Battery Swapping Station Service in a Smart Microgrid: A Multi-Method Simulation Performance Analysis

Abstract

The integration of Battery Swapping Stations (BSSs) into smart microgrids presents an opportunity to optimize energy generation, storage, and consumption. However, there exists a gap in the literature regarding the detailed analysis of the profitability of integrating a BSS within a smart microgrid, particularly utilizing second-life batteries for storage and renewable energy sources for generation. This study aims to address this gap by employing a multi-method simulation approach to thoroughly investigate the economic viability of such integration. The simulation model developed for this study is a digital twin of the microgrid, incorporating components such as the BSS, renewable energy sources (wind and photovoltaic), second-life battery storage, and utilities. By optimizing energy flows within this model, considering the cost-effectiveness of diverse generation sources and prioritizing the utilization of renewable energy, we aim to provide a comprehensive assessment of the economic benefits. Furthermore, the simulation takes into account crucial factors including battery swapping operations, warehouse management, and battery charging scheduling. The profitability analysis undertaken in this study is grounded in the objective of minimizing total costs while effectively meeting the energy demands of residential loads. Ultimately, the integration of the BSS into the smart microgrid not only targets economic efficiency but also strives to maximize the utilization of second-life batteries, contributing to the concept of a circular economy.

1. Introduction

A new paradigm of electricity production and consumption is being defined in the global landscape to fight the climate crisis and increase the overall efficiency of the energy system. Within this broader context, various strategies and methodologies have been proposed and developed by the scientific community to mitigate the human impact on the environment, particularly in transportation and energy [1].

In recent years, there has been a noticeable increase in the adoption of electric vehicles (EVs). However, certain challenges still hinder their widespread integration, and one of these challenges is the issue of extended recharging times. A potential solution to address this concern is offered by Battery Swapping Stations (BSSs) [2]. These stations allow users to swiftly exchange their depleted or nearly depleted batteries for fully charged ones [3]. They enable the reduction of recharging times to just a few minutes and allow for efficient scheduling of recharging times for depleted batteries [4]. As a result, the integration of BSSs can contribute to a significant reduction in greenhouse gas (GHG) emissions. However, to maximize the benefits of BSSs, it is essential to integrate them into intelligent electrical systems, such as smart microgrids, that heavily rely on renewable energy sources [5]. Such integration can further enhance the sustainability of the transport system by utilizing renewable power generation and facilitating efficient energy management [6]. The management of BSSs should focus on two aspects: individual-level management to ensure the efficient utilization of the battery fleet in terms of recharging and decommissioning, and management of interactions with the electricity grid and other associated elements [7].

In the literature, considerable attention has been given to researching the optimal scheduling and coordination in microgrids with BSSs. In [8], the authors introduce a bi-level optimal scheduling model to address the coordination challenges between an isolated microgrid (IMG) and electric vehicle BSSs in scenarios involving multiple stakeholders. To solve the model, they devise a hybrid algorithm called JAYA-BBA, combining a real/integer-coded JAYA algorithm and the branch and bound algorithm (BBA). The research in [9] presents an optimal dispatch strategy for a grid-connected microgrid featuring a battery swapping station and renewable energy sources. By utilizing particle swarm optimization (PSO) and a penalty function method, the authors aim to minimize power interaction with the distribution network, enhancing the efficiency and effectiveness of the microgrid system. The authors in [10] introduce a binary integer linear programming (BILP) model to jointly plan electric vehicle battery swapping stations and distribution grids with centralized charging. Their methods incorporate probabilistic estimation, integer programming, and nonlinear optimization to address planning and optimization challenges. The paper in [11] employs a decision matrix to assess economically viable options for scheduling battery swapping stations within smart microgrids. This comprehensive approach examines factors such as demand response, renewable energy sources, and market interactions, shedding light on the potential profitability and success of battery swapping stations.

A key point to discuss when considering BSS integration in a migrogrid is the energy management flow through the system. In the literature, [12] proposes a real-time energy management model for a smart-community microgrid equipped with battery swapping and renewable energy sources. Their real-time energy management algorithm, rooted in Lyapunov and queueing theory, ensures robust performance by adapting to uncertain future information. In [13], the authors put forth a method to optimize power source utilization within a network of flexible loads. Their approach employs Lagrange and KKT multipliers to tackle the optimization problem, considering constraints and uncertainties. The paper in [14] delves into the optimal power flow dynamics of microgrids featuring BSSs and Var Compensators (VCs). The authors examine energy arbitrage opportunities through BSSs and enhance voltage stability using VCs. The paper in [15] introduces a Cyber-Physical Energy Management System for optimizing the sizing and operation of networked nanogrids with a BSS. By utilizing various methodologies, the authors tackle challenges related to energy management, cyber defense, and robust optimization to design efficient and resilient nanogrids. The authors in [16] focus on optimal sizing of photovoltaic generation and battery-based energy storage in off-grid nanogrids. Through robust optimization approaches, they strive to address uncertainties and optimize capacity planning. The authors propose a mathematical model to optimize battery swapping station (BSS) loads for capacity enhancement in distribution systems. By maximizing demand response, they aim to improve utility operator performance.

