Assessing the Impact of an EV Battery Swapping Station on the Reliability of Distribution Systems

: This paper proposes a comprehensive methodological framework to investigate the potential role of the grid-connected battery swapping station (BSS) with vehicle-to-grid (V2G) capability in improving the reliability of supply in future distribution networks. For this aim, we ﬁrst develop an empirical model for describing the energy demand of electric vehicles (EVs) and their resultant available generation capacity (AGC) that can be utilized for BSS operation. Then, on this basis, a quantitative method to quantify the e ﬀ ect of grid-connected BSS on distribution system reliability is proposed. In order to capture the uncertainties associated with EV users’ behaviors, Latin Hypercube Sampling (LHS) methods were utilized to obtain the time series of the BSS tra ﬃ c ﬂow and initial State of Charge (SOC) of each EV battery, according to the probability distribution of corresponding uncertain factors whose statistics are obtained from real-world historical data. cient method to assess the reliability beneﬁts of BSS with an explicit consideration of BSS characteristics (including physical structure, charging strategy, and swapping model) is proposed, which is in contrast to most of the extant studies that only focus on the EV fast-charging paradigm and thus provide a practical tool to analyze the potential value of BSS resources in future distribution systems. (ii) The randomness of EV user behaviors in BSS operation is explicitly modeled and considered. (iii) The LHS-based sequential simulation is used to improve the accuracy and convergence performance of the evaluation, as compared to the traditional Sequential Monte Carlo Simulation (SMCS) method. To verify the e ﬀ ectiveness of the proposed approach, numerical studies are conducted based on a modiﬁed IEEE 33-bus distribution network. The simulation results show that with V2G capabilities, BSS can improve reliability to a certain extent and reduce the adverse impact on the reliability of the distribution network. In addition, EV resources should be orderly managed and exploited; otherwise, uncoordinated charging activities could impose a negative impact on the reliability performance of distribution networks. Finally, it is also shown that under the same sampling time, LHS-based sequential simulation could be better than SMCS in the accuracy and convergence speed of the procedure.


Introduction
With the rapid development of the social economy and the pressure on energy and environment, electric vehicles (EVs), as a means of transportation using clean energy, have received extensive attention in recent years. For the power system, EVs play dual roles as a controllable load and power source. The charging process can be regarded as loading from the electrical equipment, and the Therefore, in the battery swapping mode, the user can regain the required power through quick battery replacement without having to stay for a long time, which has higher convenience [14]. At the same time, compared with the traditional charging station model, BSS operators can flexibly arrange battery charging and discharging plans to deeply participate in the power market and achieve profitability [15]. For the power grid, model-based management of the BSS load is conducive to peak-shaving and valley-filling of the power grid, reducing the adverse effects on the efficient operation of the power grid caused by the random charging behavior of EV users and improving the power supply reliability and economy of the distribution system.
In spite of considerable focus given to the potential value of the BSS in the future power systems, barely any studies have investigated such an issue from the grid's point of view so far, except for [15] and [16]. In [15], an optimal scheduling model to minimize the operation cost of a grid-connected micro-grid (MG) considering the accommodation of distributed generation (DG) and BSS is proposed. The effects of var compensators, optimal BSS scheduling, and reactive power costs on active/reactive power dispatch and MG operation cost are comprehensively investigated. In [16], a dynamic operation model of BSSs in an electricity market is developed. The model is formulated based on the short-term battery management and energy bidding strategy in electricity market. The results show that the BSS makes decisions in a market environment through tracing the number of batteries in different kinds of states, and it acquires additional revenue by responding actively to the price fluctuation in the electricity market.
However, in the literature described above, barely any studies were dedicated for exploring the implication of BSSs on system reliability. In a real-world scenario, the BSS with bi-directional chargers can work as an alternative supply source and provide capacity support to the grid during emergencies by extracting energy from its replaced EV batteries. Therefore, this could mitigate the risk of loss-of-load, where the risk of loss-of-load refers to the economic loss caused by the interruption of power supply due to the failures of system components. It reflects both the possibility and severity of the power interruption and can be derived as the product of system failure probability, loss-of-load at the demand side, and the economic value of lost load. The economic value of lost load is mainly related to the duration of the power outage and the type of customers at the demand side. The risk of loss-of-load can be obtained according to the minimum path searching algorithm.
In order to fill the above-mentioned gaps, this paper proposes a comprehensive methodological framework to investigate the potential role of BSSs with V2G capability in improving the reliability of supply in future distribution networks. For this aim, we first develop an empirical model with an explicit consideration of BSS characteristics for describing the energy demand of EVs and their resultant available generation capacity (AGC), which can be utilized for BSS operation. Then, on this basis, a quantitative method to quantify the effect of a grid-connected BSS on the distribution system reliability is proposed, which provides a practical tool to analyze the potential value of BSS resources in future distribution systems compared with most of the extant studies that only focus on an EV fast-charging paradigm. In order to explicitly capture the uncertainties associated with EV users' behaviors, Latin Hypercube Sampling (LHS) methods were utilized to obtain the time series of the BSS traffic flow and initial SOC of each EV battery, according to the probability distribution of corresponding uncertain factors. The resultant LHS-based sequential simulation improves the accuracy and convergence performance of the evaluation compared to traditional Sequential Monte Carlo Simulation (SMCS) based on simple random sampling (SRS).
Compared with existing studies, the main contributions of this paper can be summarized as follows: • Proposing a comprehensive methodological framework to study the impact of BSSs on the reliability of distribution networks.

