Research on multiobjective capacity configuration optimization of grid‐connected wind–solar–storage microgrid system based on improved BWO algorithm

How to effectively utilize renewable energy and improve the economic efficiency of microgrid system and its ability to consume renewable energy has become one of the main problems facing China at present. In response to this challenge, this paper establishes a multiobjective capacity optimization model with the minimum levelized cost of energy, the maximum proportion of renewable energy consumption, and the minimum comprehensive system cost. Based on this model, a new improved beluga whale optimization algorithm is proposed to solve the multiobjective optimization problem in the capacity allocation process of wind–solar–storage microgrid system with the goal of ensuring that the microgrid can meet the maximum load demand at different moments throughout the year. In this paper, opposition‐based learning, artificial bee colony, dynamic opposite, and beluga whale optimization are combined to improve the population diversity and convergence accuracy, thereby enhancing the optimization performance of the algorithm. Finally, after finding the optimal Pareto front solution, the Technique for Order Preference by Similarity to an Ideal Solution is used to help decision‐makers select the optimal solution. Using real load data and meteorological data, the results of this paper show that the multiobjective capacity allocation optimization method of grid‐connected scenic storage microgrid system based on the improved beluga whale optimization algorithm can improve the economics of the wind–solar–storage microgrid system and promote the photovoltaic consumption simultaneously, providing a solution for the realization of low‐carbon power and regional economic development. The best‐found levelized cost of energy for the wind–solar–storage microgrid system is 0.192 yuan/kWh.


