based on the prey’s direction.

3.1. Archive Controller

All of the Pareto optimum answers that are best found are preserved in an area named the archive. Inclusion of a certain answer in the list is decided by the controller. Given below are the guidelines for archive updates:

•
If it is discovered that the archive is empty, the present answer should be adopted.
•
Any answer that is mostly owned by someone in the archive should be rejected.
•
The solution should be approved and kept in the archive if it is not dominated by the external population.
•
The archive is emptied of answers if the new element dominates them.

3.2. Grid

The adaptive grid approach produces Pareto fronts [32]. There are four areas in the main function that are being used. When populations are outside of the grid region, they are established and measured using the grid technique [33]. The grid space is produced as a result of the hypercube being eventually distributed.

3.3. Leader Selection Mechanism

Finding new answers in a given search area is the main challenge in a multiobjective search area. This problem is solved by a leadership selection process that uses the least congested search space. One of the top solutions in the search boundary is the roulette-wheel selection approach. The following is defined as equation (48):

()

where N_k is the number of Pareto-optimal answers to the kth segment, and g is a constant variable with an amount larger than 1. This technique is a traditional method that quantifies each individual’s contribution using a roulette-wheel percentage. This technique has the benefit over others in that it consistently provides a chance for each of them to be chosen. It has a manageable temporal complexity when applied concurrently. As opposed to that, the crossover and mutation techniques utilized in this study are the same as those outlined in the NSGA-II algorithm [34].

The proposed algorithm introduces several innovative features that significantly enhance its performance in addressing multiobjective optimization problems, particularly in the context of scheduling renewable-based microgrids with EVs and DR programs. The key innovations are as follows:

•
The algorithm extends the traditional SOA, which is primarily a single-objective optimization technique, to handle multiple conflicting objectives. This adaptation allows for simultaneous optimization of various goals, such as minimizing costs and emissions, while maintaining system reliability.
•
The algorithm incorporates adaptive mechanisms to dynamically adjust the search parameters. This adaptability enhances the algorithm’s ability to explore and exploit the search space effectively, leading to improved convergence rates and better-quality solutions.
•
An innovative archive controller is implemented to maintain a diverse set of nondominated solutions. This feature ensures that the algorithm can provide a comprehensive Pareto front, representing the trade-offs between different objectives. The archive controller also adopts solutions when the archive is empty, facilitating a robust search process from the beginning.
•
The algorithm is specifically designed to handle the uncertainties associated with renewable energy sources. By incorporating stochastic models for renewable generation, the algorithm can generate reliable and realistic scheduling plans that account for the variability and intermittency of renewable energy.
•
The algorithm effectively integrates EVs and DR programs into the scheduling process. This integration not only enhances the flexibility of the microgrid but also optimizes the use of available resources, leading to improved operational efficiency and reduced overall costs.
•
The proposed algorithm combines elements of seagull optimization with other optimization techniques, such as PSO and simulated annealing. This hybrid approach leverages the strengths of each technique, resulting in superior optimization performance compared to using any single method alone.

Figure 1 shows the flowchart of the suggested method. As can be seen from this flowchart, at first, the data of the DERs and network structure are entered. Then, by using these data, a backward–forward power flow has been performed. In the second step, a multiobjective optimization method has been used for the objective functions to minimize the total operation cost of the distribution system and maximize the amount of social welfare. In the end, optimal results have been obtained.

Details are in the caption following the image — **Figure 1**
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Flowchart of the proposed model.

3.4. Step-by-step Explanation of the Proposed Method

Here is a detailed step-by-step explanation of the proposed method within the context of the optimization problem. This subsection outlines the workflow of the algorithm from initialization to the final solution

Step 1: Enter data for distributed energy resources and network structure.
Step 2: Initialize the population of solutions and set algorithm parameters.
Step 3: Perform backward–forward power flow using the input data to determine the initial network state.
Step 4: Define objectives such as minimizing total operation cost and maximizing social welfare.
Step 5: Assess initial solutions against multiobjective criteria and calculate fitness values.
Step 6: Update and refine solution positions through migration and attack behaviors.
Step 7: Dynamically adjust control parameters to enhance convergence.
Step 8: Maintain and update an archive of nondominated solutions.
Step 9: Integrate stochastic models to account for renewable energy variability.
Step 10: Optimize the scheduling of EVs and DR strategies to enhance grid flexibility and reduce costs.
Step 11: Terminate the algorithm upon meeting convergence criteria and extract final nondominated solutions.
Step 12: Analyze the Pareto front to understand trade-offs and select the most suitable solutions based on practical constraints.