•
Analyzed and compared the influence of different charging strategy (peak-to-valley price-based charging and constant power charging) on the reliability of the distribution network.
• Using LHS to generate the time series of uncertain factors (including the fault status of the distribution network components, the traffic flow of the BSS, and initial State of Charge (SOC) of the replaced EV batteries), which improves the accuracy and convergence performance of the evaluation, as compared with traditional SMCS method.
The rest of this paper is organized as follows. Section 2 provides an overview of the BSS conceptual framework. Then, the assessment of available generation capacity in BSS is described in Section 3. Section 4 presents the reliability modelling of system components. On these basis, Section 5 describes the procedures for conducting the reliability assessment of distribution networks. Then, Section 6 demonstrates the numerical studies. Finally, Section 7 concludes the paper.

Overview of Battery Swapping Station
With the vigorous development of EVs and the popularization of smart grids, EV swapping stations using V2G technology, as an important backup power source, have received widespread attention in improving the reliability of the distribution network [17]. The modeling of BSS is an important step in analyzing its impact on reliability. Before modeling the BSS, without loss of generality, we make the following assumptions: (a) Assuming that all batteries are charged using slots, each battery corresponds to a slot. The battery needs to be continuously exchanged between the charging slot and the EV during the battery exchange process, while charging slots are fixed. Therefore, from the perspective of BSS, the number of charging slots is more meaningful. Therefore, a battery of a certain number refers to the battery in the slot of a certain number, not the battery itself. (b) The model in this paper takes one hour as the unit time interval. The charging and discharging power within one hour are the same, but the charging and discharging power in different hours are different. Since the time scale is one hour, and the battery replacement takes only a few minutes to complete, it is considered that the battery replacement does not require time. (c) We assume that the BSS has the ability to quickly replace batteries of EVs, and the traffic capacity of the road around the BSS is strong, which will not cause road congestion.

Structure
Different from the EV charging station, the charging object of the BSS is the battery; the EV can quickly replace the empty battery in a few minutes and replace it with a fully charged battery; then, the BSS will charge the battery in a centralized manner. This charging and battery swapping mode can ensure the extremely high battery-swapping efficiency of the BSS and EV. At the same time, since the charging behavior can be performed at any time under the control of the scheduling strategy, the economy is improved.
All batteries equipped in the BSS could be classified into three types, namely full batteries (FB), half-full batteries (HB), and available batteries (AB) [18]. A full battery refers to a battery with an SOC of 0.95, while the SOC of an available battery and a half-full battery are between 0.8 and 0.95 and less than 0.8, respectively. We define the set of half-full batteries at time t as Ω 1,t , while the set of available and full batteries as Ω 2,t .
After introducing the running process and classification of batteries, the structure of BSS can be expresses as shown in Figure 1. As we can see, EVs replace HB, which have a different SOC, and these batteries will be charged using an appropriate strategy and become FB or AB if some of them are used to discharge in order to enhance the reliability of the local distribution system. Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 20

Battery Swapping Model
Every battery in a BSS has the same running process, which can be described as a "swappingcharging-queuing-discharging-swapping" circle. When a battery is replaced from the EV (namely HB), it will be placed in the charging slot and charged according to a certain charging strategy; when the SOC of the battery reaches a threshold (in this paper, it is set to 0.95), the battery becomes an FB and enters a virtual waiting queue, waiting for the battery replacement. Each battery in the queue will be numbered, which represents the sequence of battery replacement operations; the battery with the lower number is replaced first, and the battery with the higher number is replaced afterwards. The number of the new battery entering the queue is one higher than the number of the previous battery entering the queue. Every time a battery exits the queue due to a battery change, the number in the queue will be dynamically updated; that is, one is subtracted so that the battery number in the queue is 1~n. n is the total number of batteries in the queue, namely the total number of FB and AB.
If the distribution network suffers outage, the BSS serves as a backup energy storage to inject power back to the distribution network to reduce power shortages and enhance the reliability of the distribution network. Therefore, for the full battery in the queue, the discharge operation will be performed until it reaches the lowest SOC acceptable to the EV user (in this paper, it is set to 0.8) or be swapped. This process changes FB into AB because the SOCs of these batteries are between 0.8 and 0.95 after discharging operation. The working cycle of the BSS batteries can be illustrated in Figure 2.

Charging Strategy
The charging behavior of the power station is not only related to the behavior and habits of EV users, but it is also greatly affected by the price. Different from the plug-in EV charging station, the charging object of a BSS is the EV battery, which means that the charging time cannot be affected by the arrival and stay time of the EV owners, but the charging time and power can be flexibly scheduled. BSS needs to purchase electricity from the grid to charge batteries, while the current electricity market often uses time-of-use (TOU) electricity prices or peak-to-valley electricity prices. Taking into account the economics of the overall operation of BSSs, based on the peak-to-valley price of electricity, we design the following charging strategy. The core idea is to charge as much as

Battery Swapping Model
Every battery in a BSS has the same running process, which can be described as a "swapping-charging-queuing-discharging-swapping" circle. When a battery is replaced from the EV (namely HB), it will be placed in the charging slot and charged according to a certain charging strategy; when the SOC of the battery reaches a threshold (in this paper, it is set to 0.95), the battery becomes an FB and enters a virtual waiting queue, waiting for the battery replacement. Each battery in the queue will be numbered, which represents the sequence of battery replacement operations; the battery with the lower number is replaced first, and the battery with the higher number is replaced afterwards. The number of the new battery entering the queue is one higher than the number of the previous battery entering the queue. Every time a battery exits the queue due to a battery change, the number in the queue will be dynamically updated; that is, one is subtracted so that the battery number in the queue is 1~n. n is the total number of batteries in the queue, namely the total number of FB and AB.
If the distribution network suffers outage, the BSS serves as a backup energy storage to inject power back to the distribution network to reduce power shortages and enhance the reliability of the distribution network. Therefore, for the full battery in the queue, the discharge operation will be performed until it reaches the lowest SOC acceptable to the EV user (in this paper, it is set to 0.8) or be swapped. This process changes FB into AB because the SOCs of these batteries are between 0.8 and 0.95 after discharging operation. The working cycle of the BSS batteries can be illustrated in Figure 2.