| INTRODUCTION
Given the swift growth of the world economy, the global energy supply is stretched, prompting the urgent need to accelerate the capacity for renewable energy supply. 1 In recent years, with the introduction of carbon neutrality and carbon peak goals, the incorporation of wind, solar energy, and other renewable sources into microgrids has garnered significant interest.This offers a novel pathway for China's energy to undergo a green and low-carbon transformation.As we all know, wind power and photovoltaic power generation are bound to weather conditions, and their power output is random, fluctuating, and intermittent. 2Directly feeding the generated power into the grid can impose a substantial current impact on the power system, leading to grid frequency deviation and voltage fluctuations.In such circumstances, the integration of an energy storage unit can not only accomplish peak shaving and valley filling, but also address the fluctuation issues associated with wind power and photovoltaic generation.Additionally, it enhances the microgrid's capacity to absorb energy generated by wind and photovoltaic sources. 3Hence, in the microgrid system design process, the initial step involves addressing the capacity configuration challenge within the microgrid system.This stands as a prominent and challenging issue in ongoing research on the optimization and design of microgrid systems.Due to the diverse array of power supply units within the microgrid and the evident disparities in power output characteristics, the microgrid capacity allocation problem is characterized by high nonlinearity, complexity, and uncertainty.Therefore, a reasonable method to optimize the capacity allocation of microgrid can improve the reliability and economy of microgrid to the greatest extent.
According to different objective functions, scholars have conducted extensive research on capacity allocation optimization.In reference, Ahadi et al., 4 the objective function is to minimize the total cost while considering relevant constraints.They propose a new strategy to improve battery life by utilizing the potential of renewable energy and obtain the optimal configuration.Mohammed Ridha et al. 5 use LLP as a technical evaluation index and life cycle cost and normalized energy cost as economic indices.They optimize the number of series and parallel photovoltaic modules and batteries using MOPSO and provide various configuration results under expected conditions.Haidar et al. 6 propose an optimization strategy to evaluate the performance of hybrid microgrid configuration in different rural areas of Sarawak, Malaysia.The objective function is to meet the maximum load demand while minimizing the total cost.They find the dynamic energy price of the optimal configuration using deterministic and stochastic optimization methods.In Kaabeche and Bakelli, 7 the objective functions are load defect rate and minimum UEC.They use the JAYA algorithm to solve the optimal system configuration and compare it with the ALO, GWO, and KH.The results confirm that the JAYA algorithm outperforms other algorithms.In Long et al., 8 the objective is to minimize power generation costs, maximize power supply reliability, and maximize the average power filling rate.They consider decision variables such as the number of photovoltaic arrays, the number of wind turbines, and hourly load scheduling.Finally, a two-layer model is used to determine the wind-solar installation capacity ratio.In Kiehbadroudinezhad et al., 9 the objective is to minimize total life cycle costs, minimize loss of power supply probability, and maximize reliability.Kiehbadroudinezhad et al. 10 formulate a multiobjective optimization problem by combining three objective functions, minimizing the total life cycle cost as well as the environmental impact, and maximizing the system reliability.
In addition, scholars have also proposed various capacity allocation optimization methods.Zhang et al. 11 propose a hybrid energy storage capacity allocation method based on Monte Carlo and ABC algorithms and combine a low-pass filter-based power allocation strategy with fuzzy control, which utilizes the complementary characteristics of batteries and supercapacitors to improve battery life and system stability.Ramli et al. 12 adopt the MOSaDE algorithm to optimize the design of wind/photovoltaic/diesel HMS in 20 cities in Saudi Arabia.They analyze the LPSP, COE, and RF related to system cost and reliability using a multiobjective optimization method, verifying the reliability of this approach.In Liu et al., 13 an improved method based on an energy management strategy is proposed to optimize the size and configuration of independent photovoltaic modules.Combining solar radiation, ambient temperature, and load requirements, the improved particle swarm optimization algorithm is used to optimize the configuration of photovoltaic panels and battery systems.It is concluded that the improved method is more effective in finding optimal results, with lower cost and faster convergence speed compared to particle swarm optimization and simulated annealing algorithms.Liu et al. 14 utilize the GA-PSO algorithm to optimize power and capacity under different scheduling strategies, aiming to minimize the cost of power equalization.They study the operational performance and optimal configuration of the PV-CSP system.In Kamal et al., 15 DE is used to optimize microgrids combined with wind/photovoltaic/diesel/biogas/energy storage to obtain the component configuration with the lowest energy cost.PSO and GA are also compared, and it is concluded that the DE method exhibits higher optimization performance.Zou et al. 16 optimize the PVB system and propose a multiobjective optimization design method based on uncertainty using random simulation and weight methods.This approach enables the optimal configuration of photovoltaic and battery systems under actual working conditions, surpassing traditional methods.In Bukar et al., 17 the optimal system configuration for reliable power supply is determined based on defect rate and energy cost.A rule-based energy management strategy is employed to coordinate the power flow among various components of the microgrid system.The optimal configuration problem is solved using the GOA and compared with the PSO and CS in terms of performance.
Researchers have explored the objective function and algorithms in optimizing the capacity configuration of microgrid systems.However, limited studies have been conducted on the capacity configuration optimization of scenic storage microgrid systems that incorporate three objective functions.Furthermore, in the realm of algorithm research, the Beluga Whale Optimization (BWO), a swarm-based metaheuristic algorithm introduced by Changting Zhong et al. 18 in 2022, has predominantly found application in cloud computing, feature selection, image segmentation, fuzzy control, and related areas.However, its utilization in power systems, particularly in the optimization and configuration of microgrids, remains relatively scarce.
In this article, we address the grid-connected wind-solar-storage microgrid system by establishing a mathematical model for the output power of wind and photovoltaic generation as well as energy storage batteries.Objective functions include the levelized cost of energy (LCOE), the proportion of renewable energy consumption (REPC), and minimized comprehensive system cost.The charging and discharging power of the energy storage unit, the footprint of scenic equipment, and other factors are considered as constraints.To tackle the microgrid capacity allocation problem, we propose an improved beluga whale optimization algorithm (IBWO).This includes the introduction of opposition-based learning (OBL) for population initialization, the utilization of artificial bee colony (ABC) and dynamic opposite (DO) for location update, and the incorporation of an evaluation function to verify the algorithm's comprehensive performance.Finally, utilizing the annual measured load data of Henan University of Technology and regional meteorological data, the model is solved through MATLAB under the energy dispatching strategy.The capacity allocation scheme for each unit of the system is determined using the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method, based on the Pareto solution derived from the model.The results indicate that the IBWO algorithm exhibits superior convergence speed and a well-balanced tradeoff between development and exploration, effectively avoiding local optima.The approach outlined in this paper serves as a valuable reference for the capacity configuration of a grid-connected wind-solar-storage microgrid system.This article has the following contributions: • The combination of OBL allows the algorithm to explore the search space more comprehensively, increasing the diversity of the algorithm by generating candidate solutions in opposing directions of the solution space.This helps to avoid falling into local optima, thus slowing down the problem of premature convergence.• The IBWO has been improved using ABC, which enhances its global exploration ability and stability.
Besides, the introduction of the ABC algorithm provides a wider range of search strategies that mimic the way a colony of bees forages and communicates.This integration improves the global search performance of the algorithm, thus increasing the likelihood of discovering better solutions.• Through the DO, individual beluga whales are more likely to find positions close to the global optimal value, improving search accuracy and convergence performance.This helps to improve the adaptability of the algorithm, which can respond more flexibly to different search spaces.• The IBWO was tested and compared with other excellent algorithms, proving that the IBWO has stronger performance.• We selected a reliable engineering problem about capacity configuration of grid-connected wind-solar-storage microgrid system to test the IBWO to verify its reliability in engineering problems.
After the introduction section, this study is structured as follows: a description of the grid-connected wind-solar-storage microgrid system; a mathematical model of the hybrid microgrid system; and the key points for designing this hybrid microgrid system are given in Section 2. The most important factors that should be considered to optimize the sizing of the generation system are mentioned in Section 3. In Section 4, the improved beluga whale optimization algorithm for sizing problem is investigated.Section 5 conducts experiments on real data using the IBWO algorithm in comparison with various traditional optimization algorithms and uses the TOPSIS method to obtain optimal results.Finally, the conclusions and future works are mentioned in Section 6.

