Enhanced Multiobjective Optimization Algorithm for Intelligent Grid Management of Renewable Energy Sources

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Introduction
In the contemporary era, the exhaustion of conventional energy sources, such as coal, is escalating, engendering a mounting energy crisis [1].Concurrently, there is a rapid economic development, technological advancement in power plants, and a steady surge in electricity consumption among Chinese residents [2].Te power grid's role extends beyond merely supplying electricity to households; it encompasses ensuring the quality, safety, and reliability of power transmission.Nonetheless, the grid is aficted by numerous defciencies requiring rectifcation.In remote and thinly populated regions, long-distance power generation is impractical, infating transportation costs and squandering resources.Although constructing new power plants in these areas could remedy the issue, the prolonged construction duration and exorbitant costs render this solution unfeasible.
Coal predominates as the principal power generation source, yet coal reserves are progressively diminishing year by year [3].Hence, integrating new green energy sources and seamlessly connecting their power generation networks to the larger grid could efectively address the high-power consumption dilemma in remote residential areas [4].An of-grid hybrid solar PV/fuel cell power system is designed and optimized for a desert residential community, employing an integrated modeling, simulation, and optimization approach.Te study investigates the impact of temperature and dust on solar PV panels, with the goal of increasing renewable energy penetration, reducing greenhouse gas emissions, and minimizing energy costs [5].To mitigate the energy defciency, researchers have shifted their focus towards cleaner, greener energy alternatives.Investigating these energy sources renders our energy generation technology more cost-efective and reliable, culminating in the inception of distributed generation (DG) in this societal context [6].
In recent years, the DG concept has gained widespread recognition, ofering unique benefts, such as fexible installation, high reliability, and superior energy efciency.Te system is strategically situated near the distribution grid or load (typically below 30 MW) to bolster the larger grid's economic operation.However, several unresolved challenges plague the DG system, the most pivotal being its uncontrollability relative to the grid [7].Te excessive consumption induced by a single microsource connected to the grid hinders the full-fedged development of DG.Additionally, the DG system may induce voltage and frequency fuctuations in the grid during connection, deteriorating power quality and compromising the grid's security and reliability [8].To address these issues comprehensively, the MG concept was proposed, enabling DG to maximize its advantages and potential in integrating large-scale DG power sources into the grid.MGs amalgamate DG power supplies, energy storage apparatuses, energy conversion devices, loads, protection mechanisms, and detection instruments into a compact power generation and distribution system.Tis architecture facilitates autonomous control, self-protection, and self-management.Te MG can function autonomously as a module interconnected with the larger grid, denoted as grid-connected operation, or independently as a self-contained entity, referred to as islanded operation [9].Within the MG, each internal device is meticulously confgured to furnish power to the MG's minor loads and judiciously modulate the internal voltage frequency and power to ascertain the unimpeded functioning of the MG's internal components.Conversely, the MG's external segment is governed as a discrete system by the expansive grid distribution.Te advent of MGs smoothes the grid's development, compensates for traditional DG's limitations, and stipulates superior benchmarks and prerequisites for actualizing smart grid infrastructure [10].
Te advent of MGs facilitates resolving the discord between distributed energy and the grid while optimizing the merits of DG and rectifying traditional DG's shortcomings.MG's optimal scheduling allows for the strategic management of DG power outputs and the regulation of transmission power between the MG and the main grid.Tis orchestration is designed to achieve multiple goals, including cost and emissions reduction, as well as enhanced reliability and generation efciency [11].To optimize MG operation and fully harness its benefts, it is imperative to conduct thorough research on its optimal control strategies.
For MG optimization dilemmas, employing multiobjective models renders the system more holistic and effcacious [12].Numerous studies have been undertaken to address MGs' multiobjective optimization challenges.To preserve the environment, demand response models [13] have been devised to furnish potential infrastructures that concurrently enhance efciency and reduce energy consumption.Some researchers have implemented the distributed gradient algorithm (DGA) to tackle the distributed sum optimization (DSO) problem [14].With artifcial intelligence's evolution, a plethora of intelligent algorithms have emerged.Zhang et al. [15] proposed a multiobjective freworks algorithm (MOFWA) to optimally address the multimobile charging planning problem.Younes et al. [16] employed an artifcial bee colony (ABC) algorithm to ascertain the optimal confguration results for the MG system's total operating cost.Zhu et al. [17] proposed a multiobjective gray wolf optimization algorithm (GWO) based on the multiobjective Gray Wolf optimization algorithm (MOGWO).Nevertheless, these algorithms have high computational complexity and scalability issues, which are crucial for their implementation in the real world, especially in large-scale MG systems.Vosoogh et al. [18] formulated an optimal probability model for MG energy management, considering