Battery Swapping Model
Every battery in a BSS has the same running process, which can be described as a "swappingcharging-queuing-discharging-swapping" circle. When a battery is replaced from the EV (namely HB), it will be placed in the charging slot and charged according to a certain charging strategy; when the SOC of the battery reaches a threshold (in this paper, it is set to 0.95), the battery becomes an FB and enters a virtual waiting queue, waiting for the battery replacement. Each battery in the queue will be numbered, which represents the sequence of battery replacement operations; the battery with the lower number is replaced first, and the battery with the higher number is replaced afterwards. The number of the new battery entering the queue is one higher than the number of the previous battery entering the queue. Every time a battery exits the queue due to a battery change, the number in the queue will be dynamically updated; that is, one is subtracted so that the battery number in the queue is 1~n. n is the total number of batteries in the queue, namely the total number of FB and AB.
If the distribution network suffers outage, the BSS serves as a backup energy storage to inject power back to the distribution network to reduce power shortages and enhance the reliability of the distribution network. Therefore, for the full battery in the queue, the discharge operation will be performed until it reaches the lowest SOC acceptable to the EV user (in this paper, it is set to 0.8) or be swapped. This process changes FB into AB because the SOCs of these batteries are between 0.8 and 0.95 after discharging operation. The working cycle of the BSS batteries can be illustrated in Figure 2.

Charging Strategy
The charging behavior of the power station is not only related to the behavior and habits of EV users, but it is also greatly affected by the price. Different from the plug-in EV charging station, the charging object of a BSS is the EV battery, which means that the charging time cannot be affected by the arrival and stay time of the EV owners, but the charging time and power can be flexibly scheduled. BSS needs to purchase electricity from the grid to charge batteries, while the current electricity market often uses time-of-use (TOU) electricity prices or peak-to-valley electricity prices. Taking into account the economics of the overall operation of BSSs, based on the peak-to-valley price of electricity, we design the following charging strategy. The core idea is to charge as much as

Charging Strategy
The charging behavior of the power station is not only related to the behavior and habits of EV users, but it is also greatly affected by the price. Different from the plug-in EV charging station, the charging object of a BSS is the EV battery, which means that the charging time cannot be affected by the arrival and stay time of the EV owners, but the charging time and power can be flexibly scheduled. BSS needs to purchase electricity from the grid to charge batteries, while the current electricity market often uses time-of-use (TOU) electricity prices or peak-to-valley electricity prices. Taking into account the economics of the overall operation of BSSs, based on the peak-to-valley price of electricity, we design the following charging strategy. The core idea is to charge as much as possible during the valley time when the electricity price is lower and to reduce the charging demand as much as possible during the peak time of the higher electricity price [13]. It can be expressed as: during peak time, P ch k,t = 0.5P ch rated , k ∈ Ω 1,t during shoulder peak time, P ch where P ch k,t denotes the charging power of battery k in time t; and P ch rated denotes the rated charging power of batteries.
However, adopting the above-mentioned charging strategy only guarantees the economy of BSS operation, but it cannot guarantee that BSS has sufficient battery reserves at every moment t, so that every EV user can replace the empty battery with a fully charged battery. In order to solve this problem, we introduce inventory management theory [19]. Define the minimum limit of the number of batteries that BSS can be used for replacement (namely the number of batteries in the waiting queue and also the number of set Ω 2,t elements) at time t as S 0 . When the number of available batteries at that time is lower than the minimum value, all charging slots work at full power to charge all HB so that the number of batteries in the waiting queue reaches a certain value S higher than S 0 . Among them, (S 0 , S) is defined as the buffer zone, and the lowest limit S 0 is used to ensure the normal operation of the battery swapping service without interruption due to lack of available batteries. So far, the battery charging strategy in this article can be expressed as: Then the SOC of HB during the charging period can be calculated as follows: where SOC k,t denotes the SOC of battery k in time t; η c and E rated denote the charging efficiency and rated capacity of EV batteries, respectively; ∆t denotes the unit time interval.

Management Strategy of Batteries with Different Charge Levels
It can be seen that there are batteries with different charging levels in the BSS. A reasonable management of these batteries while at the same time fully tapping the potential of battery interaction with the grid and EVs is an important issue for BSS operation. Based on the above description of the working principle of the BSS, the battery management strategy is summarized as shown in Figure 3. The BSS monitors the SOC of batteries in real time through measuring devices, and then, it controls the interaction of all batteries with the EV and the grid. When the battery replaced from the EV does not reach the minimum SOC of AB, it will be charged under the guidance of peak-to-valley electricity price while the number of AB and FB should be considered at the same time. When the distribution network fails, FB can provide V2G services to the grid to reduce the loss of load until its SOC reaches the minimum value of AB. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 20

Assessment of Available Generation Capacity (AGC)
This section introduces the assessment of available generation capacity provided by the BSS. The whole process can be decomposed into three parts, namely EV users swapping behavior modeling, BSS operation simulation, and V2G available indicator generation and AGC generation. EV users swap behavior modeling will be demonstrated in Section 3.1. The BSS operation framework has been described in Section 2, and the BSS operation aims to obtain the BSS load curve and SOC of each battery, which will be further illustrated in Figure 5; V2G available indicator generation and AGC generation will be described in Section 3.2.