| GRID-CONNECTED WIND-SOLAR-STORAGE MICROGRID SYSTEM AND MATHEMATICAL MODEL
The grid-connected wind-solar-storage microgrid system, as detailed in this article, comprises four main components: a wind power generation system, a photovoltaic power generation system, an energy storage unit, and the power grid.The system schematic diagram is illustrated in Figure 1, where the photovoltaic panels and wind turbines are linked to the microgrid system bus through inverters.The charging and discharging power of the energy storage unit is connected to the microgrid bus under the coordinated control of the battery management system (BMS) and energy management system (EMS).This arrangement ensures that the overall power of the energy storage unit is effectively coordinated and controlled by the BMS and EMS.Moreover, the energy flow within the storage unit operates bidirectionally.This bidirectional flow facilitates the transfer of renewable energy within the power supply cycle of the microgrid system, consequently diminishing the reliance on power obtained from the public grid.As a result, this setup reduces power expenditure and augments the proportion of renewable energy consumption within the microgrid system.
The primary function of the microgrid system is to integrate wind power, photovoltaic, energy storage, and the grid into a cohesive unit.This integration is achieved through EMS, ensuring seamless collaboration among all components of the system.Through this coordination, the wind power system, photovoltaic power system, and energy storage battery can leverage their respective advantages, mitigate the drawbacks of individual components, reduce instances of wind and photovoltaic energy wastage, and ultimately connect to the public grid through a point of common coupling (PCC) to facilitate energy exchange.During periods of ample wind and photovoltaic energy resources, the wind and photovoltaic power will be directly supplied to the load through the inverter.Conversely, when wind and photovoltaic power fall short, the energy storage battery is treated as a power generation unit to compensate for the deficiency.This approach mitigates the need for users to purchase additional power during periods of low wind and photovoltaic power system output, thereby reducing overall power costs.The EMS is to reasonably allocate the charging and discharging time of the system's energy storage battery according to the output of wind and photovoltaic power generation and the user's load demand.Since there are several power supply units in the system, it is necessary to consider the power output characteristics of each power supply unit under different meteorological conditions, so it is necessary to establish a suitable mathematical model for the study.

| Wind power generation model
The power generation capacity of wind turbines is influenced by the wind speed and the output characteristics of the equipment itself.When the actual wind speed is less than the cut-in wind speed or greater than the cut-out wind speed, the output power of the wind turbine is zero.When the actual wind speed is between the cut-in wind speed and the rated wind speed, the output power of the wind turbine increases non-linearly with the increase of wind speed.When the actual wind speed is between the rated wind speed and the cut-out wind speed, the wind turbine output power is the rated wind turbine power.The specific equation is a segmented nonlinear function as shown 19 : where P WIND represents the theoretical output power of wind turbine; v ci represents the cut-in wind speed of the wind turbine; v r is the rated wind speed of the wind turbine; v co represents the cut-out wind speed of the wind turbine; P WN represents the rated power of the wind turbine; v represents the wind speed at fan height, can be calculated from Equation (2).
As wind speed changes with elevation, and different observation points have varying heights, it becomes essential to convert wind speed measurements taken at different heights.The conversion formula, 20 is presented in equation: where h i refers to a specific converted elevation above ground level; h x represents the actual height above the ground level.; v x denotes the wind speed converted at this particular height; θ represents the coefficient related to the ground roughness of meteorological observatory, take 0.16.

| Photovoltaic system model
The output power of the photovoltaic system is mainly related to the solar irradiance and ambient temperature at the location of the photovoltaic panels in the panels power system, and its actual output power is proportional to the solar irradiance and inversely proportional to the ambient temperature, and its output power expression is shown in Equation (3). 13And because of the limited output voltage and power of photovoltaic modules, multiple photovoltaic panels need to be connected in series and parallel to form a photovoltaic array.
where P PV signifies the theoretical power output of the photovoltaic module; P STC represents the rated power of the photovoltaic module under standard test conditions; G c denotes the real solar irradiance at the location of the photovoltaic module; G STC represents the solar irradiance under standard test conditions; α represents the photo- voltaic derating factor; k represents the power temperature coefficient; T e represents the ambient temperature of the position of the photovoltaic module; T b represents the rated operating temperature of the photovoltaic module; T STC represents the temperature under standard test conditions.

| Energy storage battery model
Energy storage battery is an important power compensation module in the microgrid model, which is often used to compensate for the fluctuation of photovoltaic output caused by environmental and meteorological factors, and can also be converted between power generation equipment and power-using equipment under different circumstances to achieve the effect of power balance and energy buffer.The stored power before and after charging and discharging the energy storage battery is shown in Equation (4).To ensure the life and safety of the energy storage battery, it is necessary to limit the depth of discharge of the energy storage unit.The depth of discharge of the energy storage battery is an important parameter to prevent overcharging and over-discharging of the energy storage battery, and stop charging when the energy storage battery reaches the maximum set capacity of the energy storage battery, and stop discharging when the energy storage battery reaches the minimum set capacity.
where  (5)   where P t ( ) buy is the power provided by the grid at time t when the microgrid scenic power generation system and storage battery power is not enough to support the load demand; P t ( ) sell is the excess power transferred to the grid at moment t when the output power of the scenic power generation system exceeds the upper limit of the energy storage battery and the load's capacity to consume; P t ( ) load denotes the system load power at moment t.
II.The total space of the photovoltaic module installation must be within the maximum usable area, and its expression is shown.
where S occ PV .
is the available area of photovoltaic modules; S per pv .
is the area of photovoltaic modules per unit capacity; C pv is the total installed capacity of photovoltaic modules.III.Limiting the charge and discharge power of energy storage battery is critical because excessive power can accelerate the aging rate of the battery, thereby affecting its overall life.To prolong the service life of the energy storage battery, it is essential to set the charge and discharge power thresholds as shown in equation below: where k threshold is the threshold percentage of charging and discharging power of the energy storage battery; C bat represents the capacity of the energy storage battery; t Δ is 1 h.IV.Capacity limitations on the energy storage battery are essential to ensure stability and safety during use.Considering that deep discharge accelerates the degradation of the energy storage battery, it is imperative to maintain the storage power within a specified range to ensure optimal performance and longevity.
where E bat.max is the upper limit value of storage capacity of the energy storage battery; C bat represents the capacity of the energy storage battery; σ represents the discharge depth; SOC coefficient represents the upper limit coefficient of the storage capacity of the energy storage battery.