multifactor uncertainty using the 2 m point estimation method.Al-Tameemi et al. [19] combined the GWO and particle swarm optimization (PSO) algorithms to determine the optimal size and pollution minimization optimization results for diferent system components.Ghiasi [20] employed multiobjective particle swarm optimization in an intelligent approach.Tis approach conducted a thorough analysis of the new structure of alternating current (AC) and direct current (DC) systems.Subsequently, it determined the capacity and optimal design of hybrid renewable energy sources in smart microgrid (MG).Some researchers proposed and implemented an improved multiobjective diferential evolution (IMODE) optimization algorithm for generation scheduling in smart MG systems while considering economics and emissions as competing issues [21].Tese studies rely heavily on simulations or theoretical models.Te absence of real-world validation or case studies diminishes the practical applicability of the proposed algorithms and their relevance to actual MG systems.Some other researchers presented an enhanced control strategy for renewable energy resources connected to the grid through voltage-sourced converters (VSCs) in MGs [22].However, these studies do not adequately address the dynamic nature of MGs, such as varying energy demand patterns, fuctuating renewable energy sources, and real-time operational changes.
Globally, MG development is advancing towards maturity, with exceptionally developed MGs established in Europe and the United States.Europe, the pioneer in proposing "smart power networks," steers its research endeavors toward energy, environmental conservation, and sustainable development [23].Tese investigations encompass control, analysis, optimization, forecasting, multi-MG systems, and MGs' economic dispatch [24].For instance, the National Technical University of Athens (NTUA) MG is primarily engineered to scrutinize MG control strategies, mode switching operations, energy scheduling based on economic considerations, and the analysis and optimization of multilayered control structures for MGs.Te Demotec MG cluster control framework, devised by the University of Kassel's Institute of Photovoltaic in Germany, comprises multiple sub-MG network systems [25].Tis structure allows comprehensive reconfguration and optimization of the entire MG.It facilitates seamless 2 International Journal of Intelligent Systems transitions between multiple subgrid networks and islanding modes.Additionally, it assesses the impact of load fuctuations on grid stability by incorporating or excluding diverse load bursts [26].Te Labein MG in Spain's Basque Country concentrates on scheduling tactics and communication protocols for multiple MGs, centralized and decentralized control strategies for nonislanded operations, and tarif trading in a novel electricity market under MGs [27].Lastly, the CESI MG in Milan, Italy, was investigated by integrating diverse generation devices and energy storage mechanisms, while optimizing the network's communication topology to actualize optimal MG control and conduct comprehensive power quality analysis by leveraging multiple communication methods [28].
Te abovementioned algorithms used in the existing model solution are relatively single, which may result in the lack of global search and optimization ability in integrated energy system energy optimization and management.Te lack of global or local optimal solutions in practical applications may lead to a lack of overall understanding of the problem by decision makers, resulting in unnecessary diffculties or economic losses.Most of the multiobjective optimization algorithms only focus on obtaining as many global optimal solutions as possible but neglect the search for local optimal solutions.However, the research on this kind of problem is still relatively limited and the research on this kind of problem is still in the early stage.
Tis paper studies how to optimize the control of MG power load under the condition of maintaining the safe and stable operation of MG system, so as to maximize the economic and environmental benefts of MG.To augment the new energy consumption of MG and thereby enhance its operational efciency, this study initially constructs a DSM multiobjective optimization model grounded in smart grid principles to refne the load structure.Subsequently, a multiobjective optimal dispatching model for renewable energy MG is developed, focusing on economic and environmental protection objectives.Ultimately, a multimodal multiobjective optimization algorithm is employed to ascertain global and local optimal solution sets to resolve the model.Te proposed MG dispatching model's efcacy is corroborated through simulation analysis in a representative MG scenario.
Te key features and main contributions of the multimodal multiobjective optimization algorithm are as follows: (1) DSM integration: our algorithm incorporates DSM principles, aligning it with the smart grid paradigm.Tis integration enables the refnement of load structures and enhances energy consumption efciency.(2) Multiobjective optimization: the algorithm is designed to address both economic and environmental objectives, acknowledging the need to balance economic efciency and environmental protection in MG operations.(3) Global and local optimal solutions: our algorithm is equipped to determine global and local optimal solution sets.Tis feature enhances the robustness of the optimization process, ensuring a comprehensive exploration of potential solutions.
Tis paper consists of six main parts.Section 1 is the introduction, Section 2 is the demand-side management multiobjective optimization model, Section 3 is the new energy MG economic environment optimization dispatch model, Section 4 is the multimodal multiobjective optimization solution model based on local convergence index, Section 5 is the result analysis and discussion, and Section 6 is the conclusion.