4. Simulation and Numerical Results

4.1. Case Study

Two case studies, an IEEE 33-bus distribution system (Case I) and an IEEE 69-bus distribution system (Case II), are shown in Figures 2 and 3 [35] to see how well the suggested method works. As can be seen, the proposed network includes different areas with different consumptions, like industrial, commercial, and residential. Each region has several distributed energy resources and plug-in EVs that can optimally trade electric power with the grid and upstream grid. Two types of plug-in EVs containing battery EVs and plug-in hybrid EVs are taken into account for active distribution network optimization [36]. Also, the minimum and maximum amounts of solar irradiance, wind velocities, battery DoDs, and battery SoC have been added to the revised paper as shown in Table 1. The presented issue is resolved using EMoSOA in the MATLAB software in this research. The simulations are run on a laptop running Windows 10 that is equipped with an Intel (R) Core (TM), a CPU i7-4300 M, and 16 GB of RAM.

Table 1. Variables range of solar irradiance, wind velocity, battery DoD, and battery SoC.

Item	Lower bound	Upper bound
Solar irradiance (kW/m²)	500	1000
Wind velocity (m/sec) (moderate and fresh breeze)	5.5	10.5
Battery DoD (%)	40	80
Battery SoC (kW)	0	500

4.2. Discussions

The real-time market prices for a day are shown in Figure 4 [37]. These prices are required for power transaction cost calculations with the upstream grid. DSO uses market prices to determine the cost of electric power purchased or sold with the upstream grid in the proposed scheduling horizon.

The total load consumption of the network for every hour is presented in Figure 5 [38]. As indicated, this work considered consumption without using DRP and various participation factors. As it can be seen from the figure, when the amount of participation factor increases, the impact of DRP on that load profile also increases. DRP tries to transfer consumption from the peak periods to off-peak periods. This is helpful to DSO to better schedule their available sources.

The amount of active power flow transactions for two case studies is illustrated in Figures 6 and 7. These are very important figures because if congestion or overloading phenomena happen in one or some of the distribution lines, outages are the result, and DSO cannot supply the local loads. This is the cause for customer dissatisfaction, and the amount of the social welfare index is significantly reduced. For this purpose, investigation of all lines’ active power flow is a critical issue for DSO. In both figures, the red line shows the distribution line capacity [39] and compares with the blue and black lines, which show the active power flow in presence of various resources. As can be seen from the figure, the amount of power flow is remarkably reduced in the presence of PHEVs, DERs, and DRP, which shows the efficiency of the proposed model.

Figure 8 shows the effect of PHEVs, DRP, and the reconfiguration process on the suggested buses of the network, simultaneously. As can be observed, the initial configuration of the system is shown as a blue line and the best configuration of the system is indicated by the gray line, which is achieved from the proposed optimization technique. Figure 9 presents the effect of PHEVs, DRP, and the reconfiguration process on the suggested buses of the network, simultaneously. As can be observed, the initial configuration of the system is shown as a blue line and the best configuration of the system is indicated by the red line, which is achieved from the proposed optimization technique. By comparing all these lines, it is noticed that applying the proposed method has had a significant impact on DLMP smoothing.

Optimal charging and discharging pattern of EVs are determined by the suggested algorithm and presented for the two case studies in Figures 10 and 11. The obtained scheduling is the result of the pattern search method, which suggests three schemes for the EVs owner to participate. As can be seen from this figure, various kinds of EVs are charging and discharging due to the pattern. For example, in Case II, at 3:00 a.m., all of the EVs are in charging mode (all of them located in the parking lots) and use electricity of the network. Because in this time of the day, the price of electricity is cheaper and its off-peak time of the day. Contrariwise, at 7:00 p.m., all of the EVs are in discharging mode and give back their power stored to the distribution network because in this time of the day the price of electricity is high and it is the peak time of the day. Also, the dashed line in this figure shows the SoC amount of each EV. The SoC level of each EV depends on the charging and discharging in that time. At both 7:00 a.m. and 4:00 p.m., the EV owners use their device and they are not connected to the distribution network, so the DSO cannot schedule and make pattern for these times of the day.

The DERs power generation amount is illustrated in Figures 12 and 13 for two case studies. As can be seen from these figures, the sum of the hourly production of DERs is related to the wind and solar uncertainties in the distribution network.

The active power loss amount in the various conditions for two case studies is depicted in Figures 14 and 15. The blue line column shows the initial power losses of the distribution network, which is achieved from the backward–forward power flow method. The dashed brown and black columns show the amount of power losses with EV and DERs and with EV, DERs, and DRP, respectively. As compared to these columns, the amount of power losses in the black column is remarkably reduced due to the other cases. It results that the suggested approach has had a good impact on the power loss.

