Statistical analysis of storage capacity increment effect in micro-grid management with simultaneous use of reconfiguration and unit commitment

Abstract This paper aims to provide a model that combines reconfiguration with Unit Commitment (UC) and analytically examine Storage Capacity Increment Effects (SCIEs) in Micro-Grid (MG) operation. The case study includes batteries as the storage system and a conventional 10-bus MG with Wind Turbine (WT) and Micro-Turbines (MTs) as energy sources. The load demand and energy estimation of the Wind Unit (WU) with respect to wind speed changes are considered uncertain parameters. Additionally, a newly introduced algorithm and an objective function based on MG’s day-ahead benefit are employed to tackle the problem. According to Monte Carlo Simulation (MCS), a few scenarios are created for modeling uncertainties, and the MG’s optimal operation is examined under these situations. This study is based on two cases: the first examines the MG’s scheme with just one battery, and the second investigate SCIEs. This paper seeks to maximize MG’s benefit and optimize power exchange with increasing storage capacity. The statistical analysis results show that the proposed strategy can offer more cost-effectiveness, reliability, and power quality, though challenges remain.


Introduction
The demand for electrical energy is constantly increasing these days.In order to meet the increased demand, there should be a large number of power plants, each of which has advantages and disadvantages.The weaknesses of traditional power plants include low efficiency, high losses on transmission lines, longer construction time, and lower reliability.In this way, researchers have proposed a new concept called MG, which consists of Distributed Generators (DGs) such as Gas Turbines (GTs), Photovoltaic panels (PVs), Wind Turbines (WTs), Microturbines (MTs), small hydroelectric power plants, and controllable loads connected to meet the demand of consumers (Jabbari-Sabet et al., 2016).In Faisal et al. (2018), an Energy Storage System (ESS) has been used to optimize the schedule of MG, considering the islanding limitations.In order to increase the flexibility and reliability capabilities, networked MGs can be used.Networked MGs provides much better load flow control and Islanding than a single MG structure (Alam et al., 2018).Furthermore, optimal use of Distributed Energy Resources (DERs) in each MG and backup power transmission to the upstream network or other MGs not being able to meet demand is one of the important features of networks including several MGs.In other words, when MGs lack the needed power, they can benefit from the available options to compensate the demand of their consumers.To achieve this, applying techniques including the implementation of a powerful Energy Management System (EMS) and proper distribution of power in smart networks is required (Zahraoui et al., 2021).In (Chamandoust et al., 2020b), some methods based on optimization algorithms and graph theory have been used to address the increase in network loading, operational requirements, and critical loads demand priority after fault occurrence.In Seresht et al. (2023) the losses of ESS were minimized by reducing the total operation cost and output power of MG.Furthermore, a mixed integer linear programming optimization algorithm has been used to optimize the size of the DG unit and storage capacity devices.In Berrehil El Kattel et al. (2023), an algorithm based on environmental benefits prediction with a distributed cooperative control method was proposed to adjust the power exchange of the multiple energy storage units (ESUs).In Ehsan-Maleki et al. (2018), a cooperative control method of the battery storage device was considered in an MG and divided into two control subsystems for the power exchange mode of the storage device.The control strategy provides an accurate share of reactive power between the storage device units.In Hassan et al. (2023), the storage capacity of system batteries to attain a specific self-consumption rate in a power distribution system was examined.Combining a storage battery and solar power generation demonstrates that by increasing the energy selfconsumption rate in the necessary storage battery capacity, the capability of a DC supply may be decreased by around 10% compared to an AC supply.In order to better understand the capabilities of MGs, such as increasing flexibility and reliability, ensuring improved power quality, and reducing operating costs, an EMS has been presented.This system, taking into account the optimal performance of the resources in the MG and the upstream distribution system, leads to better management of consumers' demand in different conditions.MGs have a control structure with centralized or distributed management on the low voltage side, which is capable of operating in both modes of grid-connected and islanded (Nasab et al., 2023).
The paper is structured as follows: The GRSA is described in Section 4.2.1.The mathematical modeling of the problem is covered in Section 2. Section 3 presents the simulation results.Section 4 explains a statistical analysis of the simulation findings, and section 6 concludes with a few points.