Demand-Side Management Multiobjective Optimization Model
Tis paper adopts the DSM strategy based on load shifting of controllable power equipment in MG to achieve optimal control of MG power consumption load.Te DSM multiobjective optimization model is established with the objectives of improving the new energy consumption, reducing the cost of electricity purchase by customers smoothing the load, and taking the electricity demand of multiple controllable devices as the constraints.

Objective Function 1: Maximizing New Energy
Consumption.Te access of demand-side controllable equipment is controlled with the optimization objective of improving new energy consumption.When wind power and photovoltaic power generation are insufcient, the electricity consumption load is reduced, and when power generation is sufcient, the load is increased.Tis can improve the suitability of MG load and new energy generation.Te optimization objective function F 1 is shown as follows: where τ is the total number of time intervals divided by 1 d; UL(n) is the actual customer load at moment n; and R(n) is the sum of the predicted power output of the scenery at moment n.From (1), it can be seen that the higher the utilization rate of new energy the smaller the value of F1.

Objective Function 2: Load Management for Cost
Reduction.Te DSM strategy reduces the access to electricity-using equipment in the peak period and increases the access to electricity-using equipment in the low period.Tis can reduce the cost of electricity for customers and smooth the electricity load curve.Te optimization objective function F 2 is shown as follows: where u(n) is the price of electricity at moment n.
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Objective Function 3: Ensuring Load Stability.
Since the electricity price is high in the peak period and low in the trough period, F 2 will lead to a decrease in electricity consumption in the peak period and an increase in electricity consumption in the trough period.In order to prevent peakvalley interchange, using the load peak-valley diference as the objective function can ensure the smoothness of the electricity consumption load.Te optimization objective function F 3 is shown as follows: Te actual user load UL(n) at moment n in the 3 objective functions consists of uncontrollable and controllable loads, and its mathematical expression is as follows: where FL(n) is the load forecast at moment n; CL(n) is the controllable load connected at moment n; and DL(n) is the controllable load transferred out at moment n.L is the type of controllable equipment and w l is the maximum transfer time of the l-th controllable equipment.T lsn is the amount of equipment of the l-th controllable equipment transferred from moment s to moment n.T lns is the amount of equipment of the l-th controllable equipment transferred from moment n to moment s.T ls(n−z) is the amount of equipment of the l-th controllable equipment transferred from moment s to moment (n − z).T l(n−z)s is the number of devices of the l-th controllable device transferred from moment (n − z) to moment s.U l1 is the load of the l-th controllable device at the start moment.U l(z+1) is the load of the l-th controllable device at the (z + l) moment.d l is the time of the required load of the l-th controllable device.

Constraint Conditions.
Considering the actual load shifting situation and the limitation of the power demand of controllable devices, the DSM multiobjective optimization problem described needs to satisfy the following constraints.

Constraint Condition 1: Nonnegative Device Shifting.
Te number of controllable devices shifted at any moment is nonnegative.