| System energy management strategy
Wind and solar power generation are virtually pollution-free, with zero emissions during the power generation process.They do not incur additional fuel costs.Therefore, the load should use the power generated by the wind-solar power generation system first, followed by the power from the storage battery.Purchasing power from the grid is only necessary when the output from the wind-solar power system and the storage battery is insufficient to meet the load demand.
In the system EMS using net load for calculation, its expression as shown: . In this article, the control strategy for the gridconnected wind-solar-storage microgrid system is illustrated in Figure 2.This system primarily utilizes energy generated by wind and photovoltaic power generation to meet the load demand.Based on the conditions of wind and photovoltaic power generation, as well as the load requirements, the system is divided into three energy supply modes: (1) In situations where the combined power generated by wind and photovoltaic sources during a specific time period falls short of meeting the load demand, the energy storage battery is employed to compensate for the insufficient power generation.However, the energy storage battery must not be discharged below the minimum State of Charge (SOC) limit.If the output power from the combined sources is still insufficient to offset the load shortage, the remaining power needed is obtained from the power grid.(2) Balanced Generation Mode: When total renewable energy production from wind and photovoltaic | 2371 sources within a given time unit exactly matches the load demand, the load is supplied solely by the wind and photovoltaic generation system.In such cases, there is no need for the energy storage battery or the grid to intervene.(3) Excess Generation Mode: If the total renewable energy generation power generated by wind and photovoltaic sources in a given time unit exceeds the load demand, the excess power is first directed towards charging the energy storage battery.Charging of the energy storage battery ceases once it reaches the maximum SOC limit.If there is still surplus power, it can be sold to the power grid at the prevailing grid-connected electricity price.

| MICROGRID SYSTEM CAPACITY CONFIGURATION OPTIMIZATION MODEL
This paper establishes a capacity configuration optimization model for the grid-connected wind-solar-storage microgrid system as shown in Figure 3.The LCOE, REPC, and comprehensive system cost will serve as the objective function for multiobjective optimization.This approach aims to achieve the lowest LCOE, the highest REPC, and the minimum comprehensive system cost for the microgrid system while satisfying the specified requirements and constraints.
The model uses the IBWO algorithm to generate the capacity allocation scheme for wind, photovoltaic and storage.It then invokes the EMS based on the generated allocation scheme to derive the actual power balance strategy for the wind, photovoltaic and storage microgrid system.The model then feeds the calculated hourly energy consumption data of wind, photovoltaic, and storage charging and discharging in the microgrid back into the IBWO algorithm to obtain the objective function value.Finally, the wind, photovoltaic and storage capacity is iteratively optimized and updated based on the objective function value, iteratively refining the allocation scheme until the optimal configuration of wind, photovoltaic, and storage capacities is achieved.

| Levelized cost of energy
The LCOE 21 is a metric that captures the overall life cycle cost of a system, including considering various factors such as initial investment costs, operational and maintenance expenses, costs of component replacements, and the residual value of components at the end of their life cycle.The LCOE is determined by dividing the total life cycle cost of the system by the total energy generated over its operational lifespan.This calculation takes into account the time value of money, converting costs and energy from different time periods into a unified LCOE formula.
where Pr CP is the initial investment cost of the system; Pr OM is the system operation and maintenance cost; Pr RE is the replacement cost of system components; Pr EN is the residual value of components at the end of the system life cycle; E PV is the first year of photovoltaic power generation; E WIND is the power generation of the wind turbine in the first year; E ES is the discharge amount in the first year of energy storage; α is a photovoltaic derating factor; N S is the design life of the system; i is the discount rate, taking the value of 5%. 22

| Initial system investment cost
The initial investment cost of the system includes four parts: photovoltaic system investment cost, wind power generation system investment cost, energy storage battery investment cost and inverter investment cost.Cables, junction boxes and other components are included in photovoltaic system investment cost and wind system investment cost.where C pv is the capacity of photovoltaic module; C wind represents the investment cost of the wind power generation system; C bat is the capacity of the energy storage battery; Price pv is the unit capacity price of photovoltaic system; Price wind is the unit capacity price of the wind power generation system; Price bat is the unit capacity price of the energy storage battery; Price inv is the price per unit capacity of inverter.

| System operation and maintenance costs
The operational and maintenance expenses of the microgrid system encompass the maintenance costs of the wind system, photovoltaic system and storage batteries.For wind and photovoltaic systems, the maintenance expenses are based solely on their respective system capacities.However, the maintenance costs of energy storage batteries consider not only the capacity of the energy storage units but also their annual charge and discharge cycles.Additionally, the capital invested appreciates over time.Hence, in this paper, all the operation and maintenance costs from the project's inception to its conclusion are converted to the present value of the investment cost at the time of project construction using compound interest calculations.The calculation method for the operation and maintenance cost of the microgrid system is presented: where Price pv om .
indicates the annual photovoltaic system maintenance cost per kw; Price wind om .indicates the annual wind power generation system maintenance cost per kw; Price bat om .
is the maintenance cost of the energy storage system under the number of charge/discharge cycles per kwh per year; Cycle index bat .
indicates the annual charge and discharge cycles of the energy storage unit.