Both the existing literature and the problem formulated here recognize the importance of integrating various components such as BSSs, Renewable Energy Sources, and storage units. This study highlights how these components interact within the microgrid and contribute to its overall operation and profitability. The authors in [17] present an optimized placement strategy for battery swap stations (BSSs) in microgrids with micro-pumped hydro storage, photovoltaic, wind, and geothermal distributed generators. Through mathematical formulations and optimization techniques, they address challenges associated with EV charging times and cost-effectively size BSSs for maximal efficiency. The study in [18] proposes a coordinated planning approach that integrates the charging and swapping stations with the active distribution network based on electric vehicle spatial–temporal load forecasting. Using algorithms and case studies, the authors explore the efficient spatial–temporal distribution of EV charging, providing valuable insights into planning and operational strategies.

In Table 1, there is a summary of the literature referenced in this work in which are highlighted the methods and the main focuses of the different papers. The last row shows the method used in this work and the main focus in order to compare the proposal and the existing literature. While the existing literature employs various optimization techniques, algorithms, and mathematical models, this study also adds a simulation-based approach. This allows for a detailed analysis of the microgrid’s operation, considering multiple components and their interactions in a dynamic manner. The use of Discrete Event Simulation and Agent-Based modeling adds a layer of realism and complexity to the analysis. The management of energy flows is a common theme across the literature and this study. The optimization of energy transfers, balancing supply and demand, and utilizing renewable energy sources are discussed in both contexts. Unlike the referenced literature, the method proposed here for scheduling, coordinating, and managing energy flows between the BSS and the microgrid utilizes two algorithms. The first algorithm rationalizes energy flows among different grid components, while the second algorithm sizes the storage formed by the second-life batteries. Downstream of these two algorithms, the discrete event simulation (DES) and agent-based multi-method simulation approach are used to implement the resulting decisions.

Integrating a BSS and a microgrid requires coordination and synchronization between the two entities. In many cases, game theory tools and models have been utilized to address the problem [7]. Various coordination models have been proposed, such as peer-to-peer and leader–follower models, which facilitate energy exchange and revenue generation for prosumers [19]. Ni et al. [20] introduce an alternative architecture called a charging-swapping-storage integrated station (CSSIS). The management system employs the Stackelberg Game, with the microgrid acting as the leader to determine the optimal operating point and maximize profit by considering the cost of internal energy exchange with the CSSIS.

Based on the scientific literature presented here, we explore the profitability of integrating a Battery Swapping Station within a microgrid in different settings. Compared to the previously mentioned approaches, the distinguishing feature of this work is the utilization of batteries that have reached the end of their useful life for electric cars. These batteries are repurposed for a second-life battery storage system [21] to improve the management of the battery fleet, considering their gradual degradation even when discharging energy to the grid. The difference between first- and second-life batteries can be summed up as in [22], which presents a comparative analysis between new batteries used in electric vehicles (EVs) and second-life batteries repurposed for stationary applications, specifically energy storage systems (ESSs) [23,24]. This integration involves implementing a management system that utilizes decommissioned batteries [25] from BSS users to create an Energy Storage System. The Energy Storage System serves as storage for two renewable energy power plants, namely photovoltaic and wind power plants, while also considering the presence of consumer loads within the microgrid. To examine this, we conduct a multi-method simulation [26] performance analysis of battery swapping station services in a smart microgrid. A similar approach is taken in [27], but the paper lacks a consideration of charging efficiency and battery degradation in its calculations and does not include renewable energy sources in its proposal. Performance is assessed by developing a digital model of a smart microgrid, which includes a battery swapping station, storage, renewable energy sources [28], and utilities. This study shares common research objectives with the existing literature, aiming to optimize microgrid operations through BSS integration. However, it uniquely focuses on evaluating the economic viability of this integration using a simulation-based analysis, incorporating DES and Agent-Based modeling for depth and realism. Notably, the study explores off-grid operation to enhance self-sufficiency and employs second-life batteries, adding an additional layer of sustainability and economic complexity to the analysis. In summary, this work aims to answer the following research questions:

• RQ1: How can battery swapping stations be optimally managed and integrated with renewable energy sources and microgrids to efficiently utilize the battery fleet?
• RQ2: What is the profitability and performance analysis of integrating a Battery Swapping Station within a microgrid using decommissioned batteries from electric vehicles to create a second-life battery storage system, and how does this impact the management of the battery fleet and gradual degradation?

Table 1. The survey of the existing literature and the methodological focus of the present work.

Reference	Method	Focus
Li, et al., 2018 [8]	Bi-level programming approach combining JAYA and BBA algorithms.	Optimizing scheduling between isolated microgrid (IMG) and BSS.
Yan, et al., 2019 [12]	Real-time energy management model using Lyapunov and queueing theory.	Integrating battery swapping, renewables, and residential load supply.
Infante, et al., 2022 [13]	Optimization using Lagrange and KKT multipliers with constraints.	Optimization of power source utilization in flexible load networks.
Jordehi, et al., 2020 [14]	Analyzing energy arbitrage opportunities and voltage stability enhancement.	BSS and Var Compensators for optimal power flow in microgrids.
Jordehi, et al., 2021 [17]	Mathematical optimization for BSS placement with mixed energy sources.	Efficient BSS placement considering various distributed generators.
He, et al., 2023 [18]	Algorithmic coordination of charging and swapping based on EV load forecasting.	Coordinated planning and management of EV charging and swapping.
Garcia-Guarin, et al., 2020 [11]	Decision matrix for assessing BSS scheduling strategies in smart microgrids.	Profitability and success of BSS integration in microgrids.
Ban, et al., 2019a [15]	Cyber-physical energy management with robust optimization for nanogrids.	Optimal sizing and operation of nanogrids with battery swapping.
Ban, et al., 2019b [16]	Formulation and optimization of PV and storage sizing in off-grid nanogrids.	Efficient sizing of renewable energy and storage components.
Song, et al., 2019 [9]	Optimization algorithm for dispatch strategy in grid-connected microgrids.	Minimizing power interaction with distribution network using BSS.
Alharbi, et al., 2023 [29]	Mathematical model for optimizing BSS load flexibility in distribution.	Enhancing capacity of distribution systems with BSS load optimization.
Shaker, et al., 2023 [10]	Probabilistic estimation, integer programming, and nonlinear optimization.	Joint planning of BSS and distribution grid with centralized charging.
This work	Optimization of energy flows and size storage in a system involving a BSS and a microgrid. The resulting decisions implemented through DES and an AB multi-method simulation approach.	This work aligns with the existing literature in terms of optimizing microgrid operation with BSS integration, but it adds a distinct focus on evaluating profitability through simulation-based analysis.

