Evaluation and Improvement of Backup Capacity for Household Electric Vehicle Uninterruptible Power Supply (EV-UPS) Systems

Abstract

The use of electric vehicles (EVs) for household uninterruptible power supplies (UPSs), particularly in rural areas, can greatly improve household power reliability. However, because EVs are mobile, the evaluation of backup capacity for EV-UPS systems is completely different when compared to traditional UPSs. As a result, the focus of this paper is on the evaluation and improvement of backup capacity for EV-UPS systems. The architectures for EV-UPS systems are presented first. The methodology for calculating backup capacity for EV-UPS systems is then presented, followed by four detailed cases based on different grid failure times. Furthermore, the impact of system operating parameters on backup capacity, such as different load power, EV mobility pattern parameters, and grid outage durations, is investigated. The results of backup capacity in cases of different operating parameters are detailed using an EV mobility model. An improved strategy for increasing backup capacity is proposed, in which more backup energy can be released during a power outage. Meanwhile, the next trip requirement is unaffected. The backup capacity with the improved strategy is then calculated and compared to the results with the traditional strategy. Finally, a 5 kW EV-UPS experimental platform is constructed, and the experimental results are presented to validate the proposed method.

1. Introduction

Greenhouse gas emissions and global warming currently pose a serious threat to our environment. It is widely acknowledged that using electricity instead of gasoline to power transportation can significantly reduce greenhouse gas emissions and combat climate change [1]. As a result, the development of electric vehicles is becoming a global trend. Furthermore, EVs with bidirectional capabilities can serve multiple functions in smart power systems [2]. Bidirectional EV systems are currently available in three configurations: vehicle to home (V2H), vehicle to vehicle (V2V), and vehicle to grid (V2G) [3].

Power flows between EVs and homes in V2H applications. The system configuration is relatively simple and straightforward in practice. In [4], EVs are used as energy storage to smooth household loads in V2H applications, particularly when renewables are used. In addition, to optimize home power consumption with EVs, optimal centralized scheduling has been proposed [5]. Furthermore, Nissan proposed the scenario of building smart homes using “LEAF to Home” systems. Reference [6] extends bidirectional EV systems to function as UPSs to improve household power reliability. It is well known that current household power is not as reliable as expected, particularly in remote areas. Using British Columbia as an example, the average number of power outages in the province is two per year, with each outage lasting an average of three hours [7]. Furthermore, in rural areas, these figures are even worse. In Valemount, British Columbia, for example, power outages occur eight times per year and last an average of 4.5 h. As a result, by using EVs as UPSs for households, particularly in rural areas, the reliability of household power can be greatly improved. Furthermore, when EVs are parked at home, the stored energy can be fully utilized in EV-UPS systems. EVs also have a much faster response time and lower operating costs when compared to home backup generators [8]. As a result of these benefits, EV-UPS systems have gained a lot of attention from researchers and industries.

Traditionally, UPS architectures are classified into three types: online, offline, and line-interactive [9]. Among the three configurations, the offline structure is suitable for household EV-UPS systems due to its simple design, low cost, and high density. As a result, offline EV-UPS system architectures have been investigated, and numerous on-board and off-board bidirectional topologies have been proposed. The two-stage architecture, consisting of a front-end ac/dc followed by an isolated dc/dc, is typically chosen for on-board bidirectional converters [10]. Interleaved boost, bridgeless/dual boost, and bridgeless interleaved boost are some of the popular front-end ac/dc converters [10]. The typical topologies for isolated dc/dc converters include full-bridge LLC resonant converters, interleaved ZVS FB converters with voltage doublers, and zero-voltage switching (ZVS) FB converters with capacitive output filters [10,11].

Another area of study for researchers is the operating modes and transition between different modes for offline EV-UPS systems. Reference [6] details two cases for the transition to backup mode, which are the EV only plugged in at home and the EV plugged in and also charging. The results, however, are only verified with linear loads, which is deemed unrealistic. As a result, [12] includes a more detailed analysis and experimental validation for nonlinear electrical appliances. A fast grid failure detection with bidirectional converters is critical during the transition. Reference [12] examines and compares two grid failure detection algorithms: rms voltage calculation for half-cycle grid and rms voltage estimation using a Kalman filter. A sliding window rms calculation is typically used for grid failure detection in order to reduce detection time [13].