| Residual value of components at the end of life cycle
In the later stage of microgrid equipment, the equipment needs to be scrapped when it reaches its service life, and the surplus value of scrapped equipment needs to be calculated.The formula for calculating the residual value of components at the end of life cycle is shown.
In the formula, rate tax means the income tax rate, with a value of 15%; N RE represents the year of system component replacement; The residual value of components at the end of the life cycle is calculated at 5% of the purchased value of components.

| The proportion of renewable energy consumption
The peak load period of the power grid often does not coincide with the peak output power period of the wind and photovoltaic power generation modules.To address this mismatch, some wind and photovoltaic power generation systems rely on energy storage batteries for time shifting, while others can operate in grid-connected mode.To maximize the utilization of renewable energy within the system, the optimization of the renewable energy consumption ratio is considered as the objective function under the grid-connected state of surplus power.The formula for this objective function is presented as: where E t ( ) indicates the electricity sold to the grid when wind and photovoltaic output exceeds the capacity of the storage battery and load to consume.

| The comprehensive system cost
The comprehensive cost of the system includes the installation cost, operation and maintenance cost and interaction cost with the power grid.This objective function makes the comprehensive cost of the system optimal, and the expression of the objective function is: where fit CF is the comprehensive system cost; Pr E interaction cost between microgrid and public grid.Among them, the interaction cost between microgrid and public grid is expressed as follows:   | 2373 where Price buy is the unit price of electricity purchase; Price sell represents unit price for electricity sales; E buy represents the number of purchases of electricity from the power grid; E sell represents the number of sales of electricity to the grid.

| BELUGA WHALE OPTIMIZATION ALGORITHM (BWO)
A meta-heuristic algorithm called beluga whale optimization algorithm was proposed in 2022, which inspired from the living behaviors of beluga whales in the ocean.Beluga Whale Optimization algorithm (BWO) establishes three stages such as beluga exploration, exploitation and fall, and its equilibrium factor and beluga fall probability are adaptive. 18

| Initialization
Based on the population mechanism of the BWO algorithm, beluga whales are regarded as search agents, and each beluga whale represents a candidate solution with the effect of moving in the search space by changing its position vector.The matrix of search agent positions is modeled as: where n represents the number of search agent beluga whales, and dim is the dimension of the design variable.The fitness of beluga whales is expressed as: .
To allow the BWO algorithm to smoothly transition from exploration to exploitation, an equilibrium factor is introduced, which changes continuously with the iterative process: where t is the current iteration, T is the maximum iteration, and B 0 is a random number change in the range of (0,1) at each iteration.If B > 0.5 f the exploration stage will begin, and if B 0.5 f  the exploitation stage will start.With the increasing number of iterations, the probability of the exploitation phase increases, and the probability of exploration phase decreases.

| Exploration phase
Since beluga whales are highly social animals, beluga whales hunt by sharing positional information with each other, so they need to consider the relationship between the best individual and other individuals, and beluga whales' positions are updated as follows: where +1 is the position of the i-th individual on the jth dimension during the t + 1 iteration.p j is randomly selected in [1,dim], and it is not equal with P 1 .X i p t , j represent the position of the i-th individuals under t interation, and r 1 and r 2 are random numbers between (0,1).According to the dimension chosen by odd and even numbers, the updated position reflects the synchronous or mirror behaviors of beluga whales in swimming or diving.

| Exploitation phase
The development phase of the beluga optimization algorithm was inspired by the feeding behavior of beluga whales, which can forage and move collaboratively based on the location of nearby belugas.In this process, they hunt by sharing information about each other's location, which needs to be considered in relation to the best individual and other individuals.Assuming that beluga whales are able to successfully capture prey using the Levy flight strategy, a mathematical model of the process is expressed as follows: where X i t and X r t represent the current position of the i and random individuals in the T iteration.X i t+1 is a new position of the i-th individual, X best t is the best position, and r 3 and r 4 are random numbers between (0,1).C 1 is a random number that measures the intensity of Levy flight.
where u and v are random numbers obeying a normal distribution, and β is a constant set to 1.5.

| Whale fall
The beluga whales either moved elsewhere or were shot down and fell to their deaths in the deep sea.To ensure a constant population size, the location of beluga whales and the step size of the beluga fall were used to determine the location of the update.The mathematical model is represented as follows: where r 5 , r 6 and r 7 are random number between (0,1).X step represents the step size of whale fall.
) represents the step size factor related to the probability of beluga whale fall and population size.u b and l b are the upper and lower bounds of variables.The probability of a beluga whale fall is calculated as a linear function, and the formula is as follows: Over the course of the iterations, the whale fall probability has been trending downward, ostensibly as the beluga whale approaches food its risk of death decreases.

| IMPROVED BWO ALGORITHM
The BWO method has a limitation in that it may experience premature convergence.Additionally, the algorithm is only suitable for addressing singleobjective optimization problems, and is not appropriate for direct application to multiobjective optimization problems that involve a set of optimal solutions (nondominated solution set).Therefore, it is necessary to improve the traditional BWO to address the multiobjective problem of capacity allocation in scenic storage microgrid systems.By incorporating OBL, ABC, and DO into BWO, more effective random candidate solutions can be obtained.This integration enhances the diversity and consistency of candidate solutions, improves the quality of the population solution set, and accelerates the overall search process.