Literature review
A novel load restoration optimization model is proposed in (Nikoufard & Hatami, 2017) to coordinate topology reconfiguration and MG formation while addressing various practical limitations.The introduced method has been used for the operational flexibility of the network to provide more critical loads.In Zand et al. (2023), a method of sizing power resources concerning DG's characteristics, system loads, and energy storage devices was presented.Using the Life Cycle Cost (LCC) theory, an objective function accounts for operational costs, environmental and construction maintenance costs, recycling profits, and compensation for energy shortages.Based on an ordered binary decision flowchart, an algorithm to solve the MG reconfiguration problem while minimizing the cost of power losses was proposed in (Samavat et al., 2023).Despite the fact that MGs have two states, most challenges would be related to grid-connected MGs, and the use of optimal and economic methods is mainly necessary.The challenges are mostly because of the operating time of connected MGs, which is almost great.On the other hand, due to the uncertainties of distributed energy resources (transient and temporary nature), large changes in load demand, and the occurrence of high-impact, low-probability disturbances in MGs, there is a possibility of large deviations in voltage and frequency.Therefore, MGs' analysis in islanded mode in addition to the normal operation mode of connecting to the network is of great importance (Zand et al., 2023).In the previous works, various types of MG management models have been reviewed, each of which has advantages and disadvantages.But in general, the distributed method has more pleasant characteristics compared with the centralized method.The main drawback of centralized method can be seen in the low flexibility when adding new components to the model and the high volume of calculations (Gong et al., 2016).In Xu et al. (2019), a tri-objective optimization problem for the optimal scheduling of an energy hub system (EHS) to minimize operation cost, emission pollution, and deviation from desired values is presented.The model considers Demand-side Management (DSM) strategy for optimal shifting of electrical deferrable loads (EDLs) based on day-ahead prices.Reserve scheduling is proposed by interruptible loads (ILs).The results show that the EHS's operation cost and emission pollution decrease with EDLs, while the simultaneous participation of EDLs and ILs results in reduced costs and emissions.Many studies have been conducted in the field of applying energy management systems to MGs.In Chamandoust et al. (2019), a new framework for home energy management in the form of an energy hub based on renewable resources using the probabilistic optimization method is presented.In the proposed framework, various energy converters and storage devices, such as hybrid electric vehicles, a thermal storage unit, solar panels, and household appliances, are considered in this energy hub.In Rastegar et al. (2016), the day-ahead scheduling problem of a smart microgrid (SMG) as a multi-objective function aiming to minimize operation costs, load curtailment costs, and coordinate shiftable loads and wind turbine output power is modeled.It introduces a new Demand Side Management strategy to improve customer satisfaction and WT penetration.The model considers stochastic output power and the scheduling of shiftable loads based on WT availability.In Chamandoust et al. (2020), the application of advanced measured data for the development of energy forecasting and operation planning services in distribution networks consisting of major distributed energy resources and its use in the energy management system of the distribution network is proposed.In (Azizivahed et al., 2017), a new approach based on multi-objective energy management for optimal exploitation of distribution networks in the presence of distributed generation resources and battery energy storage systems are introduced.A hybrid advanced evolutionary algorithm was proposed to solve the multi-objective energy management problem.In Lotfi (2020), a prediction-based twolayer energy management system for MGs consisting of energy storage systems including batteries and super storages is presented.The long-term costs of batteries and super storage was modelled and converted into short-term costs associated with real-time operation.In (Padmanaban et al.), the energy balance of distribution system operators (DSO) has been impacted by the high penetration of renewable energy sources and EES systems in electrical distribution grids.A tri-objective model is developed to minimize operation costs, emission pollutions, load expectation loss, and RESs output power deviation.The DSM strategy involves joint scheduling of RESs and deferrable loads, with uncertain behaviour modelling using stochastic optimization.In Chamandoust et al. (2020a), an optimization algorithm for planning the consumption of several smart homes with distributed energy resources is proposed.In the proposed approach, the centralized optimization problem for home energy management was divided into a two-level optimization problem, where the first and second levels are related to the local and global home energy management systems, respectively.In Peivandi et al. (2023), a robust energy management system for islanded MGs is presented, which has also been considered as a static model of the frequency system simultaneously.In this system, in order to investigate a robust hierarchical reservation management structure for energy and frequency, the problem was transformed into a mixed-integer linear programming model.In Zhang & Wai (2021), a multi-objective optimal scheduling of a Smart Energy Hub System (SEHS) for the day ahead is proposed.The objectives include minimizing operation cost and emission pollution, minimizing loss of energy supply probability, and ensuring optimal electrical and thermal load profiles.The third objective is to flatten demand profiles using Demand Side Management.The MG has been overgrown in recent years because of its benefits, including the simplicity with which distributed renewable energy may be integrated and its operational flexibility.In Chamandoust et al. (2020), a real-time decentralized