EV Users Swap Behavior Modeling
The uncertainty in EV users' behaviors should be fully considered and investigated; otherwise, it may cause the erroneous calculation results [20,21]. EV users arrive at the BSS at different times, replacing empty batteries with different SOCs and leaving with fully charged batteries. Therefore, the number of EVs arriving at the BSS and the SOC of the replaced batteries at each moment are uncertain variables for the BSS operator. In order to allow for these uncertainties, we first determine the probability distribution of two uncertainty variable, and then generate a sequence of vehicle flow at the BSS and the initial SOC of the empty batteries through a sampling method.
Considering a small quantity of EVs arriving in the early morning and different traffic flow at different times, it is hard to obtain a uniform form of a probability density function (PDF) to perform sampling. From another point of view, the average number of visits to the BSS per day is roughly fixed, and the moment of each visit roughly obeys a certain probability distribution. We can sample the time of each visit and finally aggregate the data to get the time series of traffic flow. In this paper, we adopt the PDF of the arrival time of each EV provided in [22] as the PDF of the occurrence of each BSS visit. In [22], it is assumed that there is no visit from 0:00 to 7:00. However, considering that the BSS has full-time service capabilities and diverse users, not single local users, this assumption is no longer suitable. So we modified the PDF, slightly increasing the probability of arriving in the early morning. It is assumed that there are about 510 times visits in a typical day. We simulated each visit to obtain the arrival time of each visit and further formed the EV flow of a whole year. Through using a modified PDF, the EV flow in a day-scale can be generated. The modified PDF of each visit's arriving time and the corresponding EV flow in a typical day are depicted in Figure 4. It can be seen from Figure 4 that most of the EV power exchange demand is concentrated in the time period 7:00-20:00, and the demand for power exchange in the early morning hours is very small. As analyzed later, the time difference of the power exchange demand makes the V2G of the BSS also have time difference characteristics.

Assessment of Available Generation Capacity (AGC)
This section introduces the assessment of available generation capacity provided by the BSS. The whole process can be decomposed into three parts, namely EV users swapping behavior modeling, BSS operation simulation, and V2G available indicator generation and AGC generation. EV users swap behavior modeling will be demonstrated in Section 3.1. The BSS operation framework has been described in Section 2, and the BSS operation aims to obtain the BSS load curve and SOC of each battery, which will be further illustrated in Figure 5; V2G available indicator generation and AGC generation will be described in Section 3.2.

EV Users Swap Behavior Modeling
The uncertainty in EV users' behaviors should be fully considered and investigated; otherwise, it may cause the erroneous calculation results [20,21]. EV users arrive at the BSS at different times, replacing empty batteries with different SOCs and leaving with fully charged batteries. Therefore, the number of EVs arriving at the BSS and the SOC of the replaced batteries at each moment are uncertain variables for the BSS operator. In order to allow for these uncertainties, we first determine the probability distribution of two uncertainty variable, and then generate a sequence of vehicle flow at the BSS and the initial SOC of the empty batteries through a sampling method.
Considering a small quantity of EVs arriving in the early morning and different traffic flow at different times, it is hard to obtain a uniform form of a probability density function (PDF) to perform sampling. From another point of view, the average number of visits to the BSS per day is roughly fixed, and the moment of each visit roughly obeys a certain probability distribution. We can sample the time of each visit and finally aggregate the data to get the time series of traffic flow. In this paper, we adopt the PDF of the arrival time of each EV provided in [22] as the PDF of the occurrence of each BSS visit. In [22], it is assumed that there is no visit from 0:00 to 7:00. However, considering that the BSS has full-time service capabilities and diverse users, not single local users, this assumption is no longer suitable. So we modified the PDF, slightly increasing the probability of arriving in the early morning. It is assumed that there are about 510 times visits in a typical day. We simulated each visit to obtain the arrival time of each visit and further formed the EV flow of a whole year. Through using a modified PDF, the EV flow in a day-scale can be generated. The modified PDF of each visit's arriving time and the corresponding EV flow in a typical day are depicted in Figure 4. It can be seen from Figure 4 that most of the EV power exchange demand is concentrated in the time period 7:00-20:00, and the demand for power exchange in the early morning hours is very small. As analyzed later, the time difference of the power exchange demand makes the V2G of the BSS also have time difference characteristics. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 20 The other uncertainty of EV user behavior is the SOC of replaced batteries. The general processing method is assuming that the user behavior obeys a certain probability distribution according to local user preference. Here, we adopt normal distribution [23], which described as:

Calculation of the AGC of BSSs
As described above, the BSS can inject the extra power of an FB into the grid when the distribution network suffers an outage. This process is defined as V2G service. From this perspective, BSS can be viewed as a backup resource. To research an enhancement of reliability of the distribution network with the penetration of BSS, an assessment of available generation capacity, which means discerning how much power the BSS can inject into the grid when the distribution network fails, is necessary. The following describes the calculation method of AGC.
As mentioned above, each battery has to go through a "swapping-charging-queuingdischarging-swapping" cycle repeatedly. Suppose that the initial time when the battery k is fully charged in the c k th cycle is t full c k ,k , the time when it is swapped is t swap c k ,k , and the time when the power available for V2G is released completely is t end c k ,k . Then, the indicator variable nk,t that the battery k can perform V2G service at time t can be obtained by Equation (5): Among them, when nk,t is 1, it means that V2G service is available, and when it is 0, it cannot; t end c k ,k can be calculated by Equation (6): where P dch rated denotes the rated discharging power of batteries; and η d denotes discharging efficient of EV batteries.
After calculating nk,t at each time, the AGC at each time t can be obtained by Equation (7): where P AGC t denotes the AGC that can be obtained in each time t and N denotes the number of all batteries in the BSS.
After introducing the calculation method of AGC and the working process of V2G, the whole procedure of AGC assessment can be demonstrated as shown in Figure 5. The other uncertainty of EV user behavior is the SOC of replaced batteries. The general processing method is assuming that the user behavior obeys a certain probability distribution according to local user preference. Here, we adopt normal distribution [23], which described as:

Calculation of the AGC of BSSs
As described above, the BSS can inject the extra power of an FB into the grid when the distribution network suffers an outage. This process is defined as V2G service. From this perspective, BSS can be viewed as a backup resource. To research an enhancement of reliability of the distribution network with the penetration of BSS, an assessment of available generation capacity, which means discerning how much power the BSS can inject into the grid when the distribution network fails, is necessary. The following describes the calculation method of AGC.
As mentioned above, each battery has to go through a "swapping-charging-queuingdischarging-swapping" cycle repeatedly. Suppose that the initial time when the battery k is fully charged in the c k th cycle is t f ull ck,k , the time when it is swapped is t swap ck,k , and the time when the power available for V2G is released completely is t end ck,k . Then, the indicator variable n k,t that the battery k can perform V2G service at time t can be obtained by Equation (5): Among them, when n k,t is 1, it means that V2G service is available, and when it is 0, it cannot; t end ck,k can be calculated by Equation (6): where P dch rated denotes the rated discharging power of batteries; and η d denotes discharging efficient of EV batteries.
After calculating n k,t at each time, the AGC at each time t can be obtained by Equation (7): Appl. Sci. 2020, 10, 8023 where P AGC t denotes the AGC that can be obtained in each time t and N denotes the number of all batteries in the BSS.
After introducing the calculation method of AGC and the working process of V2G, the whole procedure of AGC assessment can be demonstrated as shown in Figure 5.

Reliability Modeling of Distribution Network
We choose the external grid, transformers, transmission lines, BSS, and load demand (load buses) to constitute the distribution network we researched. Generally, there are several types of distribution generation resources. For simplifying the model, we assume that whole distribution network gets electric delivery from the external grid by step-down transformers instead of a penetration of distribution resources. However, it also means that once there is some external grid or transformers, the only backup resource is BSS V2G power. Available generation from the external grid can be calculated by Equation (8): where P g t denotes the available generation from the external grid; and β For load demand, on the one hand, when the load bus fails, the real-time load level of the load point directly determines the power not supplied and the severity of the fault; on the other hand, the failure frequency of the load bus will also affect the reliability of the distribution network. In this study, we use a chronological profile [24] to represent the system load demand. It has been exploited from the average value of raw residential load data for the past five years and transformed discretely for each hourly-based time-period. Identical to β grid t and β transformer i,t , the outage state of load buses can also be sampled by its mean time to failure (MTTF) and mean time to repair (MTTR) using the SRS or LHS

Reliability Modeling of Distribution Network
We choose the external grid, transformers, transmission lines, BSS, and load demand (load buses) to constitute the distribution network we researched. Generally, there are several types of distribution generation resources. For simplifying the model, we assume that whole distribution network gets electric delivery from the external grid by step-down transformers instead of a penetration of distribution resources. However, it also means that once there is some external grid or transformers, the only backup resource is BSS V2G power. Available generation from the external grid can be calculated by Equation (8): where P g t denotes the available generation from the external grid; and β grid t and β trans f ormer i,t are the indicators that represent whether the external grid or the transformers between the external grid and distribution network fail at time t. If so, take the value 0; otherwise, take 1. P trans_max i represents the maximum capacity of transformer i. Ω T is a set of transformers.
For load demand, on the one hand, when the load bus fails, the real-time load level of the load point directly determines the power not supplied and the severity of the fault; on the other hand, the failure frequency of the load bus will also affect the reliability of the distribution network. In this study, we use a chronological profile [24] to represent the system load demand. It has been exploited from the average value of raw residential load data for the past five years and transformed discretely for each hourly-based time-period. Identical to β grid t and β trans f ormer i,t , the outage state of load buses can also be sampled by its mean time to failure (MTTF) and mean time to repair (MTTR) using the SRS or LHS method [25].

Evaluation of Distribution Network Reliability
An assessment of BSS for the improvement of distribution network reliability is the last but also important part of our work, which will show a positive role in reliability enhancement. The whole procedure consists of three parts, namely initialization of the base data, optimal power flow, and reliability criterion calculation. The process is as follows:

1)
Using LHS to form the behavior patterns of EV users and distribution components failure states. The behavior patterns of EV users include the time series of the arriving EV number and SOC of each replaced empty battery, while the distribution components failure states consist of a time series of the failure states of the external grid, transformers and load buses. 2) According to the procedure described in Section 3.2, calculate the available generation capacity P AGC t and real-time load of BSS P BSSL t . Therefore, the total available generation capacity provided by the whole system P tg t can be described by the summation of power from grid P g t and P AGC t ; the total load of distribution P td t can be calculated by adding the load of every load bus and P BSSL t .