Constraint Condition 2: Device Quantity Limit.
Te number of controllable devices does not exceed the total number.
where NC(s) is the total number of controllable devices with power demand at the moment s.

Constraint Condition 3: Minimum Connection Time.
Each controllable device is connected for more than the required time to disconnect.
where U l(n−z+1) is the load of the l-th controllable equipment at the moment of (n − z+1).

Constraint Condition 4: Device Shifting Sequence.
Controllable equipment loads can only be moved forward in time, adhering to a specifc sequence, and the transfer duration must not exceed the predetermined limit.
Under the constraints of equations ( 7)-( 11), the min F 1 , F 2 , F 3   problem is solved with the number of accesses of controllable devices at each moment in 1 d as the decision variable.Tis yields the real load profle that satisfes the desired target with the participation of user-side controllable devices and the accesses of controllable devices within the MG at diferent moments in 1 d.

New Energy MG Economic Environment Optimization Dispatch Model
Tis paper establishes a new energy MG model as shown in Figure 1, includes wind turbine (WT), photovoltaic (PV), diesel generator (DE), microturbine (MT), batteries (BAT), and controllable loads.Te MG is connected to the grid through a main isolator and can purchase power from the grid when MG capacity is insufcient.Te dispatch model of this MG is developed with the optimization objectives of economy and environmental friendliness.

Objective Function 1: Economic Efciency Objective.
To improve the economic efciency of station MG operation, the economic objective of station MG dispatch is expressed by the operating cost C opt of station MG.It includes the fuel cost of traditional distributed power sources, the operation and maintenance cost of distributed power sources and energy storage systems, and the cost of station area MGs interacting with the larger grid through contact lines.Tis paper optimizes the decision variables, such as the 4 International Journal of Intelligent Systems output power of distributed power sources and the charging/ discharging power of the energy storage system, to minimize C opt .Te optimization objective C opt is expressed as follows: where T a is the number of DGs in the MG and N is the total number of time intervals divided by 1 d.C fuel,y (n) is the fuel cost of the y-th DG at moment n.C om,y (n) is the operation and maintenance cost of the y-th DG at moment n.C grid (n) is the cost of the MG's interaction with the larger grid at moment n.Te fuel cost of the MG is specifcally expressed as follows: where C MTf is the fuel cost of MT; C is the unit price of natural gas.LHV is the low heating value of natural gas.U MT is the output power of MT. η MT is the output efciency of MT; C DEf is the fuel cost of DE; and U DE is the output power of DE. α, β, c are the fuel cost coefcients of DE.
Te O&M cost of power equipment in MG is usually related to the output power of power equipment, and the calculation formula is shown in equations ( 14) and (15).
where ζ y is the operation and maintenance cost factor of the y-th DG.U DG,y (n) is the output power of the jth DG at time n.MG operates in the grid-connected state and purchases power from the larger grid when the generation unit is under-generated, and the interaction cost at this time is as follows: where C buy (n) is the price of electricity purchased by the MG from the larger grid at moment n.U grid (n) is the power of interaction between the MG and the larger grid at moment n.International Journal of Intelligent Systems where T e is the pollutant gas type.e DG,y,r , e BAT,r , and e grid,r are the coefcients of the y-th DG, energy storage system, and the r-th pollutant gas emitted from the large grid, respectively.U BAT (n) is the output power of the energy storage system at moment n.U grid (n) is the output power of the large grid at moment n. ζ r is the treatment cost coefcient of the r-th pollutant gas.

Constraint Conditions
where U new (n) and U Load (n) are the new energy generation power and total load of users at time n, respectively.

Constraint Condition 2: Power Constraint of DG and
Large Grid Output.
where U min DG,y and U max DG,y are the lower and upper limits of the output of the y-th DG, respectively.U min grid and U max grid are the lower and upper limits of the output of the large grid, respectively.

Constraint Condition 3: Climbing Constraint of DG and Large Grid Output
where ΔU dn DG,y and ΔU up DG,y are the downhill and uphill constraints of the y-th DG, respectively.ΔU dn grid and ΔU up grid are the downhill and uphill constraints of the large grid, respectively.U DG,y (n − 1) is the output power of the y-th DG at the moment n − 1. U grid (n − 1) is the output power of the large grid at the moment t-1.