energy management for hybrid energy systems being compatible with sudden changes, including the failure of certain devices, in network structure is presented.The energy management problem was also defined as a non-cooperative, competitive model.In the above studies, only the connection of energy hubs and smart homes with each other and in connection with the distribution network or MG has been considered, and power exchange between different MGs and the distribution network in normal operation mode has not been investigated.A smart distribution system may consist of several MGs.It can be shown that connecting multiple MGs together or with a distribution system can create stronger control and more reliability in future smart distribution systems.Operators of distribution systems and MGs can benefit from lower operating costs, and customers can benefit from a more reliable and cheaper source of electricity.Therefore, it is necessary to consider the multiple connections of MGs (Yin et al., 2018).In Padmanaban et al. (2023a), a hybrid structure of market operators and distribution networks in a system consisting of several MGs is presented.The controller used is a hierarchical two-level controller, and the capabilities of this system in optimal control of MGs, including distributed energy resources, have been studied.In Yamashita et al. (2021), the optimal rearrangement of a set of networked MGs is proposed to provide optimal network power for a one-day period.For all MGs connected to the main grid and also those islanded ones, optimal load flow has been used to determine the output of distributed generation resources and inter-regional power exchange of MGs, and hourly technical and environmental restrictions have been considered.In Padmanaban et al. (2023b), a hierarchical optimization algorithm to coordinate the exploitation of distribution systems and several MGs is proposed.This paper only considers the grid-connected mode of MGs, and the uncertainty of distributed generation resources and load demand is not considered.In Tian et al. (2015), a tri-objective optimal performance of a smart hybrid energy system (SHES) with customer participation, aiming to minimize operation costs, emission pollution, and customer satisfaction is presented.The system uses demand response programs like demand curtailment, demand shifting, and onsite generation.The shuffled frog leaping algorithm (SFLA) is used to generate nondominated solutions, and the hybrid approach of fuzzy method and weight sum is used to select the best solution.In Zhang et al. (2021), a probability index to control voltages and currents in lines and buses for some MGs is proposed.In Arefifar et al. (2016), a self-healing structure for fault occurrence in networked MGs is proposed, and the output of distributed generation resources in this condition with the normal operation mode is compared.Decentralized energy management was used for self-healing mode, and centralized management was used to optimize distributed generation resources in MGs.The exchanged power in MGs and the penalty factor of this power in normal operation mode are not included.Furthermore, load flow restrictions and the voltage of buses are not investigated in this study.In Ahmadi et al. (2020), a method for power distribution of energy storage devices and sharing of renewable energy resources in a network, including networked MGs, is proposed.The problem was also formulated as a multi-objective optimization model where MGs are networked based on predetermined priorities.A new method for fair and sustainable energy sharing among networked MGs with minimum information received from the upstream network is proposed.The innovations of the proposed method are its application at the sellers' level and the introduction of a new pricing mechanism.In all researches conducted for the normal operation of networked MGs, only centralized management has been used, and their goal has been to meet the demand of consumers in the most economical way possible.In order to cover the existing gap and improve the energy management system in previous works, especially (Azizivahed et al. 2017), a flexible distributed management for optimal management of generation and exchanged power between grid-connected MGs in normal operating mode is proposed in (Liu et al., 2022).In Holland (1975), the research explores dynamic distribution feeder reconfiguration for improved grid performance, addressing operational issues, and enhancing energy delivery, loss, and cost in energy storage, distributed generation, and solar systems.In (Al Salami, 2009), a joint operation of Distributed Generation Units (DGUs) and Shunt Capacitors (SCs) in the presence of a Demand Response Program (DRP) is proposed.The time of use (TOU) mechanism is used to alter consumption patterns and improve distribution system performance.Results show that using the proposed approach reduces energy loss, operational costs, and ENS and reduces energy not supplied.In Kennedy and Eberhart (1995), the study presents a multi-objective optimization model for dynamic feeder reconfiguration in smart networks, considering distributed generators, energy storage systems, and solar photovoltaic units.It also considers operational cost, energy loss, and voltage stability index as objective functions.Distribution Feeder Reconfiguration (DFR) and capacitor allocation are crucial in distribution systems to reduce power losses, improve reliability, and maintain voltage.However, the DFR problem is complex and nonlinear, making precise optimization methods necessary.In Liu et al. (2021), a hybrid optimization method for dynamic Distribution Feeder Reconfiguration (DFR) in distributed generation, energy storage systems, and photovoltaic units is proposed to effectively solving the complex optimization problem, combining particle swarm optimization and Modified Shufed Leaping algorithms.In Hamdan et al. (2022), the impact of renewable energy sources on distribution systems' operation and security is explored, introducing dynamic distribution feeder reconfiguration as an efficient approach for managing energy loss and operational costs.
Table 1 compare the utilized optimization algorithm to optimize the objective function defined to solve the energy management problem.