3) Start a new simulation year.
For each time t, if P td t is greater than P tg t , it means that the distribution system suffers an outage. Perform optimal power flow with the goal of minimum load shedding and determine the load shedding amount in each load point. 4) Calculate the reliability criterion of the distribution system, including the system average interruption frequency index (SAIFI), system average interruption duration index (SAIDI), system expected energy not supplied (SEENS), load average interruption frequency index (LAIFI), load average interruption duration index (LAIDI), and load average expected energy not supplied index (LEENS). 5) Judge whether the procedure converges. Choose SEENS as the basis for convergence judgment.
If σ(SEENS)/ √ N y × E(SEENS) ≤ 0.05, the procedure converges, where σ(·) and E(·) denote the standard deviation and expectation of the sample and N y denotes the total simulation years [18]. Otherwise, repeat (1)-(4) until it converges. 6) Take the average value of reliability indexes of each simulation year as the final index values.
The flow chart of the assessment procedure of the reliability of a distribution network can be seen in Figure 6. Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 20 Figure 6. Flowchart of evaluation algorithm.

Numerical Study
In these sections, we first introduced the base data of both the distribution system and the BSS. Then, we compared the reliability between three cases, including the distribution system without BSS, with BSS but without V2G, and with BSS and V2G. To demonstrate the positive role of an appropriate charging strategy, we also compared the reliability under two BSS charging strategies, namely the strategy we proposed and constant power charging. Finally, we investigate the different effects on reliability assessment using two simulation methods (LHS-based sequential simulation and SMCS).

Data
In this paper, a numerical simulation analysis is performed on the modified IEEE 33-bus distribution network [26]. The structure of the network can be seen in Figure 7. There are about 1200 residential customers and the total peak load is 18 MW. The peak load and number of households at each load is listed in Table 1. For simplicity, we assumed that all load points share the same load factor-that is, the ratio of actual load to peak load. The load factor of a typical day is depicted in Figure 8 [27]. The BSS is equipped in bus 30 and the maximum load is 2.1 MW. The whole distribution system is served by an external grid. Two 110/10 kV substation transformers transform electric power from the grid to the distribution network. When the external grid or transformers fail,

Numerical Study
In these sections, we first introduced the base data of both the distribution system and the BSS. Then, we compared the reliability between three cases, including the distribution system without BSS, with BSS but without V2G, and with BSS and V2G. To demonstrate the positive role of an appropriate charging strategy, we also compared the reliability under two BSS charging strategies, namely the strategy we proposed and constant power charging. Finally, we investigate the different effects on reliability assessment using two simulation methods (LHS-based sequential simulation and SMCS).

Data
In this paper, a numerical simulation analysis is performed on the modified IEEE 33-bus distribution network [26]. The structure of the network can be seen in Figure 7. There are about 1200 residential customers and the total peak load is 18 MW. The peak load and number of households at each load is listed in Table 1. For simplicity, we assumed that all load points share the same load factor-that is, the ratio of actual load to peak load. The load factor of a typical day is depicted in Figure 8 [27]. The BSS is equipped in bus 30 and the maximum load is 2.1 MW. The whole distribution system is served by an external grid. Two 110/10 kV substation transformers transform electric power from the grid to the distribution network. When the external grid or transformers fail, the BSS V2G power serves as a backup resource. The MTTR and MTTF of the external grid, transformers, and load buses are listed at Table 2 Figure 8. Variation of load factor in a typical day. Figure 8. Variation of load factor in a typical day. Without a loss of generality, we assumed that the EVs that the BSS served are the same type. Therefore, the types of batteries replaced are identical. EUQC (EU Quick-Changing) version is finally selected to represent the whole EV type. The main reasons are twofold. EUQC is the latest quick-change version of the BAIC New Energy EV Company [28]. It is the most popular in China, and its proportion is increasing. EUQC has a large-capacity ternary lithium battery of 45 kWh. For the BSS with V2G capability, it will have a better performance in improving the reliability of the distribution network. All BSS parameters can be seen in Table 3. Table 3. BSS parameters applied in the paper.

Results
In this section, to compare the effect of BSS on the reliability of the distribution network, we assigned three cases:

1)
Case-1: The distribution network does not have a BSS, and all electrical power is provided by the external grid. When the grid fails, the system has no backup power source. 2) Case-2: The distribution network is equipped with a BSS, but it does not have the capability of V2G. It is equivalent to increase the load on the distribution network. 3) Case-3: The distribution network is equipped with a BSS and has the capability of V2G. In the event of a grid failure, BSS can be used as a backup power source to supply power back to the distribution network.
In order to quantify the effect of BSS on the reliability of the distribution network, we use SAIFI, SAIDI, and SEENS as system reliability indexes, and LAIFI, LAIDI, and LEENS as load point reliability indexes. According to the simulation results, the reliability indexes of the distribution network in the three cases are shown in Tables 4-6.   From Tables 4-6, the following can be found: When the system is connected to a BSS without V2G capability, the power distribution system's SAIFI, SAIDI, SEENS, LAIFI, LAIDI, LEENS, and other indicators will increase accordingly, of which SAIFI, SAIDI, and SEENS will increase by 0.0309 time/c-y, 0.5896 h/c-y, and 12.103 MWh/y, respectively. The reason is that simply connecting the BSS to the distribution network will increase the system load value and the maximum load utilization hours, increase the load loss caused by the fault, and reduce the system reliability.
When the system is connected to a BSS with V2G capability, the batteries of EVs can interact with the distribution network in the form of V2G. According to the calculation, the LEENS of load point 29 near the BSS point 30 of the EV was reduced from 3.9898 to 3.3938 MWh/y, and the LAIDI was reduced from 5.8540 to 5.0834 h/c-y. It can be seen that the access of BSS significantly shortens the LAIDI near the BSS load point and reduces power loss. That is, BSS can be used as a distributed energy storage device to restore power to some important loads in the event of a grid failure. The available generation capacity P AGC and charging load P BSSL curves in a typical day are depicted in Figure 9. At the same time, the values of SAIFI, SAIDI, and SEENS of the system are increased from 0.6466 time/c-y, 2.9339 h/c-y, 40.8239 MWh/y to 0.6313 time/c-y, 2.8657 h/c-y, 39.8603 MWh/y, that is, the BSS with V2G relatively improved the reliability of the distribution system. Therefore, the use of a large number of V2G technologies can improve energy efficiency, help alleviate the contradiction of power grid peak shortage, and improve the reliability of the distribution system.

Comparison of of Different Charging Strategies
This paper studies the influence of orderly charging and disorderly charging of a BSS on the reliability of a distribution network. Orderly charging is the charging strategy proposed in this paper, which is based on the premise that the available batteries in stock are greater than a certain limit, and the charging power is flexibly adjusted under the action of peak-valley electricity prices. The disordered charging refers to a constant-power charging paradigm, for which the charging power is a constant value whenever the charging is done. In this case, since the charging power is constant and cannot be dynamically adjusted with changes in electricity prices, the overall charging load of the BSS will change at the same time as the disorderly swapping demand of EV users, which brings a serious peak load of the distribution network similar to that of charging stations. Therefore, it is a disorderly charging strategy. The reliability indexes of the distribution network under the disorderly charging strategy are listed in Table 7.

Comparison of of Different Charging Strategies
This paper studies the influence of orderly charging and disorderly charging of a BSS on the reliability of a distribution network. Orderly charging is the charging strategy proposed in this paper, which is based on the premise that the available batteries in stock are greater than a certain limit, and the charging power is flexibly adjusted under the action of peak-valley electricity prices. The disordered charging refers to a constant-power charging paradigm, for which the charging power is a constant value whenever the charging is done. In this case, since the charging power is constant and cannot be dynamically adjusted with changes in electricity prices, the overall charging load of the BSS will change at the same time as the disorderly swapping demand of EV users, which brings a serious peak load of the distribution network similar to that of charging stations. Therefore, it is a disorderly charging strategy. The reliability indexes of the distribution network under the disorderly charging strategy are listed in Table 7.
It can be seen from Table 7 that under the action of disorderly charging, a BSS not only cannot improve the reliability of power supply, but it further reduces the reliability. This is due to the high coincidence rate of the peak demand for EV replacement and the peak power consumption. Therefore, this uncontrolled charging method will further increase the peak-to-valley difference of the system. In the event of a power failure in the system, the system usually bears a greater load power loss. The orderly charging transfers the charging work as far as possible to the night, which plays the role of peak shaving and valley filling. It is equivalent to rational use of the system load valley time. The load of BSS during orderly and disorderly charging on a typical day is shown in Figure 10. When a small-scale fault occurs, the reliability is less affected than disorderly charging. What is more, under the same peak-to-valley price, the charging costs of orderly and disorderly charging in a typical day are $4573.3 and $5254.7, respectively. It can be seen that a reasonable charging strategy has an important influence on the reliability of the power system and also provides some potential economic benefits. It can be seen from Table 7 that under the action of disorderly charging, a BSS not only cannot improve the reliability of power supply, but it further reduces the reliability. This is due to the high coincidence rate of the peak demand for EV replacement and the peak power consumption. Therefore, this uncontrolled charging method will further increase the peak-to-valley difference of the system. In the event of a power failure in the system, the system usually bears a greater load power loss. The orderly charging transfers the charging work as far as possible to the night, which plays the role of peak shaving and valley filling. It is equivalent to rational use of the system load valley time. The load of BSS during orderly and disorderly charging on a typical day is shown in Figure 10. When a small-scale fault occurs, the reliability is less affected than disorderly charging. What is more, under the same peak-to-valley price, the charging costs of orderly and disorderly charging in a typical day are $4573.3 and $5254.7, respectively. It can be seen that a reasonable charging strategy has an important influence on the reliability of the power system and also provides some potential economic benefits.