Table 1. The survey of the existing literature and the methodological focus of the present work.

Reference	Method	Focus
Li, et al., 2018 [8]	Bi-level programming approach combining JAYA and BBA algorithms.	Optimizing scheduling between isolated microgrid (IMG) and BSS.
Yan, et al., 2019 [12]	Real-time energy management model using Lyapunov and queueing theory.	Integrating battery swapping, renewables, and residential load supply.
Infante, et al., 2022 [13]	Optimization using Lagrange and KKT multipliers with constraints.	Optimization of power source utilization in flexible load networks.
Jordehi, et al., 2020 [14]	Analyzing energy arbitrage opportunities and voltage stability enhancement.	BSS and Var Compensators for optimal power flow in microgrids.
Jordehi, et al., 2021 [17]	Mathematical optimization for BSS placement with mixed energy sources.	Efficient BSS placement considering various distributed generators.
He, et al., 2023 [18]	Algorithmic coordination of charging and swapping based on EV load forecasting.	Coordinated planning and management of EV charging and swapping.
Garcia-Guarin, et al., 2020 [11]	Decision matrix for assessing BSS scheduling strategies in smart microgrids.	Profitability and success of BSS integration in microgrids.
Ban, et al., 2019a [15]	Cyber-physical energy management with robust optimization for nanogrids.	Optimal sizing and operation of nanogrids with battery swapping.
Ban, et al., 2019b [16]	Formulation and optimization of PV and storage sizing in off-grid nanogrids.	Efficient sizing of renewable energy and storage components.
Song, et al., 2019 [9]	Optimization algorithm for dispatch strategy in grid-connected microgrids.	Minimizing power interaction with distribution network using BSS.
Alharbi, et al., 2023 [29]	Mathematical model for optimizing BSS load flexibility in distribution.	Enhancing capacity of distribution systems with BSS load optimization.
Shaker, et al., 2023 [10]	Probabilistic estimation, integer programming, and nonlinear optimization.	Joint planning of BSS and distribution grid with centralized charging.
This work	Optimization of energy flows and size storage in a system involving a BSS and a microgrid. The resulting decisions implemented through DES and an AB multi-method simulation approach.	This work aligns with the existing literature in terms of optimizing microgrid operation with BSS integration, but it adds a distinct focus on evaluating profitability through simulation-based analysis.

The evaluation includes several key aspects:

• Market Share Served: This refers to the number of users served by the swapping station.
• User Behavior: User behavior is reflected in the state of charge (SOC) of the battery when brought for swapping.
• Electricity Consumption: This aspect encompasses the energy demand from the conventional grid and the withdrawal of energy from battery storage.

The paper is structured as follows. The first section focuses on the operating principles of each agent involved separately, as well as their interactions. The second section provides detailed definitions of the different aspects of the system and describes the hypotheses on which the work is based. The third section examines the relevant cost structures of the model, presents simulation results, and concludes the study.

2. Problem Formulation

The objective of this study is to evaluate the profitability of integrating a Battery Swapping Station (BSS) into a smart microgrid system. A multi-method simulation approach was employed for the analysis, in particular, AnyLogic software version 8.8.1. was utilized to create a digital twin of the microgrid. The approach employed combines Discrete Event Simulation ([30]) and Agent-Based modeling. The scheme of the digital twin model is as shown in Figure 1.

In the simulation model, the top-level agent (Main) represents the smart microgrid, which consists of several components. These include the BSS containing two low-level agents: Battery and Car. Additionally, there is the Second-life Battery Storage unit, the two Renewable Energy Sources (RESs)—PV panels and a wind turbine—and finally, the Utilities component responsible for incorporating residential loads. The microgrid can operate in two modes: grid-connected or off-grid. In the grid-connected mode, it supplements internal generation with power from the traditional grid during periods of high demand. However, this study focuses on achieving off-grid operation, aiming for greater independence from the utility grid in terms of generation. Surplus renewable energy generated is utilized to charge the storage batteries, reducing the need to sell energy surplus to the utility grid. Consequently, there is a unidirectional energy flow from outside to inside the microgrid. The second-life battery storage can be recharged in two ways: overnight and daytime recharging. Overnight recharging occurs during off-peak hours when energy prices are lower. The process minimizes the cost of external energy and takes advantage of low demand from utilities. Overnight recharging is conducted in standard mode, requiring approximately 5 h for a complete recharge (0.2 C). Daytime recharging takes place during the remaining hours of the day, utilizing renewable sources to recharge the batteries in the BSS. Each hour, an assessment takes place to determine if surplus energy is available after meeting the demand. If an energy surplus exists, a decision is made whether to use it for a standard recharge on multiple batteries or a fast recharge on a smaller number of batteries. If the surplus is insufficient to charge all discharged batteries with a standard recharge, a fast recharge is performed on as many batteries as possible. To perform a profitability analysis of the integration of BSSs into a smart microgrid, we identified two critical elements for optimization: minimizing the cost of energy exchange across all system components and determining the storage composition in terms of the number and mix of types. The overall operation of the digital twin involves managing generation and demand, simulating the optimal transfer of energy between them, and aligning it with the activities of the BSS. The management of energy flows in the microgrid is influenced by consumer demand and cost-effectiveness. Energy usage from different sources is determined by economic considerations while considering availability. In this study, microgrid management can be based on either a system where the microgrid is owned by a distribution system operator (DSO) or a consortium of users who act as both producers and passive consumers. The difference lies in the profit distribution, where the DSO profits in the first case, while individual users benefit from the cost difference between the current generation and external grid energy supply in the second case.