Innovation of the study
The aim of this study is to: (1) Investigate the effect of increasing storage capacity on MG's management using simultaneous reconfiguration and unit commitment.
(2) Combine reconfiguration and unit commitment in a comprehensive model.
(3) Investigate the effects of increasing storage capacity on MG's performance.
(4) Provide a new algorithm and objective function to solve the problem.
(5) Investigate the effects of increasing the storage capacity on the exchanged power, MG's benefit, and power exchange with the upstream network.
Additionally, the ability of a recently developed optimization method (GRSA) to solve the specified objective function is tested.

Overview of GRSA
A novel Metaheuristic Algorithm (MHA) influenced by General Relativity Theory (GRT) is known as the General Relativity Search Algorithm (GRSA) (Beiranvand & Rokrok, 2015).In GRSA, an agent tensor is considered and moves in the least-active direction in a space devoid of external nongravitational forces.For updating the agents in GRSA, step length and step direction are independently determined using particle velocities and geodesics, respectively.GRSA starts with randomly generated initial agents in the problem geometry and dimension.Each agent (particle) is a feasible solution to the problem represented by a tensor.According to general relativity theory, a particle follows a geodesic path depending on the gravitational fields around the curved space-time and its energy momentum.It goes toward the optimum location, where there is less action.The objective function of the optimization problem is determined for each particle.The velocity and geodesic tangent of a particle serve as the basis for determining the step length and step direction used to update its position.
Large gravitational fields substantially impact how other particles construct geodesics, although how these particles evolve mostly depends on their geodesic tangent and energy momentum.GRSA evolves to solve the optimization problem by repeatedly computing step length and direction for each particle position.Step length and step direction in GRSA are calculated using existing relativistic equations for energy-momentum, the geometry of curved space-time, and geodesic tangent vectors.The Einstein's field equation, which also produces a new position for the particles, applies the gravitational field of particles in space time.The simplified GRSA flowchart is shown in Figure 1, and further information about this optimization technique is provided in (Beiranvand & Rokrok, 2015).The result of the paper shows that GRSA can be used to optimize large amounts of data with good performance in solving optimization problems.Table A1 lists the parameters of the utilized optimization algorithm.
The steps of the proposed GRSA approach are illustrated below: (i) Generate a random initial tensor for population of particles, (ii) Divide initial tensor to some subspaces uniformly, (iii) Calculate Action (cost function) for all particles, (iv) Assign ratio of kinetic energy to the mass energy conversion for each particle, (v) Calculate velocity of particles, (vi) Compute step length of motion for particles, (vii) Compute step direction for particles, (viii) Update position of particles, (ix) Perform mutation operation for the number of S particles with the worst positions using Einstein's equation, (x) Repeat steps (iii) to (ix) until the stop criteria is satisfied, (xi) End.

Mathematical modeling
Increasing economic efficiency is a significant and inalienable issue that power system owners face.Therefore, examining ways of increasing MGs' benefit will be one of the most involved problems.Some methods to achieve the desired goals include UC and reconfiguration.Simultaneous use of UC and reconfiguration in various ways, such as reducing losses, increasing power transfer capacities, and so forth, can increase economic efficiency (Jabbari-Sabet et al., 2016).Here, an increment in storage capacity has been regarded to investigate its effect on MT's

Algorithm
Reference Adaptability Convergence Speed power exchange, MG's benefit, and power exchange with the upstream network.This paper considers some device parameters as decision variables per hour: P mt , P bat , P grid, and n_topology.Therefore, the decision variable vectors of the main structure that must be calculated for each hour and the day ahead are equal to 6 and 144, respectively.In another case, the system will be checked for increased MG storage capacity, and additional battery variables will be added to the decision variables.This results in an increase of 7 to 168 for each decision variable that needs to be computed for the hour and day ahead.