| Opposition-based learning
The first step of the BWO algorithm is to randomly generate the initial population during the initialization stage.However, if there are no prior conditions regarding the search space information, the population generated in this manner may not be uniformly distributed.Additionally, the algorithm relies on the optimal solution within the initialized population to update the positions of other individuals, and this individual updating strategy has its limitations.If the optimal solution within the initial population points in the opposite direction of the global optimum, it may impede the BWO algorithm from converging easily to the global optimal solution.To overcome this issue, incorporating OBL can enhance the quality and diversity of the initialized population solution set.OBL involves utilizing reverse solution for a given population during the initialization process and selecting the most suitable solution from the entire set of solutions.This helps mitigate the limitation posed by the reliance on a single optimal solution within the initial population, contributing to improved convergence and exploration capabilities of the BWO algorithm.
The inverse solution is expressed as shown in Formula ( 27), 23 LB is the lower limit of the interval, UB is the upper limit of the interval, X is the solution between the upper and lower limits shown in Formula (28), and the inverse solution is expressed as X ̄shown in Formula (29).The above equation can be extended to multidimensional search space, and the position of each search individual and its reverse position are represented by the equation.
Combining OBL with BWO algorithm population initialization steps, it is summarized as follows: First, randomly initialize the initial position X of BWO, denoted as x x x ( , , …, ) . Then, solve for the opposition-based position X ¯corresponding to the BWO initial position X , resulting in .
Finally, select the n most suitable positions as the initial population of the BWO algorithm from the union of X X ( ¯)  .This process improves the diversity and quality of the initial population, leading to better algorithm performance.

| Artificial bee colony algorithm
The BWO algorithm may encounter local convergence issues in the later stages of the iterative process.To prevent the algorithm from getting trapped in local optima during iterations, the concepts of following and scouting bees from the ABC algorithm can be incorporated. 24This integration helps mitigate the shortcomings of the BWO algorithm to a certain extent and contributes to enhanced global search capabilities.After the introduction of the ABC, the bee colony undergoes initialization.If the optimal solution obtained from this initialization exceeds the performance of the adopted BWO optimization algorithm, the global optimum discovered within the bee colony is integrated into the position update formula of the BWO algorithm.The integration of this method considerably broadens the search range of the IBWO algorithm, enhances the diversity of the population, and improves the overall exploration capabilities.Equation ( 30) represents the individual update formula for the bee colony.

( ) (
) where x i k+1 and x i k denote the position of the i-th individual when iterating to the k+1st and k-th generations; ω is the inertia weight; c 1 and c 2 are the learning factors; rand 1 and rand 2 are random numbers between (0,1); x ABCbest is the optimal solution calculated by TOPSIS for the nondominant solution set of ABC; x BWObest represents the optimal solution calculated by TOPSIS for the nondominant solution set of BWO algorithm.
At the same time, the idea of scout bees jumping out of local optimum is introduced into the BWO algorithm, and the search method of following bees is improved.The generation of new nectar source location is related to the location of the nectar source itself and the adjacent area, and the information of the nectar source location will directly affect the search ability of the bee colony.Therefore, the method of following bees searching for new nectar sources is changed to an adaptive search method, which can well balance the global search and local search ability.
During the initial stage, when the honey source has been searched less than half of the specified limit, the bees in question will explore the area surrounding the global TOPSIS optimal point determined by the ABC algorithm.In the middle stage, the global TOPSIS optimal point identified by the BWO algorithm takes precedence, and the bees will explore in the direction of the BWO TOPSIS optimal point.During the late stage, when the number of searches reaches the upper limit, the scout bees will reselect a new honey source.This strategic approach allows the bee colony to adapt its behavior throughout the iterative process.

| Dynamic opposite
Dynamic opposition (DO) 25 is a combination of quasiopposites and quasi-reflections.By incorporating DO into the BWO algorithm, the search space can dynamically expand.In cases where the population gets trapped in a local optimal solution, DO enables the algorithm to break free from this local optimum.It restarts the exploration process of the BWO algorithm, thereby enhancing the algorithm's optimization performance.The specific calculation formula for DO is as follows: where X ̄is the inverse solution; X r is a random inverse solution; X ̄do is a dynamic inverse solution; Jr is the jump rate that determines the execution probability of the dynamic reverse learning process.Both the dynamic inverse solution and the stochastic inverse solution are affected by a random number between [0, 1], which provides a new position and makes the current position jump out of the local optimum.

| Solution steps of IBWO algorithm
The specific steps of using IBWO algorithm to find Pareto frontier and obtain the optimization results of grid-connected wind-solar-storage system capacity allocation are as follows, and its algorithm flow chart is as Figure 4.
Step 1: Initialize population of beluga whale and artificial bee colony.First, input hourly illumination intensity, wind speed, ambient temperature, load time series data, equipment-related parameters, population size, maximum iteration times of the algorithm, and optimize the upper and lower limits of object capacity.Taking the capacity of a wind turbine, photovoltaic, and energy storage battery as decision variables, the BWO was initialized by OBL and the fitness function was calculated.The optimal individual of ABC was found by ordering nondominant solutions with TOPSIS.
Step 2: During the exploration and development stages, updates are made to the capacity of the wind turbine, photovoltaic system, and energy storage battery.The output power of the wind turbine and photovoltaic generation is calculated using annual meteorological data.Then, the microgrid system control strategy is used to calculate the LCOE, REPC, and comprehensive system cost fitness functions.This approach comprehensively evaluates and optimizes microgrid system performance by considering various factors and objectives.The optimal individual of BWO was found by TOPSIS.The position of ABC is updated in the falling stage of BWO.After calculating the fitness function between ABC and BWO, the crowding degree is calculated and the nondominant solution is sorted to update the position of BWO.
Step 3: The DO strategy is used for individual beluga whales, which involves calculating the degree of crowding and sorting nondominant solutions.A set number of individuals are selected and stored in the external database of nondominant solutions, while others are eliminated.The optimal individual position is then updated using the TOPSIS method.This strategy improves the diversity and quality of solutions in the population, enhancing exploration and convergence capabilities in the optimization process.
Step 4: Judge whether the algorithm reaches the maximum iteration number, if it reaches the maximum iteration number, output the external nondominated solution set, otherwise transfer to Step (2).