Constraint Condition 4: Energy Storage System Operation Constraint
where E BAT (n), E min BAT , and E max BAT are the lower and upper limits of energy storage capacity and energy storage capacity at moment n, respectively.U ch (n) and U dch (n) are the charging and discharging power at moment n, respectively.U max ch and U max dccx are the maximum values of charging and discharging power, respectively.η ch and η dch are the charging and discharging efciency of the energy storage system, respectively.

Constraint Condition 5: Rotating Standby Constraint
where R up y (n) and R dn y (n) are the climbing capacity available from the y-th DG at time n.R up grid (n) and R dn grid (n) are the climbing capacity available from the large grid.R up sys (n) and R dn sys (n) are the positive rotating standby demand and negative rotating standby demand of the system at time t, respectively.
Under the constraints of equations ( 19)-( 25), the multiobjective optimization problem of min C opt , C plut  , which is the mathematical model of MG dispatch.Te optimization includes variables at each MG 1 d time period: output power of distributed sources, energy storage system charging/discharging power, and power purchased from the larger grid by MG.Te fow diagram of new energy MG scheduling with DSM in this paper is shown in Figure 2.

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Multimodal Multiobjective Optimization Solution Model Based on the Local Convergence Index
Many engineering applications in the real-world often require the consideration of multiple optimization objectives.Usually, the diferent objectives are mutually constrained and can only be traded of to obtain a satisfactory solution for the decision maker.Multiobjective optimization problems (MOPs) can be represented as follows: min where Ω is the feasible domain of the problem and o w (i) is the i-th objective function value of the decision vector.Unlike a single-objective optimization problem with a single global optimum, in a multiobjective optimization problem, there are multiple nondominated solutions, which are called Pareto optimal solution sets.Te solution i G dominates the solution i H when and only when In general, multiobjective evolutionary algorithms (MOEAs) give a set of mutually exclusive solution sets, called Pareto solution set (PS).Also, the mapping of PS on the objective space is called Pareto optimal front (PF).

Local Convergence Metrics.
Traditional MOEAs focus more on the convergence of the solution set, so most algorithms choose convergence as the frst criterion for the selection of ofspring individuals.Te multimodal multiobjective optimization algorithms designed based on traditional MOEAs are taken into account of the diversity of decision spaces and therefore can obtain more equivalent PSs.However, traditional algorithms tend to focus only on obtaining global PSs, thus discarding the search for local PSs.In order to enhance the search capability of the algorithm for local PS, a local convergence index is proposed by referring to the meta-adaptation value proposed in the SPEA2 algorithm [29].Tis paper emphasizes local Pareto optimal solutions and provides guidance for selecting parent individuals by calculating a local convergence index X x LC for each solution.For the solution i x , the local convergence index is calculated as follows: where M x denotes the number of neighboring solutions of solution i x .D y,x ∈ 0, 1 { }, where D y,x � 1 denotes the solution i x Pareto-dominated solution.When X x LC � 0, it means that solution i x is not dominated by any of its neighboring solutions, that is, solution i x is locally Pareto optimal.S x denotes the number of times that solution i x Pareto dominates its neighboring solutions.Te larger the value of S x , the better the relative performance of solution i x .Te specifc calculation procedure is as follows: Figure 3 shows a schematic diagram of the calculation of the local convergence metric proposed in this paper.Unlike the SPEA2 algorithm, the meta-adaptation value needs to be compared with all the individuals in the population.In the calculation of the local convergence index, individuals are only compared with their own neighboring solutions to improve the convergence of the local optimal solution.Specifcally, for solution G in the decision space, it is in the local PS (circle region).In traditional MOEAs, solutions G International Journal of Intelligent Systems and H, located in the global PS (where point C is situated), are dominated by C, leading to their exclusion from the evolutionary process.In the calculation of the local convergence index, solution G is compared with its own neighboring solutions (in the current schematic, only solution H is a neighbor) in the calculation of the dominance relation.In this case, solution G is a nondominated solution, which can be retained and successfully proceed to the next evolution.Te concept of neighbors is used in the calculation of the local convergence index, and the defnition of neighboring solutions in the decision space is subjective and requires the introduction of parameters.In this paper, two solutions i x and i y are called neighbors when and only when their Euclidean distance is less than Q.Te calculation is as follows: where D denotes the number of decision variables.i max