WT probabilistic model
In recent decades, the increasingly expansion of wind power generator applications in MG and grid networks as renewable, clean power is visible.Wind speed data is considered an input of equipped WT in a third-duct bus.The collected data over the 12 years (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011) for each hour of the day ahead is the databases.This indicates that there will be 12 distinct wind speeds during the day.
The following is how the Weibull parameters are determined (Jabbari-Sabet et al., 2016): The following is the definition of the Weibull density function (f(w)) for each hour (Chamandoust et al., 2020): The method for calculating wind speed is based on matching the Weibull Cumulative Distribution Function (CDF) graph with a random number for each hour in the range [0, 1].By applying this method, 24 wind speeds will be achieved individually.The calculation of P wind based on wind speed for each scenario is as follows (Jabbari-Sabet et al., 2016): The method used to convert the wind speed forecast into the wind power forecast determines the stochastic model of a wind unit's wind power production.The examination of the wind speed/wind power curve of the wind turbine generator is used to carry out this transformation.The wind power forecast distribution differs from the wind speed forecast distribution because of the nonlinearity of the wind power curve.
For undefined inputs like wind speed and load demand, the MCS, which models uncertainty, produced various scenarios.As a result, the system is examined in various generated scenarios based on deterministic inputs.For scenario aggregation, the expected value (f) is calculated as follows (Yin et al., 2018): A stopping rule can be used to decide whether or not the estimation appears to be precise enough throughout the simulation in order to determine the number of samples to be used in advance.After each sample is obtained, there is no necessity to recheck the stopping rule.The simulation is often divided into a number of batches, with a specific number of samples in each batch.After every batch, the stopping rule is examined; if it is not satisfied, a new batch is executed.The so-called coefficient of variation (C vx ) is defined as follows (Jabbari-Sabet et al., 2016): The outcome is satisfactory, and the simulation can be ended if c vx would be less than a certain relative tolerance.

Load model
A normal distribution function is used to model the uncertainty of the load (Padmanaban et al., 2023a).
Due to its stochastic nature, the actual peak load and the predicted peak load will differ.Thus, load forecasting uncertainty is a crucial factor in efficient load dispatch.The modelling of the difference would be as a normal distribution function.

Objective function
By subtracting cost from income in the ways outlined below, OF, as the benefit of MG, is obtained as follows (Chamandoust et al., 2020): The overall system income, which includes revenue from the sale of thermal energy as well as revenue from the sale of electrical energy to customers in the microgrid control area, is the first term of the objective function.The overall operating cost is the second term in the objective function.This cost includes the cost of purchasing electrical energy from independent generator units, the cost of purchasing energy from the local grid, the cost of purchasing gas for thermal loads in the time that thermal energy production is insufficient (included in the boiler cost function), the cost of producing energy using generator units that are part of the micro grid, such as microturbines, fuel cells, PV and wind turbines, and the cost of an energy storage system.

Cost function
Cost includes C mt , C wind , C bat , c network , c loss and c switching .The overall cost is formulated according to equation ( 10) (Yin et al., 2018).
In equation ( 10), C mt includes C Fuel;mt , C O&M , C st;mt , C capital;mt and C em;mt .The turbine cost is expressed as equation ( 10) in which C capitalÀ wind and Com wind are modeled as follows (Yin et al., 2018): The control and management of generation changes are always needed for storage devices.One of the most significant components of MG's storage devices is batteries, which appropriately reduce the mentioned fluctuations.Battery cost is calculated as follows (Padmanaban et al., 2023a): The cost of the network is primarily due to the power purchased from the global network.Therefore, reducing or increasing the amount of purchased power directly affects network costs.The network cost is formulated in the below equation (Chamandoust et al., 2020).
The losses are calculated based on the losses of lines per hour, which after the backward/forward load flow study is done as follows (Chamandoust et al., 2020): The C switching , which results from reconfiguration and includes initial installation expenses and the costs associated with changing topologies by opening some lines and closing others, is as follows (Jabbari-Sabet et al., 2016):