3. System Components and Operational Framework

To delve into the workings of a Battery Swap Station (BSS) integrated into a smart micro-grid, it is important to understand the system components involved. The system comprises a BSS, renewable energy sources (specifically a wind turbine and a photovoltaic panel farm), a storage system consisting of second-life batteries, and utilities, including residential loads.

In the BSS, users (the Car agents) can swap their depleted batteries with fully charged ones, allowing them to continue using electric vehicles without the need for extended charging periods. The station manages the logistics of battery storage and retrieval.

The renewable energy sources play a vital role in the micro-grid.

The storage system, composed of second-life batteries, serves as an essential component of the micro-grid. It enables the storage of surplus energy generated by the renewable sources during periods of high production. This stored energy can be utilized during times of increased demand or when the renewable sources are less productive, ensuring a steady and reliable power supply.

The utilities represent the various loads within the micro-grid, including residential consumers. By integrating the BSS and renewable energy sources into the micro-grid, these utilities benefit from sustainable and efficient energy resources.

The simulation operates as follows (Figure 2). Each hour, a certain amount of energy is generated from the renewable sources and storage, while a certain amount of energy is required by the residential utilities and the BSS. These energy demands and supplies are compared and various logical processes are executed. The distribution of energy from generation to utilities is prioritized based on the unit cost of each energy source, with renewables having the highest priority, followed by storage and then the utility grid. When the renewable energy supply meets or exceeds demand, the demand can be fully met and the surplus energy is used to charge the second-life batteries in storage. If the renewable energy supply is less than demand, energy from storage or the utility grid is used to meet the demand. To determine which second-life battery to discharge to meet utility needs, the batteries are prioritized based on their state of health (SOH). The second-life batteries can be charged in two modes: nocturnal or diurnal. In the nocturnal mode, the batteries are charged using energy from the utility grid when it is at its lowest price. In the diurnal mode, surplus energy generated by the renewables is used to charge the batteries, either in a standard or fast mode depending on the amount of surplus energy available. As the batteries have a limited lifespan, the storage must be replenished periodically. The simulation model monitors the SOH of batteries in both the storage and the BSS and transfers batteries from the BSS to storage once they reach the end of their first life, to maximize the use of batteries in line with the principles of the circular economy. The batteries in the simulation are modeled as agents, with a state chart that tracks their status, including fast charging, standard charging, discharging, storage, and end of life. The BSS model simulates various operations, including swapping, warehouse management, and battery charging process scheduling. The model takes into account technical and economic evaluations to account for all associated costs and revenues. An optimization model is employed every hour to select the generation source that meets users’ requirements. The primary objective of this model is to achieve economic efficiency by determining the most cost-effective energy source.

The optimization model incorporates costs associated with energy generation but does not consider revenues received from utilities for each generation.

To incorporate the optimization model into AnyLogic, the GLPK (GNU Linear Programming Kit) library was utilized. By leveraging the capabilities of the GLPK library, the digital twin’s optimization model can effectively determine the optimal generation source, considering the objective of minimizing total costs. This integration ensures that the twin operates in an economically efficient manner, making informed decisions on energy sourcing and minimizing overall costs.

$$z_1=C_{WT}·kW{h}_{WT}\left(t\right)+C_{PV}·kW{h}_{PW}\left(t\right)+C_{SLBs}·kW{h}_{SLBs}\left(t\right)+C_{UG}\left(t\right)·kW{h}_{UG}\left(t\right)$$

(1)

$$kW{h}_{WT}\left(t\right)+kW{h}_{PW}\left(t\right)+kW{h}_{SLBs}\left(t\right)+kW{h}_{UG}\left(t\right)=De{m}_{RL}\left(t\right)+BS{S}_{Limit}\left(t\right)$$

(2)

$$0\le kW{h}_{Wt}\left(t\right)\le P_{Wt}\left(t\right)$$

(3)

$$0\le kW{h}_{PW}\left(t\right)\le P_{PW}\left(t\right)$$

(4)

$$0\le kW{h}_{SLBs}\left(t\right)\le kW{h}_{2discharge}\left(t\right)$$

(5)

$$0\le kW{h}_{UG}\left(t\right)<kW{h}_{U{G}_{Limit}}$$

(6)

The generation cost of a plant can be represented by a quadratic function of the generated power [31]. For example, for the i-th plant, it would be as follows:

$$C\left(P_i\right)=\alpha ·P^2\left(t\right)+\beta ·P_i\left(t\right)+\gamma$$

(7)

The coefficients $\alpha$, $\beta$, and $\gamma$ refer to maintenance, fuel, and labor costs, respectively. The cost per kWh of renewable generation is approximately zero, which is due to the absence of fuel usage and infrequent maintenance.