| Data preparation
To assess the feasibility of the proposed model and algorithm, this paper presents a case study using a local building as an example.The model and algorithm are applied to optimize the energy system of the building, multiple objectives.This practical application aims to demonstrate the effectiveness and practicality of the proposed approach in a real-world scenario.Hourly load demand data were recorded for only floors one through six of the building in a given year through the energy meter.The missing data were interpolated by averaging two adjacent values, and normalized and scaled according to the total annual energy consumption data for all floors of the building, as shown in Figure 5D.Hourly photovoltaic power generation per unit capacity over the entire year is also simulated using meteorological data, including hourly wind speed, solar radiation, and temperature in the local area, as illustrated in Figure 5.The irradiance and temperature data were obtained from the historical reanalysis data set of European Centre for Medium-Range Weather Forecasts (ECMWF) and were provided by Xi He Energy Big Data Platform. 26The relevant parameters of wind power, photovoltaic, and battery are shown in Table 1.Power customers can charge the energy storage at a low electricity price, and supply the load from the energy storage during the peak electricity period, thus reducing the power cost.Time-of-use electricity price has a great impact on the total cost of users and indirectly affects the return speed of microgrid systems.Peak-valley electricity price, electricity price time, and on-grid electricity price reference. 22This method is implemented in a MATLAB environment, the population size of the improved BWO algorithm is set to 100, and the iteration times are 100.
All the experiments in this paper were completed on a computer with a 7th Gen Intel(R) Core(TM) i5-7300HQ processor with a primary frequency of 2.50 GHz, 16 GB of memory, and the operating system 64-bit Windows 10 using MATLAB2023a.

| Multiobjective optimization problem
In the context of multiobjective optimization problems, the concept of pareto dominance is employed to assess the performance of the proposed IBWO algorithm.Since the BWO algorithm is only suitable for solving singleobjective optimization problems and is not suitable for F I G U R E 5 hourly data of wind speed, solar radiation, ambient temperature, and load demand in 1 year (A is hourly data of wind speed in 1 year; B is the hourly data of solar radiation within 1 year; C is the hourly data of the environment within 1 year; D is the hourly data of load demand in 1 year).direct application to multiobjective optimization problems involving a set of optimal solutions (non-dominated solution set), the BWO algorithm is not selected as a control group for experiments in this article.In this study, NSGA-II, MOPSO were selected as the control group and IBWO to obtain the pareto solution set in 30 independent runs, respectively.Subsequently, several widely utilized performance evaluation indices, including GD (generational difference), 27 IGD (inverted generational difference), 28 MD (mapped diversity), 29 Spacing, 30 Spread, 31 HV (hypervolume), 32 and PD (pure diversity), 33 are employed to assess the convergence, accuracy, and diversity of the algorithm, and the parameters of these algorithms are set as shown in Table 2.
To calculate the evaluation function, it is necessary to fit the Pareto real surface.In this paper, the above three algorithms are selected to calculate the Pareto surface respectively.The external pareto repository size set to 10,000.The population size is set to 100, and the iteration times are 100.After the pareto results of the three algorithms are integrated and sorted by nondominant solutions, the pareto fitting surface is shown in Figure 6.With the increase of LCOE, the REPC in the system is on the rise.When LCOE reaches the best, the REPC in the system is the lowest, and when the REPC in the system is the highest, the comprehensive system cost is high, so it is difficult to directly get the optimal solution by comparing the fitness function values.
Table 3 express the average value of each index of each algorithm.The analysis reveals that the NSGA-II algorithm excels in terms of HV among the three algorithms, indicating its superior overall performance when HV is considered as the benchmark.The MOPSO algorithm, on the other hand, outperforms in terms of the GD index, showcasing its effectiveness its effectiveness specifically in solution set convergence.Notably, the IBWO algorithm proposed in this paper attains optimal across various metrics, including IGD, Spacing, Spread, and PD.This highlights the comprehensive effectiveness of the IBWO algorithm in addressing the multiobjective optimization problem.The attainment of optimum results in terms of IGD indicates that the IBWO algorithm exhibits optimal comprehensive performance when IGD is utilized as the evaluation standard.Likewise, achieving optimum results in terms of Spacing indicates that the uniformity of IBWO The optimal scheme and the worst scheme are determined by the positive ideal solution and negative ideal solution formulas, which are shown: .
According to Equation (35), the closeness degree between each scheme and the optimal scheme is calculated, and the relative sticking progress value is calculated according to TOPSIS method, and then the advantages and disadvantages of the schemes are sorted.