Analysis on the Performance of Sampling Methods Adopted
For comparing the performance of LHS-based sequential simulation and traditional SMCS, this procedure uses LHS and SRS to sample the EV traffic flow, empty batteries' SOC, and system failure status in each period. For SMCS, traditional techniques sampling from the probability distribution through random or pseudo-random numbers are used. Among them, SRS is widely used. The SRS technique is completely random, and any given sample may fall anywhere within the input distribution range. The LHC involves the stratification of the input probability distribution. Stratification divides the cumulative curve into equal intervals of cumulative probability levels (0 to 1.0). Then, it randomly samples from each interval or creates "stratification" of the input

Analysis on the Performance of Sampling Methods Adopted
For comparing the performance of LHS-based sequential simulation and traditional SMCS, this procedure uses LHS and SRS to sample the EV traffic flow, empty batteries' SOC, and system failure status in each period. For SMCS, traditional techniques sampling from the probability distribution through random or pseudo-random numbers are used. Among them, SRS is widely used. The SRS technique is completely random, and any given sample may fall anywhere within the input distribution range. The LHC involves the stratification of the input probability distribution. Stratification divides the cumulative curve into equal intervals of cumulative probability levels (0 to 1.0). Then, it randomly samples from each interval or creates "stratification" of the input distribution. It samples the values in each interval and then sorts them, so that the correlation between each sample is minimized.
In order to compare the difference between the two sampling methods, we list the row correlation between samples when the two sampling methods are used. For EVs, row correlation refers to the correlation between the time of arrival of different visited vehicles in a day and the initial SOC; for system components, it is the correlation between the failure states of different components. It can be seen from the Table 8 that when using LHS, the row correlation between samples is very small. Studies have proven that the correlation of smaller sample rows will bring greater accuracy [29]. Similarly, Figure 11 plots the convergence of the simulation results when using different sampling methods. It can be seen from the figure that the procedure of LHS-based sequential simulation converges faster than SMCS, the number of iterations is reduced, and the simulation time is shortened. This is because in the case of the same sampling times, the sampling coverage of LHS is larger and can better reflect the true probability distribution of random variables, so that the difference between the results of each iteration is reduced. It comes to the conclusion that under the premise of the same number of samples, LHS-based sequential simulation is better than SMCS in terms of convergence speed and calculation accuracy.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 18 of 20 components. It can be seen from the Table 8 that when using LHS, the row correlation between samples is very small. Studies have proven that the correlation of smaller sample rows will bring greater accuracy [29].  Figure 11 plots the convergence of the simulation results when using different sampling methods. It can be seen from the figure that the procedure of LHS-based sequential simulation converges faster than SMCS, the number of iterations is reduced, and the simulation time is shortened. This is because in the case of the same sampling times, the sampling coverage of LHS is larger and can better reflect the true probability distribution of random variables, so that the difference between the results of each iteration is reduced. It comes to the conclusion that under the premise of the same number of samples, LHS-based sequential simulation is better than SMCS in terms of convergence speed and calculation accuracy.

Conclusions
This paper studies the potential benefits of BSS on the power supply reliability of a distribution network. We develop an empirical model with an explicit consideration of BSS characteristics for describing the energy demand of EVs and their resultant AGC, which can serve as a backup source in case of an outage in distribution systems. Then, on this basis, a quantitative method to quantify the effect of a grid-connected BSS on distribution system reliability is proposed, which provides a practical tool to analyze the potential value of BSS resources in future distribution systems compared with most of extant studies that only focus on an EV fast charging paradigm. We also adopt LHS-based sequential simulation to explicitly capture the uncertainties associated with EV

Conclusions
This paper studies the potential benefits of BSS on the power supply reliability of a distribution network. We develop an empirical model with an explicit consideration of BSS characteristics for describing the energy demand of EVs and their resultant AGC, which can serve as a backup source in case of an outage in distribution systems. Then, on this basis, a quantitative method to quantify the effect of a grid-connected BSS on distribution system reliability is proposed, which provides a practical tool to analyze the potential value of BSS resources in future distribution systems compared with most of extant studies that only focus on an EV fast charging paradigm. We also adopt LHS-based sequential simulation to explicitly capture the uncertainties associated with EV users' behaviors, improve the result accuracy, and accelerate the convergence of the evaluation compared to traditional SMCS based on SRS. The results of the numerical study show that: BSS without V2G function will increase the loading level of the distribution network. When the grid is encountered with contingencies (line failures), the distribution network will suffer from a larger power supply shortage, which will reduce the reliability of the distribution network. However, as the BSS with V2G capability can be used as a backup energy source to reverse power to the grid during these emergencies, it could be helpful to reduce the power shortage and improve the reliability of power supply, if utilized appropriately.
The charging strategy based on the peak-valley pricing scheme could have a positive effect on the peak-shaving and valley-filling of distribution grids. However, as for disorderly charging, due to the overlapping effect that exists between the peak power consumption and the peak BSS charging load, it could bring serious peak load, aggravate the peak-to-valley difference, and finally impact the smooth operation of the power grid. So, when the grid is involved in a failure event, it will often suffer from a greater power supply shortage, and the reliability will be further reduced.
As a stratified sampling method, LHS covers a wider range under the same sampling times, and the row correlation between samples is smaller, so LHS-based sequential simulation is more accurate than SMCS and has a faster convergence speed.
Our research still needs improvement in some aspects. In future research, the problem of road congestion near BSSs should be considered, which reflects the interaction between BSSs, distribution networks, road networks, and EV users. What is more, although the swapping time is very short, assuming battery swapping requires no time is still risky. We can use a smaller time scale or adopt queuing theory to fully consider this factor. Finally, the charging strategy we used can improve the reliability of the distribution system and provide economic benefits at the same time, but it is still not the optimal strategy. Designing a better charging strategy that can fully exploit the reliability enhancement and economic benefits of BSSs is also an interesting task.
As an intelligent power component, the BSS will play an increasingly important role in large-scale EV access to the grid and improve the reliability of the distribution network. Hopefully, the outcomes of this research can provide some reference value for the BSS planning, construction, and operation of distribution networks in the context of future smart cities.