The objective function (Equation (1)) represents the total cost of generation offered to utilities. It includes costs associated with wind turbine generation ($C_{WT}$), photovoltaic (PV) generation ($C_{PV}$), energy from the storage composed of Second-Life Batteries (SLBs) ($C_{SLBs}$), and energy sourced from the utility grid ($C_{UG}\left(t\right)$).

Equation (2) represents the energy balance constraint, where the sum of energy generated from wind turbines ($kW{h}_{WT}\left(t\right)$), photovoltaic systems ($kW{h}_{PW}\left(t\right)$), storage composed of Second-Life Batteries ($kW{h}_{SLBs}\left(t\right)$), and the utility grid ($kW{h}_{UG}\left(t\right)$) equals the demand from utilities ($De{m}_{RL}\left(t\right)$) and the limit of the Battery Swapping Station ($BS{S}_{Limit}\left(t\right)$).

Equations (3)–(6) represent constraints on the energy generation from each source, ensuring that the generated energy does not exceed the maximum power capacity of wind turbines ($P_{Wt}\left(t\right)$) and photovoltaic systems ($P_{PW}\left(t\right)$), and the available energy for discharge from the storage ($kW{h}_{2discharge}\left(t\right)$). The constraint in Equation (6) ensures that the energy sourced from the utility grid ($kW{h}_{UG}\left(t\right)$) is within the limit ($kW{h}_{U{G}_{Limit}}$).

The generation cost of a plant can be represented by a quadratic function (Equation (7)), where $\alpha$, $\beta$, and $\gamma$ represent coefficients associated with maintenance, fuel, and labor costs, respectively. The cost per kWh of renewable generation is considered zero due to the absence of fuel usage and infrequent maintenance.

The cost of energy obtained from the utility grid is based on the average household user’s payment, adjusted for the time of day. A 10% reduction is applied to exclude transmission costs from high or very high voltage to medium voltage, benefiting residential users participating in the microgrid.

The cost of energy from the storage composed of Second-Life Batteries (SLBs) is considered to be zero, since the costs are treated as initial investment costs, not on a per kWh basis.

The objective function represents the total cost of generation offered to utilities, while the decision variables represent the generation rates from each source to meet the utilities’ demands. The cost coefficients in the model prioritize renewables and storage over externally sourced energy. The optimization of the objective function is subject to constraints, including the availability of each source at a specific time and the requirement to meet the entire demand.

3.1. Battery Swapping Station Operations

The battery swapping station model simulates different operations including the swapping process, warehouse management, and the battery charging process scheduling. The swapping demand is hourly [6], as in Figure 3, and refers to a general swap that must be associated with a specific battery category according to percentage defined in

Table 2. Car categories.

Car Category	Percentage [%]	Capacity [kWh]
A	16.9	20
B	35.0	30
C	46.0	40
D	2.1	100

.

The swapping process involves cars and batteries. The model generates an agent, which is a car, and then checks to see if there is a suitable battery for that agent. If there is one, the discharged battery begins charging and the warehouse battery reaches the mounting state. The model also accounts for backlog. The purposes of the scheduling process are many; overall, it provides for charging a specified amount of batteries based on demand forecast for the next hour, and it allows for fast charging of the fewest number of batteries possible as well as charging as many batteries as possible whenever there is a surplus of energy generation. Without loss of generality, the interarrival time of cars is generated in the model following a Gamma distribution. The Gamma distribution is characterized by shape parameter $\alpha$ and scale parameter $\beta$, allowing for the manipulation of variability levels. This continuous probability distribution includes the exponential distribution as a special case, as in [8] and in the present work (when $\alpha$ = 1). By adjusting the value of $\alpha$, it becomes possible to model variability that exceeds the exponential distribution when $\alpha$ < 1, and variability that is lower than the exponential distribution when $\alpha$ > 1. The versatility of the Gamma distribution enables the modeling of both high-variability and low-variability scenarios. The charging process can be categorized as either fast or standard. Fast charging fully charges a battery within one hour, utilizing an electric current equal to the battery’s capacity (referred to as 1 C). On the other hand, standard charging (referred to as 0.2 C) takes approximately five hours to complete.

3.2. Renewable Energy Sources and Their Operation Parameters

The operations of Renewable Energy Sources (RESs), the wind turbine and the photovoltaic panel farm, are based on assumptions derived from the scientific literature. The wind turbine is considered to have a rated power of 500 kW and its rated output is modelled as in [8].

$$P^{WT}=\left\{\begin{array}{c}0v<v_{in},v>v_{out}\hfill \\ {P_{*}}^{WT}·\frac{v-v_{in}}{v_{*}-v_{in}}{v}_{in}\le v\le v_{*}\hfill \\ {P_{*}}^{WT}{v}_{*}\le v<v_{out}\hfill \end{array}\right.$$

(8)

Its functioning parameters are described in

Table 3. Wind turbine parameters.

Wind Turbine Parameters
Speed	[m/s]
cut-in speed	2.5
cut-out speed	25
rated speed	12

as in [32].