| Analysis of optimization results
The obtained capacity allocation schemes and fitness function values are shown in Table 4. Figure 7 illustrates the power output of each component in the system under the optimal wind and solar storage capacity configuration determined by TOPSIS.In most cases, the total renewable energy generation produces excess power even after meeting the load demand.However, there are instances where the power generation system output falls short of meeting the load demand.During such occurrences, the system relies on the energy stored in batteries and the exchange of power with the grid to maintain a balanced power state within the system.It shows that the power of the storage battery and the power purchased and sold by the grid are constantly changing, which proves the influence of the energy storage system and the grid on the system power balance.When the generation is less than the load demand, the storage battery discharges preferentially causing the battery power to drop, and when the SOC minimum is reached, the power purchased from the grid begins to increase.From January to March and June to September, microgrid generation decreases.However, due to the inherent characteristics of the building, the load demand reaches its lowest point during these periods, and in some instances, there is almost negligible load demand.As a result, the storage battery fluctuates above and below the maximum SOC during these times.The sales of electricity to the grid are almost equal to the generation.From March to June, the microgrid F I G U R E 7 Power output of system under wind-solar-storage configuration to the grid aligns closely with the power generation.
WANG ET AL.
| 2381 generation is higher, the load is basically satisfied, and the load demand basically reaches the maximum value of the year.When the microgrid power generation system generates sufficient power, the energy storage system can improve the microgrid system's own power consumption capacity, increase the system's renewable energy consumption ratio, and reduce the amount of power sold to the grid.During the time periods of 0:00-8:00 a.m. and 18:00-24:00 p.m., the microgrid power generation system power generation experience low output due to the absence of light.To maintain normal operation during these periods, the system relies on discharging the storage battery or purchasing power from the grid.The priority is given to discharging the storage battery to meet the load demand, while the storage battery is used simultaneously to reduce power consumption costs during high-tariff daytime hours.For the remaining time periods, the load is primarily supplied by the storage battery, with additional power purchased from the grid to meet load demand and reduce expenses during peak daytime tariffs.This strategy optimizes energy usage and reduces costs by taking advantage of stepped electricity price changes throughout the day.During the valley power period, the power is purchased from the grid to supply power to the load and storage battery to meet the load demand and at the same time to reduce the expenditure of electricity under the high electricity price during the daytime.
Considering that the optimization of energy storage charging and discharging strategies is done in terms of days, the initial daily power constraints of the energy storage under such conditions have an impact on the optimization strategy, and the results of the comparison of the evaluation indexes under the same configuration conditions with different initial SOC strategies are shown in Table 5.
From the results shown in Table 5, it can be seen that the user is able to obtain the maximum economic benefit when the initial value is set to 80%.This is due to the fact that the beginning of each day falls in the valley power time period, and the energy storage needs to be charged during this period to meet the subsequent load supply demand.If the residual power of the storage is not appropriate, it will affect the balance of supply and demand of the microgrid system, resulting in having to resort to the regional power grid to ease the power balance, which in turn affects the system's low tariff arbitrage.Therefore, the setting of the initial SOC of energy storage is related to the time-sharing tariff.

| CONCLUSION
To optimize the configuration of a grid-connected wind-solar-storage microgrid power supply, this paper presents a microgrid power supply optimization model.The model considers the LCOE, the PREC, and the comprehensive system cost in the microgrid.An improved multiobjective beluga whale optimization algorithm is used to solve the model.The Pareto optimal solution is determined using the TOPSIS method.This approach integrates multiple objectives and utilizes advanced optimization techniques to balance various factors in the microgrid power supply configuration.The optimal configuration of microgrid power supply capacity is obtained by considering the effects of residual feedin tariff, load characteristics, and peak/valley tariff on the configuration of grid-connected wind-solar-storage microgrid power supply.
The simulation analysis shows that the IBWO algorithm, which incorporates opposition-based learning, artificial bee colony, and dynamic opposite strategies, exhibits stronger local optimization and global optimization capabilities.This improvement allows it to more effectively address multiobjective optimization problems.The study applies an algorithm to the load data of selected buildings and conducts multiobjective optimization configuration for a grid-connected wind-solar-storage microgrid.To strike a balance between the economy of the system and reducing the annual comprehensive system cost of the buildings, the TOPSIS evaluation method is employed, while ensuring the proportion of renewable energy consumption.These findings are a valuable reference for designing and applying grid-connected wind-solar-storage microgrid systems.
Although this study has achieved a series of useful results, we should also note that there are some limitations of the study.First, the model considers factors such as LCOE, PREC, and integrated system cost of microgrids, but in practice, it may face other complex contexts and uncertainties, such as climate change, policy adjustment, and so forth, which have not been adequately taken into account in this study.Therefore, in future studies, further model expansion is needed to more comprehensively consider the impact of these external factors on microgrid power allocation.In addition, the improved multiobjective IBWO algorithm was used in this study, and although significant results were achieved in the simulation and analysis, the applicability of the algorithm still needs to be carefully considered.In future work, we will improve the performance of IBWO in engineering problems, so that it can satisfy the requirements of most of the engineering problems.

CONFLICT OF INTEREST STATEMENT
Author Wang Tao is employed by Beijing Boshenkang Technology Co Ltd.The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

3
Capacity allocation optimization model of windsolar storage microgrid system.
T A B L E 4Abbreviations: LCOE, levelized cost of energy; REPC, renewable energy consumption.
T A B L E 5 Comparison of evaluation functions for different initial charge states.: LCOE, levelized cost of energy; PV, photovoltaic; REPC, renewable energy consumption; SOC, state of charge. Abbreviations