Figures 16 and 17 illustrate the value of voltage magnitudes for each node of the two case studies. Due to these graphs, the blue dashed line shows the initial voltage magnitudes that are obtained from the backward–forward power flow technique. The permissible dynamic stability limitation of the voltage in the distribution network is defined from 0.9 to 1.1 per unit. The red and black dashed lines of these graphs show the amount of voltage magnitude with EV and DERs and with EV, DERs, and DRP, respectively. As can be seen, the suggested method has had a good impact on the voltage profile improvement.

Figures 18 and 19 show the energy not supplied for each section. The ENS of each section is calculated by using the objective function (20), and the suggested algorithm is used to minimizing the total amount of ENS in order to enhance the reliability service goals.

Figures 20 and 21 show the SAIFI, SAIDI, and CAIDI indices as essential reliability metrics for the 33-bus and 69-bus distribution networks, respectively. The results depicted in these visual representations underscore the noteworthy impact of integrating plug-in hybrid EVs and implementing DR programs in conjunction with the reconfiguration technique. Evidently, this combined approach stands out as a potent strategy, leading to a discernible enhancement in the reliability indices of the distribution systems. The demonstrated outcomes underscore the efficacy of synergizing emerging technologies and innovative strategies to bolster the robustness of these vital networks.

Tables 2 and 3 display the values of the first and second objective functions. These tables present the objective function values both before and after the implementation of the proposed method.

Table 2. The value of first objective function.

Case study	Operating cost with distributed generation sources after load flow ($)	Operating cost with electric vehicles, demand response program, and network reconfiguration ($)	Percentage improvement in operating cost (%)
33-Bus system	4517.00	3618.25	19.89
69-Bus system	35,368.10	28,677.16	18.91
85-Bus system	77,748.60	45,700.00	41.22

Table 3. The value of second objective function.

Case study	ENS amount before the proposed method implementation	ENS amount after the proposed method implementation
33-Bus system	4513	4080.12
69-Bus system	9628	8873
85-Bus system	80,447	63,103

Figure 22 plots the operation cost of the microgrid with the amount of ENS. It demonstrates the trade-offs between these two objectives. In the figure, the blue points represent the optimal solutions, showcasing the best balance between minimizing both the operational costs and the ENSs.

The performance of the EMoSOA in comparison with other algorithms, such as PSO, GA, and gray wolf optimization (GWO) algorithm, is presented in Figure 23. According to this figure, the speed and convergence rate of the EMoSOA are higher compared to other optimization methods.

5. Conclusion

This paper introduces a novel multiobjective optimization model where the first objective is to minimize the total operation cost of the microgrid and the second objective is to maximize the reliability index by reducing the amount of system energy not supplied. The first objective includes the cost of power trade-off with the upstream grid, charging and discharging costs of EVs, and renewable energy generation costs. In this work, collaborative DR programs and a new pattern of EVs are used to manage the amount of branch overloading or congestion phenomena and to smooth the amount of DLMP with the aim of maximizing the social welfare index. In order to solve the proposed hard MINLP problem to reach the global optimum solutions, an EMoSOA algorithm is used. The results of this study demonstrate the effectiveness of the proposed strategy in mitigating the line overloading or congestion in the distribution network. Specifically, the analysis shows that the proposed approach has reduced the occurrence of line overloading or congestion to 54% and 70.5% of the initial capacity for Case I and Case II, respectively. Moreover, the incorporation of PHEVs, DERs, and DRPs has contributed to a significant decrease in power losses in the distribution network, achieving a reduction of 5.62% and 3.95% for Case I and Case II, respectively. Additionally, the proposed method has successfully improved the voltage profile by 2.1% and 1.5% for Case I and Case II, respectively, compared to the previous state. These findings highlight the potential of the proposed strategy to enhance the performance and efficiency of distribution networks, providing a useful framework for future research and development in this area. Here are some potential future works:

i.
Exploring the potential benefits of integrating energy storages into MGs to enhance their flexibility and resilience.
ii.
Conducting field experiments and pilot studies to evaluate the real-world performance and scalability of the proposed management strategies in different settings.
iii.
Evaluating the environmental and economic benefits of the proposed scheduling and management strategies and comparing them to other approaches for achieving sustainable and efficient energy systems.