The model includes just one wind turbine but it could also include more. In that case, the interaction between them must be taken into account [32]. The solar farm provides for about 500 kW peak power and its rated output is modelled as in [8].

$$P_{PV}=A_{PV}·{\eta }_{PV}·\zeta$$

(9)

where $A_{PV}$ is the irradiation area of each individual panel, ${\eta }_{PV}$ is the panel’s conversion efficiency, and $\zeta$ is the solar irradiation.

Its functioning parameters are described in

Table 4. Solar farm panel parameters.

Solar Farm Panels Parameters
Efficiency (${\eta }_{PV}$) [%]	14
Area ($A_{PV}$) $\left[\frac{m^2}{kW}\right]$	25.7
Mean Solar radiation ($\zeta$) $\left[\frac{kW}{m^2}\right]$	0.266257

:

It is meant to be made of polycrystalline panels whose efficiency is set at about 14% [33]. The photovoltaic plant is thought to operate only during certain hours of the day, from 5 a.m. to 8 p.m., whereas the wind turbine is supposed to work 24 hours per day. Wind and solar power systems are weather-dependent, which is why they are modelled using a stochastic model, which is, in both cases, the Weibull distribution (Equation (10)).

$$f(v,\lambda ,k)=\frac{k}{\lambda }·{\left(\frac{x}{\lambda }\right)}^{k-1}·e^{-{\left(\frac{x}{\lambda }\right)}^{k-1}}$$

(10)

The distribution for modeling solar power [34] and wind power [32] is constructed using different shape and scale parameter values, as shown in

Table 5. Weibull distributions.

Parameter	Wind	Solar
$\lambda$ (scale parameter)	2	284
$\alpha$ (shape parameter)	12	7.31

.

The plants have been sized on the mean hourly demand coming from both utilities and BSS; residential loads have been modelled referring to a summer day [31], as in Figure 4.

3.3. Modeling and Operation of Energy Storage System

The energy storage system is primarily designed to address the unpredictability of wind and solar energy while facilitating peak shaving and load leveling. It operates by storing surplus energy when available (charging the batteries) and discharging the stored energy when the supply does not meet the demand from utilities.

The size of the storage, determined through an optimization model, represents the number of available batteries. Considering the average hourly demand and the need to address the unpredictability of wind and solar energy, as well as demand variability, the objective function of the model aims to minimize the gap between supply and demand. This allows the smart microgrid to primarily operate in an off-grid mode.

The optimization model is inspired by the one described in [9], but in this case, it runs only once using mean values instead of 24 times per day (hourly). Constraints primarily pertain to the various types of batteries. The optimization problem is solved using the GNU Programming Kit Linear (GPLK) library, connected with the AnyLogic simulator.

The provided equations and explanations enable a mathematical representation of the optimization problem and provide a framework for finding the optimal solution in terms of battery categories and quantities. This contributes to the analysis of the system’s profitability and efficiency. The objective function denoted in Equation (11) aims to be minimized.

$$\begin{array}{c}\hfill z_2=|P_{BSS}+P_{RL}+{\Delta }_{BSS}+{\Delta }_{RL}-P_{WT}-P_{PV}-(C_A·SO{H}_{SLB})·N_A\\ \hfill -(C_B·SO{H}_{SLB})·N_B-(C_C·SO{H}_{SLB})·N_C-(C_D·SO{H}_{SLB})·N_D|\end{array}$$

(11)

$$\begin{array}{c}\hfill (C_A·SO{H}_{SLB})·N_A+(C_B·SO{H}_{SLB})·N_B+(C_C·SO{H}_{SLB})·N_C+\\ \hfill (C_D·SO{H}_{SLB})·N_D\ge {\Delta }_{BSS}+{\Delta }_{RL}+P_{BSS}+P_{RL}-P_{WT}-P_{PV}\end{array}$$

(12)

$$N_C>N_B$$

(13)

$$N_B>N_A$$

(14)

$$N_A>N_D$$

(15)

$$1\le N_A$$

(16)

$$1\le N_B$$

(17)

$$1\le N_C$$

(18)

$$1\le N_D$$

(19)

i = A,B,C,D refers to battery categories, and $C_i$ represents each category’s battery capacity, as in Table 2. The objective function (Equation (11)) represents the total cost of generation offered to utilities ($z_2$). It includes terms related to the energy demand from the battery swapping station ($P_{BSS}$), energy demand from residential loads ($P_{RL}$), variations in the battery swapping station energy demand (${\Delta }_{BSS}$), variations in the residential load energy demand (${\Delta }_{RL}$), energy supply from the wind turbine ($P_{WT}$), energy supply from the photovoltaic panel farm ($P_{PV}$), and costs associated with the second-life batteries in each category ($C_A,C_B,C_C,C_D$) multiplied by the state of health of the second-life batteries ($SO{H}_{SLB}$) and the number of batteries in each category ($N_A,N_B,N_C,N_D$).

The goal is to find values for $N_A,N_B,N_C,N_D$ that minimize the objective function $z_2$ while satisfying the constraints specified in Equations (12)–(19). These constraints define relationships between the numbers of batteries in different categories, ensuring certain conditions are met. For example, the constraint $N_C>N_B$ indicates that the number of batteries in category C must be greater than the number in category B.

Second-life batteries have previously been used in electric vehicles during their first lives. The state of health (SoH) is a parameter that can be utilized to determine the beginning and end of a battery’s life. The SoH is calculated by dividing the discarded capacity ($C_{discarded}$) by the total capacity ($C_{total}$) and multiplying by 100. The state of health is calculated as follows [35]:

$$SOH[\%]=\frac{C_{discarded}}{C_{total}}·100$$

(20)

For second-life batteries, the first life typically lasts from 100% SoH to 80% SoH, while the second life continues until 60% SoH. However, the end of the first life can be defined differently based on various factors [36].