Algorithmic Framework. Based on the local convergence indicator, a multimodal multiobjective evolutionary algorithm (MMEA based on local convergence indicator,
X LC -MMEA) is proposed in this paper.Te algorithmic framework of X LC -MMEA is represented by algorithm 1.Like most MOEAs, X LC -MMEA consists of the following steps: population initialization, mating selection, ofspring generation, and environment selection.Te study introduces a local convergence index to identify global and local Pareto solutions.Tis index is employed as a binary competition criterion in selecting parent individuals, accelerating the algorithm's convergence and enhancing local exploration capability.Specifcally, two solutions are randomly selected from the current population and their local convergence index values are compared.If their local convergence metrics are the same, the one with the smaller crowding distance is selected.Tis process will be repeated until N individuals are selected.After that, the selected parent individuals will generate progeny using SBX and polynomial mutation (PM).Figure 4 shows the fow diagram of algorithm 1.

Environment Selection Strategy.
In this paper, a new environment selection strategy is designed for the search problem of local PS.Te environment selection strategy utilizes the crowding distance as a second criterion, considering both the decision space and target space.It helps in selecting individuals that contribute to a uniformly distributed solution set.In this section, the ILC-based environment selection strategy is discussed in detail, and the basic idea is represented by algorithm 2 (see Figure 5).
X LC -MMEA uses the crowding distance as a second criterion to select individuals in the population.In general, traditional MOEAs focus more on the uniformity of the solution set distribution in the target space, while the proposed algorithm focuses more on the uniformity of the decision space.Tis can be illustrated by the distribution of the target space and decision space in Figure 6.
Te left portion of Figure 6 illustrates that the solution is optimally dispersed across the decision space, albeit suboptimally dispersed in the objective space, aligning with conventional multimodal evolutionary algorithms (MMEAs).Conversely, the central part of Figure 6 indicates that the solution is inadequately distributed in the decision space but is optimally distributed in the objective space, mirroring traditional multiobjective evolutionary algorithms (MOEAs).Te quintessential state for solution distribution, depicted on the right side of Figure 6, entails the solution being optimally dispersed in both the decision and objective spaces.To realize this objective, an enhanced method for computing the population crowding distance is delineated hereinafter.
where ‖i y − i x ‖ denotes the Euclidean distance between i x and i y .o(i x ) represents the normalized value of the target vector corresponding to the solution i x .Before the calculation, the values of i x and i y need to be normalized.Te new crowded distance considers the solution set's relative positions in both target and decision spaces, ensuring

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Input: maximum number of function evaluations T FE , population size T Step 1: Initialize the population Pop Step 2: Calculate the local convergence index X LC and crowding distance CD of the population, which are used to select the parent individuals.
Step 3: Select parent by convergence index and crowding distance using binary competition.
Step 5: Generate a new population Pop by environmental selection Step 6: Update the current function evaluation count: FE = FE + T ; Step 7: If FE < TFE, then skip to Step 2 and continue the run.
Output: optimal solution set Pop.International Journal of Intelligent Systems a more uniform distribution across both.In addition, in order to better balance the diferences between the two spaces, the algorithm uses a uniform normalization strategy for the vectors in both spaces.

Result Analysis and Discussion
In the experiments, a typical MG structure is used in this paper.Tis MG structure includes elements, such as wind turbines, photovoltaic generation, and controllable loads.Te specifcation of this test network includes the capacity, initial state, connection mode, and power consumption requirements of each element in the MG.