System constraints
It is assumed that the MG can interchange power with the upstream network because it is linked.Voltage magnitude, power balance, and other limitations must be within acceptable bounds to meet the stability standards.Therefore, concerning the existing constraints and load demand, power exchange (buy power) should be made with the upstream network for some hours, especially peak load hours.These are the system limitations: (1) Topology: MG topology needs to be radial and loop-free.
(2) Node voltages need to stay within reasonable bounds, where is in the acceptable voltages (V min <V K <V max ).
(3) The maximum allowable current (I max K ) must not exceed the branch currents.(4) Power balance constraints should be met, and all loads should be supplied.
According to the amount of power that would be exchanged with the upstream network, the MG must be capable of operating at less than the maximum amount allowed by the exchange network ( P grid � � � � <P max grid ).Equation ( 16) implies that the production capacity of an MT must be within the limits of its permissible production unit (P min � P mt � P max ) (Chamandoust et al., 2020).
Equations ( 17) and ( 18) show the battery's charging and discharging power within the permissible battery-defined range (P batÀ min � P bat � P batÀ max ).

Solving method
The first step of the implemented algorithm in each hour of the current scenario, which is illustrated in Figure 3 (Jabbari-Sabet et al., 2016), is to use a probabilistic method to calculate the demand at each load location and the output power of the WT.Therefore, the matrix dimension for day-ahead load demand and WT output power in the current scenario equals 1 × 24 and 10 × 24 (10 bus load demand in each hour), respectively.The next step is the development of decision variables over a 24-hour period based on the GRSA algorithm with respect to their limitations.Additionally, all the decision factors for the day ahead are simultaneously optimized.The quantity of MG's benefit, ideal unit set points, and MG's topology for each hour are carried out after sufficient scenario creation.Next, it is decided what the expected value of each variable will be.As a suggestion for the next day, the average for continuous variables, MG's advantage, and the most common topology of each hour are found.The studied MG consists of three MTs, a WT, and one battery.This MG is seen in Figure 2, which is connected to the upstream network on one bus.
The second condition, which shows an additional battery in 8 th bus in addition to the primary components of the MG, is where the impact of the storage capacity increase was examined.

Simulation result and discussion
In the implemented MG, shown in Figure 2, all the loads and requirement data are the same as the parameters presented in (Lotfi, 2020).Table 2 shows the codes attributed to each of the 11 acceptable topologies for each hour in the MG.This code demonstrates the lines that are active or unused.The uncertainty values of WT output and load demand for each hour have been determined and are shown in Table 3.Additionally, Table 4 presents the hourly power market price.Two cases serve as the foundation for the structure of the paper, which can be described in more depth as follows: First: analyzing and optimizing MG's benefit in using probabilistic reconfiguration and UC in the presence of one battery.
Second: analyzing and optimizing MG's benefit in using probabilistic reconfiguration and UC in the presence of two batteries.

Analysis of defined cases
The results of the system parameters after applying the implemented algorithm are presented in Table 5.As it is obvious, due to the low power price early in the day, the network power exchange is such that the battery has started charging and MTs capacity production is less.The numerical result shows that the behavior of the additional battery is similar to that of the main one.It starts charging in the early hours of the day and discharging in the peak load condition.In the hours of (15-22), a higher rate of sold energy is visible in the second case.Additionally, purchased power from the upstream network has been reduced in the hours between 19 and 22 because of the second battery presence.It is also observed that 1 th and 11 th topologies have the most repetitions.To accurately investigate the obtained results, analyses are shown in the next section.The exchange of power with the upstream network, the battery power exchange, and the sold and purchased power of both cases in each hour are displayed in Figures 4 to 6, respectively.A comparison of two cases in peak load hours (dotted area) depicted in Figure 5 shows that power exchange with the upstream network, purchased power, is lower in the second case.In Figure 6, the second case has similarly superiority over the first case, as the purchased power in hours (19-20) is much lower and in hours (21-22) is slightly higher.

First case
The comparison between the obtained results of this study and Jabbari-Sabet et al. ( 2016) regarding MG's benefit would be available in Table 6.It should be noted that the results of this research, which uses the GRSA for optimization, have improved significantly compared with the same situation in (Jabbari-Sabet et al., 2016).