The energy storage system comprises a combination of second-life batteries with different percentages. The number of batteries in the Battery Swapping Station (BSS) and the storage batteries are proportional to the current percentage of electric vehicles on the road. Each battery category has a specific capacity, as shown in Table 2, which provides data from the Association of Foreign Automotive Companies Operating in Italy in the Distribution and Sales of Motor Vehicles in 2019.

The aging process of batteries and second-life batteries is taken into account by considering the lost cycles, which are influenced by factors such as operating temperature, depth of discharge, state of charge, and electric current [37]. In this study, the aging process assumes a linear relationship between lost cycles and decreasing capacity, as the total number of lost cycles is relatively low compared to the threshold at which a non-linear aging process would occur [38]. Batteries and second-life batteries are assumed to operate within a state of charge (SOC) range of 20% to 80%, which is modeled using a Beta distribution [38].

When discharging second-life batteries to meet utility needs, the order of discharge is determined based on the SoH of the batteries. The batteries can be ordered either ascendingly or descendingly, resulting in a uniform or uneven level of degradation.

Second-life batteries can be charged in two modes: nocturnal or diurnal. Nocturnal charging involves recharging the batteries using energy from the utility grid at its lowest price, leading to a full recharge in standard mode for all discharged batteries. Diurnal charging, on the other hand, utilizes surplus energy generated by renewable plants. If the surplus energy is sufficient to increase the SOC of all discharged batteries by at least 20%, a standard charge is performed. Otherwise, the available surplus energy is used to charge as many batteries as possible in fast mode.

Both second-life batteries and batteries have a limited SoH and eventually need to be discarded. To optimize the use of batteries and adhere to the principles of the circular economy, the digital twin employs a mechanism to transfer batteries from the BSS to the storage when a battery from the BSS reaches the end of its first life and a battery from the storage reaches the end of its second life.

To facilitate the processes described above, batteries are modeled as agents with a state chart representing the different states they can transition through, including fast charging, standard charging, discharging, warehouse, and end of life. The batteries can change states on an hourly basis as the charging and discharging processes are managed on an hourly schedule, with batteries spending no more than an hour in the charging or discharging state, depending on the required SOC for a full charge.

4. Results

Anylogic was used to run simulations over a 20-year period. The decision to run the simulation over a 20-year period is rooted in the fact that this duration aligns with the expected lifetime of the key components within our system, including the PV panels and the wind power plant. The values assigned to parameters and variables vary across all simulation settings. In particular, those varying are the size of the energy storage (the number of batteries installed), range anxiety [8,39] (represented as the SOC with which customers bring batteries back), utility grid energy usage limitations, the number of batteries the BSS uses to serve the customers, and a parameter that manages the degradation mode of batteries as uniform or uneven. Data collected through simulations are discussed in the following sections. Simulations of the global digital twin’s operation were conducted across 162 scenarios. These scenarios were differentiated by varying certain model parameters, including the following:

• Range anxiety of station customers: This parameter represents the state of charge at which batteries are returned to the station. The scenarios included 30%, 50%, and 70% of the nominal capacity of the battery.
• Number of batteries for customer service at the swap station: Scenarios were tested with 400, 500, and 600 batteries available for customer use.
• Number of second-life batteries installed in storage: Different scenarios considered 14, 22, and 30 second-life batteries integrated into the storage system.
• Limit of energy that can be drawn from the grid: Scenarios were evaluated with limits of 1800 kWh, 2500 kWh, and unlimited energy withdrawal from the grid.
• Uniform degradation of batteries/non-uniform degradation of batteries: This parameter explored the impact of batteries degrading uniformly or non-uniformly over time.

By exploring these various scenarios, the simulations aimed to analyze the performance and outcomes of the integrated system under different conditions and configurations.

4.1. Payback Period

The payback period is approximately 2 years; as shown in Figure 5, it increases as the number of second-life batteries installed in the storage increases. Each of them involves a purchasing and decommissioning cost, as well as the cost of a charger. It is also demonstrated that as the SOC increases, the payback period decreases. This is due to the lower amount of energy supplied by the BSS to the customers.

4.2. Cash Flows

According to a positive payback period, the cash flows (Figure 6) are positive too; they also turn out to be much higher than investments.

4.3. Revenues

Revenues are sensitive to changes in range anxiety; as it rises, revenues fall because the BSS sells less energy to customers. Range anxiety represents the SOC with which the batteries are brought back to the swapping station.

Revenues can be also divided into amounts derived from the energy sold in the BSS and the amounts derived from the microgrid operation (actually from the energy sold to the residential utilities).

Microgrid revenues are higher than BSS revenues for a few reasons (Figure 7). First, there is an higher demand, and second, a limit has been imposed to the BSS. Unlike residential loads, BSS loads can go into backlogs; those backlogs actually represent free swapping for customers. Residential backlogs could have been predicted using a demand side management model (Figure 8).

4.4. Degradation Costs

The degradation cost of the batteries installed in the BSS is directly associated with the number of life cycles lost by each battery and, consequently, with the state of charge (SOC) at which they have been recharged (Figure 9). A higher SOC indicates lower utilization of the batteries, resulting in a reduced degradation cost. In other words, when the batteries are charged to a higher SOC, they experience less degradation over their lifespan, leading to cost savings in terms of battery degradation.