Comparative Analysis of Diferent Dispatching Cases.
To validate the models and methods delineated in this paper, three MG dispatching scenarios are conceptualized, utilizing a typical MG structure as the research arithmetic: (1) development of an MG dispatching model without accounting for DSM; (2) formulation of a DSM optimization model to optimize the load with the aim of minimizing the customer's electricity procurement cost, followed by the construction of an MG dispatching model; and (3) formulation of a DSM multiobjective optimization model, followed by the development of an MG dispatching model, and resolving the model utilizing a multimodal multiobjective optimization algorithm.
Te study incorporates the load under diferent scenarios: without DSM optimization, with DSM singleobjective optimization, and with DSM multiobjective optimization, into the MG economic environment dispatching model to provide a detailed analysis.Te utilization of new energy output is visually represented in Figure 7.As discernible from Figure 7, the utilization rate of new energy output is diminished in the absence of DSM optimization owing to the discord between the timing and magnitude of new energy output and load demand.Owing to the substantial quantity of "abandoned wind and light," the traditional DG output and the aggregate amount of electricity procured by the MG from the grid are considerably elevated.Te economic implications are signifcant, as the MG incurs higher costs in procuring electricity from the grid and relies more heavily on conventional energy sources.Tis translates into increased operational costs and potentially higher greenhouse gas emissions due to greater dependence on nonrenewable energy.Introducing single-objective DSM optimization brings about substantial improvements in MG performance.Te introduction of single-objective DSM optimization can signifcantly improve MG performance by introducing DSM multiobjective optimization for both economic and environmental goals.Tis plan makes more efcient use of energy and reduces costs, while signifcantly reducing carbon emissions and environmental impact.With the help of DSM, MG is able to utilize new energy sources more efciently and reduce its reliance on conventional power generation, thereby reducing carbon emissions and environmental impact.

Comparative Analysis of Diferent Algorithms.
In this section, the load data of a typical daytime in summer and winter in a region are selected to test the MG economic environmental dispatch model.Literature [30], literature [31], and the proposed algorithm are used to solve the model.Te operating cost, power purchase cost, environmental cost, and single-day integrated cost of the MG are compared, and the calculation results of the three algorithms are shown in Table 1.Te integrated energy satisfaction, PV consumption rate, and electricity autonomy rate of the system at the optimal solution are also analyzed, and various indicators are shown in Figure 8.
In Table 1, the optimization results for the MG economic environmental dispatch model during a typical summer and winter day are presented.Te proposed algorithm consistently outperforms literature [30] and literature [31]   Literature [31] Literature [30] (a) Proposed Literature [31] Literature [30] [30] and literature [31], respectively.In winter, the reduction is even more pronounced, with a 19.4% and 40.2% improvement over literature [30] and literature [31].While the operating and power purchase costs decrease signifcantly, there is a slight increase in environmental cost.Tis tradeof is crucial for achieving a balance between economic efciency and environmental sustainability.
Figure 8 provides a comprehensive evaluation of the MG scheduling model's performance.Te proposed algorithm achieves a higher integrated energy satisfaction of load users (0.97 and 0.95 for the two typical days), indicating an effcient utilization of available energy resources.Moreover, the average PV consumption rate of the proposed algorithm is 23% and 49.6%, which is signifcantly higher than literature [30] and literature [31], demonstrating the algorithm's efcacy in harnessing solar energy.Te electricity autonomy rates are 0.36 and 0.52.Although only slightly better, it signifes the system's ability to operate independently.Tese results afrm that the proposed algorithm not only minimizes costs but also enhances the satisfaction of energy demand while maintaining environmental benefts.
Tree algorithms are used simultaneously to optimally solve the MG economic environment dispatch model at two typical day times under the same operating conditions.Te maximum number of iterations in the algorithm is 200, and the search population is 30 (see Figure 9).From Figure 9, it can be seen that in summer and winter time, the algorithm of this paper has fewer computational results than the literature [30] and literature [31], and the number of iterations used to converge to the optimal solution is the least.In summer, the proposed algorithm achieves the optimal solution at the 90th iteration, while the algorithms in literature [30] and literature [31] only fnd the local optimal solution in the whole process.In winter, the proposed algorithm achieves the optimal solution at the 15th iteration, and the algorithm in literature [31] falls into the local optimal solution at the 6th generation until the end of the solving process.Te algorithm of literature [30] keeps jumping from the local solution to a better local solution but does not fnd the optimal solution.Te convergence accuracy, solution speed, and global search capability of the algorithm in this paper show obvious superiority.
Te experimental results depicted in Figure 9 underscore the superior convergence efciency and accuracy of the proposed algorithm in comparison to literature [30] and literature [31].In both summer and winter scenarios, the algorithm of this paper demonstrates a notable reduction in computational iterations required to reach the optimal solution.During summer, the algorithm achieves global optimality at the 90th iteration, while the algorithms in literature [30] and literature [31] only fnd the local optimal solution in the whole process.It stands in stark contrast to the local optima found in literatures [30,31].In winter, the proposed algorithm converges to the optimal solution at the 15th iteration, outperforming literature [31], which remains trapped in a local optimum.Te algorithm of literature [30] keeps jumping from the local solution to a better local solution but does not fnd the optimal solution.Te proposed algorithm's advantages include high convergence accuracy, swift solution speed, and superior global search capability.Tese characteristics make it a robust and efcient tool for optimizing microgrid operations, especially in dynamic and time-sensitive scenarios, afrming its practical applicability in real-world energy management.
Figure 10 visually displays the curves of all algorithms on problems with PS.As can be seen from Figure 10, the proposed method is able to fnd both global and local PSs of the problem, and the obtained PF distribution is more uniform.Tis is because the method introduces a new way of Proposed Literature [30] Literature [31]   International Journal of Intelligent Systems calculating population crowding, which can better balance the uniformity of the distribution in the target space and the decision space.