Nomenclature

BES: Battery energy storage
CHP: Combined heat and power
CM: Congestion management
DER: Distributed energy resources
DLMP: Distribution locational marginal pricing
DoD: Depth of discharge
DRP: Demand response program
DSO: Distribution system operator
EMoSOA: Multiobjective seagull optimization algorithm
ENS: Energy not supplied
FACTs: Flexible AC transmission systems
GWO: Gray wolf optimization
GA: Genetic algorithm
MG: Microgrid
MST: Minimal spanning tree
PDF: Probability density function
PHEV: Plug-in hybrid electric vehicle
PSO: Particle swarm optimization
SoC: State of charge
WT: Wind turbine
t: Index of time
l: Index of line
b: Index of SEVs
k: Index of DERs
N_DER: Set of DERs
N_SEV: Set of SEVs
N_l: Set of distribution system line
F₁: First objective function (total operating cost of microgrid)
F₂: Second objective function (costumers’ energy not supply)
C^Upstream: The cost function of power exchange with upstream grid
C^DER: The cost function of power generated by DERs
C^ch/Dch: The cost function of charging and discharging power by EVs
C^DR: The cost function of demand response implementation
C^Cong: The cost function of congestion phenomena
C^Loss: The cost function of microgrids power loss
: The hourly amount of power exchange with upstream grid
: The cost factor of the upstream grid at time t
: The amount of power generation by DERs at time t
: The cost factor of DERs at time t
P_bt: The amount of power charged/discharged of EVs at time t
C_bt: The cost factor of charged/discharged of EVs at time t
U_bt: The operation factor at time t
DR_t: The amount of power consumption in demand response program
P_t,l: Active power flow of lth line
: Capacity of active power flow at lth line
μ_t: Cost coefficient that converts the amount of power to cost
R_l: lth line resistance
I_lt: The amount of current of line l at time t
ENS_i: Energy not supplied at bus i
P_i(…): The portion of each kind of loads including industrial commercial, residential, general, and agriculture
k_i: The importance of ith load in the distribution network
λ: Failure rate
U: Average outage time
r: Repair rate
: The amount of power consumption at time t
: The amount of charged power by PEVs at time t
: The amount of discharged power by PEVs at time t
: The amount of power losses at time t
: The amount of generated power by PV arrayes
: The amount of generated power by WTs
: The amount of generated power by CHP units
V_i: Voltage magnitude at ith bus
: Minimum and maximum bound of voltage profile
v: Wind speed of the farm under study
v_c in: Cut-in speed
v_c out: Cutout speed
v_rat: Rate speed of the WT
c₁, c₂: Acceleration coefficients
T_C, T_ref: Cell and air temperature of PV units
T_a: Ambient temperature
G_ING, G_STG: Solar irradiance in standard and study condition
G: Global solar radiation
NOCT: Normal operating cell temperature of PV
: Rated power of the WT installed in bus i
P_STG: Rated output power by the module under standard test condition
x, γ: Beta function parameter
Fr_k: Frequency of event k
Pr_k: Probability of event k
ACIF: Average cutoff frequency of the consumer
ACIT: Average customer outage time

Disclosure

A preprint has previously been published [40].

Conflicts of Interest

The authors declare no conflicts of interest.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Open Research

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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All articles

Multiobjective Day-Ahead Scheduling of Reconfigurable-Based Microgrids Through Electric Vehicles and Demand Response Integration

Abstract

1. Introduction

1.1. Background and Context

1.2. Literature Review

1.3. Novelties and Contributions

1.4. Paper Organization

2. Problem Formulation

2.1. First Objective Function (Total Operating Cost of Microgrid)

2.1.1. The Cost of Power With Upstream Grid

2.1.2. The Cost of DERs

2.1.3. The Cost of Charge/Discharge of the Plug-In EVs

2.1.4. The Implementation Cost of DR Program

2.1.5. The Cost of Congestion

2.1.6. The Cost of Power Losses

2.2. Second Objective Function (ENS)

2.3. Constraints

2.3.1. Equality Constraints

2.3.2. Inequality Constrains

2.4. DER Modeling

2.4.1. Wind Turbine

2.4.2. Solar Cell

2.4.3. Combined Heat and Power Units

2.4.4. Consumption Load

2.5. Radiality Constraint

2.6. PHEVs Modeling

2.7. Distribution Locational Marginal Pricing Concept and Calculation

3. Providing an Overview of Evolutionary Multiobjective SOA (EMoSOA)

3.1. Archive Controller

3.2. Grid

3.3. Leader Selection Mechanism

3.4. Step-by-step Explanation of the Proposed Method

4. Simulation and Numerical Results

4.1. Case Study

4.2. Discussions

5. Conclusion

Nomenclature

Disclosure

Conflicts of Interest

Funding

Open Research

Data Availability Statement

References

Figures

References

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