4.5. Utility Grid Energy

Energy can be also traded from the utility grid. This happens whenever renewable sources do not meet energy demand; this source of energy relates to an higher unit cost (Figure 10). Since the aim of the smart microgrid was mainly to work in off-grid mode, this observation was expected to occur as the number of storage batteries increased. However, this effect could have been reached only if the sizes of renewables also increased along with the amount of storage batteries; otherwise, there would not be much energy to be charged into storage.

4.6. Discarded Batteries

Using a uniform degradation model for second-life batteries makes the most out of the batteries. This way, a lower number of batteries reach their end of life (Figure 11).

The number of batteries which reach their end of life is different as the number of batteries in the BSS increases (Figure 12); this is because a higher number of them means they are less likely to be charged and discharged often, and so they will also be less likely to be discarded quickly.

4.7. Comparing Paybacks of BSS in Smart Micro-Grid and as a Stand-Alone Entity

Simulations results show that inserting a BSS in a smart microgrid is a profitable business (Figure 13). It seems especially profitable when compared to the operations of a BSS connected to the utility grid (Figure 5). Not only are the revenues higher, but the overall payback period is also much shorter.

What we have learned from the analysis of the data collected through digital twin simulations suggests that the business investigated in this study is profitable. The cash flows generated by the system are significant, and the investment in the Battery Swap Station (BSS) is expected to be recovered in a short period. This indicates that integrating the BSS within a microgrid and combining it with alternative energy sources can yield better results compared to operating the BSS as a standalone entity. Additionally, the reuse of second-life batteries which were previously used in electric vehicles proves to be a positive aspect of the business. These batteries have a lower market price compared to new electric batteries, and their longevity is considerable when they are managed. As a result, the cost of installing a storage unit using second-life batteries is optimal and fulfills its intended purpose. This approach allows for the full utilization of battery packs that would otherwise be prematurely recycled. The analyses conducted highlight the importance of a well-managed approach to the use of batteries in terms of degradation. By carefully managing the degradation process, optimal results can be achieved in terms of the timing of battery depletion. This knowledge can inform decision-making processes and contribute to the overall efficiency and success of the battery swapping system. Overall, the findings suggest that the integrated operation of a BSS within a microgrid, combined with the reuse of second-life batteries, has the potential to create a profitable and sustainable business model.

5. Conclusions

The BSS integrated into a smart micro-grid consists of a battery swapping station, renewable energy sources (wind turbine and photovoltaic panel farm), a storage system comprising second-life batteries, and utilities such as residential loads. Just like the existing literature, this study aims to optimize the operation of microgrids with BSS integration. However, here the emphasis is on evaluating the profitability of this integration, which involves comprehensive simulation-based analysis using AnyLogic software. This extends beyond optimization to consider economic viability. The proposal allows for efficient battery swapping, harnessing renewable energy, optimizing energy storage, and providing reliable and sustainable electricity to meet the demands of various consumers within the micro-grid. The results of the study demonstrate that contextualizing a battery swapping station within a microgrid and managing the two entities in a coordinated manner is more profitable compared to managing the station as a single entity. The coordinated management approach includes activities such as energy sales to residential consumers, the utilization of second-life batteries, and maximizing the use of renewable energy through storage. These strategies result in increased cash flows and significantly reduce the payback period. The payback period for the integrated management approach is approximately 2 years considered as a mean value, compared to a mean value of 5 years for single management. The profitability of the investment is further confirmed through calculations of Net Present Value and Internal Rate of Return.

Reusing batteries from the battery swapping station in storage proves to be a viable business strategy. It enables the avoidance of premature battery disposal and extends their overall lifespan. The impact of the storage included in the model, in terms of energy delivered compared to the total, is approximately 6%. This value could be increased by sizing renewable plants differently. This can be achieved by following the evaluation provided through a sensitivity analysis regarding the impact of varying the peak power of renewable plants. This analysis may influence the percentage of energy used by each source and, consequently, impact the revenues.

The study also highlights the importance of considering the timing of battery depletion and how they are handled. Managing batteries with a uniform degradation pattern minimizes the number of depleted batteries at any given time, allowing for efficient replenishment of the storage system. On the other hand, a non-uniform degradation pattern may lead to suboptimal utilization of batteries, resulting in more spent batteries than necessary.

The limitations of the proposed approach mainly stem from the fact that the simulation model relies on certain functional assumptions that may not always hold true. While the study focuses on evaluating the profitability of microgrid BSS integration, it may not encompass all relevant economic factors or external influences, such as policy changes and technological advancement. To assess these limitation, there are several potential directions to further develop this work, and the following options are particularly interesting:

• Sensitivity analysis regarding the utilization of renewable sources.
• Load prediction for the Battery Swapping Station (BSS).
• Management of a cluster of microgrids.

The first point aims to investigate how the variation in the nominal capacity of renewable plants impacts the cash flows of the model. This analysis would involve resetting the parameters defined in the current digital twin model. The second point involves adopting an alternative strategy to the current approach. It would entail removing the power constraint of the BSS and prioritizing its loads over residential ones. Consequently, it may be necessary to develop a demand-side management model for residential loads. The third point explores the management of a cluster of microgrids, allowing for energy trading between them. The objective is to optimize the coordination of loads in each microgrid and minimize reliance on the traditional grid.

These directions offer promising avenues for further research and can significantly enhance the current model. They provide opportunities to explore sensitivity, optimize load management, and investigate the benefits of interconnecting microgrids for energy trading.