Sensitivity Analysis of Local Convergence Index.
Te algorithms are compared with the current state-of-the-art algorithms (literature [32], literature [33], and literature [34]) in terms of F1 for diferent X LC values.Te comparison results are shown in Figure 11.
From Figure 11, it can be seen that when the X LC value is small, the F1 value of this paper's algorithm at diferent values is higher than the other compared algorithms.Moreover, the selection of diferent X LC values for this paper's algorithm has less impact on the algorithm's detection results.Te results from the sensitivity analysis clearly indicate the robustness and adaptability of the proposed algorithm across diverse operating conditions.

Conclusion
In this study, a multiobjective optimization methodology for a new energy MG incorporating DSM is devised, with a focus on the primary objectives of minimizing the operational cost of the MG system and reducing the environmental impact.Initially, a DSM optimization model is developed, emphasizing load shifting in controllable devices while considering the utilization rate of new energy, electricity procurement costs for customers, and load leveling.Subsequently, an MG scheduling model is formulated to incorporate both economic and environmental protection objectives.Eventually, the experimental conclusions are as follows: (1) quantitative analysis: the comparative experimental results of diferent scheduling cases prove that the DSM multiobjective optimization in this paper can save economic costs more efectively and at the same time greatly reduce carbon emissions and the impact on the environment.(2) Qualitative analysis: in the summer, the proposed algorithm achieves an integrated cost that is 32.6% and 38.9% lower than that of literature [30] and literature [31], respectively.In the winter, the proposed algorithm achieves integrated costs 19.4% and 40.2% lower than literature [30] and literature [31], respectively.Moreover, our multimodal multiobjective optimization solution model, based on the local convergence index, is a fexible framework that can be fne-tuned to address the specifc needs and constraints of diferent MGs or regions.Te local convergence index allows

Proposed
Literature [32] Literature [33] Literature [34]  However, the methodology in this paper may not take into account all types of controllable devices and their diferent characteristics.Adaptive control strategies that can be adaptively tuned to the specifc characteristics and requirements of newly introduced devices will be further investigated in the future to ensure wider applicability.Furthermore, due to its complexity, it is challenging to implement the algorithm in real-world MGs.In particular, external factors, such as numerous controllable devices, diferent load profles, and weather need to be taken into account.Future research will customize the algorithm for diferent real-world MG scenarios so that it can be seamlessly integrated into multiple environments.
and minimum values of the dth decision variable, respectively.

Figure 3 :
Figure 3: Schematic diagram of local convergence index.

Figure 5 :
Figure 5: Flowchart of environment selection strategy.
in terms

Table 1 :
Objective function optimization of the integrated energy system.