Second case
In this section, SCIEs in MGs will be investigated in two cases.It is examined how this strategy affects MGs' benefits as it is presented in Table 7 and Figure 7.The numbers listed in Table 7 are displayed with the words A, B, C, and D, respectively.Figure 7 can graphically express the difference between these values.The values associated with the letter D are more significant than the others, as it is obvious in this Figure .One of these values, about 4420 cents, relates to the difference in values of MG's benefits in the second case, which is lower than that of it in the first case, about 4029 cents.In fact, the presence of the second battery make simultaneous use of UC and probabilistic reconfiguration more effective in increasing the MG's benefit.Overall, the additional battery in both modes of operation leads to an increase in MG's benefits.Furthermore, the superiority of the method presented in (Jabbari-Sabet et al., 2016) is understandable through the values shown in both cases.

Data analysis
Many statistical parametric tests are based on normally distributed data.Here, the normal distribution of the data is made with the Kolmogorov-Smirnov test.The obtained result shows that the p-value for most of the variables is more than 0.05, and their distribution is normal.The hypotheses of H1, H4, and H3 in peak load hours are examined using "sign test," a non-parametric version of the paired sample t-test.The "Pearson correlation coefficient" is also used to analyze additional hypotheses.The following are the hypotheses of this study:

Results and discussions
Table 8 lists the sign test results for H1, H2, H3, H4, and H5.In addition, it shows the mean and standard deviation of the studied factors in two cases.The results show that the storage capacity increment has not statistically changed all five variables (P MT1 ,P MT2 ,P MT3 , P grid and P bat ) of MG's structure.The hypotheses of H1 (only in a 24-hour period) and H4, as their p-values are less than 0.05, are confirmed.Therefore, the variables that have meaningful changes are in bold type.In addition, concerning the difference between lower and upper limit values with a 95% confidence level, a comparison of the mean values of variables can be statistically derived.The comparison based on the mean value of the variables also yields similar results.Meanwhile, comparing the changes in two variables of P MT1 and P grid clearly shows further change in the P MT1 .There is no meaningful correlation between D1, D2, and D3 in the 24 hours of the day.In other words, the change in these variables will not necessarily be associated with each other.In some conditions, there is a negative correlation between two variables.It means that the change in one variable is in the reverse direction of the other.Conversely, the analysis of the correlation between defined variables in peak load hours shows that approximately the same results, except in some cases with different methods, are obtained.

Conclusion
In this paper, a microgrid including wind turbines, gas turbines, and a battery is considered, in which the costs are minimized with the optimization algorithm.It analyzes storage capacity increase effects (SCIEs) in the MG's operation.To be more specific, we added a battery to this system, and the results proved that during the peak hours, the system was profitable, and its performance improved.The numerical result shows that the behavior of the additional battery is similar to that of the main one.It starts charging in the early hours and discharging in the peak load condition.In the second case, more sold energy is visible in the hours of (15-22).Additionally, purchased power from the upstream network has been reduced in the hours between 19-22 because of the second battery presence.As it is evident, applying a storage capacity increment leads to an increase in all benefits connected to the simultaneous use of UC and probabilistic reconfiguration.To give more details, in the only UC method, there is a positive change from the first to the second case.In the simultaneous use of UC and probabilistic reconfiguration, there is also an improvement in MG's profit.From sign test results in applying the proposed scenarios, the change in Pgrid during both 24-hour and peak-load-hours period would be confirmed.Additionally, in applying storage capacity increment, changes in the output power of microturbines are not in reversed in most cases, which can be helpful.

Figure
Figure 3. General organization of the employed algorithm.
Figure 4. Charge and discharge characteristics of both batteries.

Code 1 th case 2 th case 1 th case 2 th case 1 th case 2 th case 1 th case 2 th case 2 th case 1 th case 2 th case 1 th case 2 th case
Table 9 lists the correlation in two periods between defined variables as below: D1= P MT1 variation in the pass from Case1 to Case2 D2= P MT2 variation in the pass from Case1 to Case2 D3= P MT3 variation in the pass from Case1 to Case2

Table 7 . Comparison of MG's benefit in both cases Mode of operation Mean value of MG's benefit Second case (cent) First case (cent)
Figure 7. MG's benefit in both cases.