The significant difference between EV-UPS systems and traditional UPSs is that the EV battery is mobile, and the system can only back up the grid when the EV is plugged in [8]. Furthermore, when the grid fails, the EV battery is not always full, and the stored energy is dependent on the EV mobility pattern and charging scheduling. As a result, the backup capacity of EV-UPS systems differs significantly from that of traditional UPSs. However, there have been few papers that discuss how to evaluate backup capacity for EV-UPS systems. There are two important criteria for evaluating backup capacity in UPS systems: (1) the backup energy that UPSs can provide, and (2) the backup time that UPSs can cover [13]. These two criteria are closely related in EV-UPS systems to the EV mobility pattern and charging scheduling. It is difficult to precisely model driving habits and battery state of charge (SOC) for EV mobility. Most existing studies predict EV availability using historical data and model EV behavior as an arrival and departure process. The Gaussian distribution, Poisson process, and Markov chain [14] are used to model the arrival and departure time. Furthermore, the EVs have varying SOCs, which are also modeled as normal or lognormal distributions. Numerous strategies for EV charging scheduling have been proposed, which basically fall into three categories [15]. The first category is from the perspective of the grid, and the optimization goals include minimizing power variances, minimizing power losses, and maximizing grid reliability. The second category is from the perspective of users, and the optimization objectives include minimizing charging costs, increasing EV average SOCs, and increasing user convenience [16]. Furthermore, a few papers [15] jointly optimize the benefits of both grid-side and EV-side benefits. A variety of smart charging/discharging algorithms, such as convex optimization, linear programming, game theory, swarm particle optimization, and heuristic methods, are proposed to implement these functions. Reference [17] proposes a methodology for managing smart home appliances alongside EVs, taking into account demand rebound and consumer convenience indices, in order to reduce network stress, congestion, and demand rebound. Reference [18] develops a model to forecast maximum demand based on the increasing penetration of EV consumers. Reference [19] proposes a frequency regulation strategy with support for electric vehicles based on a novel fuzzy-based dual-stage controller and a modified dragonfly algorithm.

In general, no papers have been reported to develop strategies to improve backup performance for EV-UPS systems. As a result, the purpose of this paper is to evaluate and improve the backup capacity of household EV-UPS systems. The main contributions of this paper are listed below.

(1)

Based on the EV mobility pattern, a methodology for calculating backup capacity for EV-UPS systems is proposed.

(2)

The effect of system operating parameters on backup capacity for EV-UPS systems is thoroughly examined. Load power, EV mobility pattern parameters, and grid outage duration are among the operating parameters.

(3)

An improved strategy is proposed to maximize backup capacity while maintaining the need for next-day trips.

2. EV-UPS Architecture

2.1. Single-EV UPS Architecture

Figure 1a depicts the original household architecture, with the load supplied by the grid. Refrigerators, air conditioners, lights, cooking stoves, washers and dryers, and other major appliances are included. If there is only one EV, the simplest architecture for the EV-UPS system is as shown in Figure 1b, which includes a bi-dc/ac converter.

The EV-UPS system has three operating modes, as illustrated in Figure 2. The EV-UPS system differs significantly from traditional UPS systems in that it is mobile. The EV cannot charge or discharge itself when it is traveling and not at home (see Figure 2a). When the EV is plugged in and the grid is normal, it can be charged using the bi-dc/ac converter, as illustrated in Figure 2b. In the event that the grid fails, the EV discharges power to supply the load, as shown in Figure 2c.

2.2. Multiple-EV UPS Architecture

The number of EVs in a large household or apartment complex is usually greater than one. Figure 3 depicts two different types of multiple-EV UPS architectures. To achieve modular design, all EV connections to the grid or to the load must be the same. There are no dc-buses in this architecture, and each EV is connected to the grid via a bi-dc/ac converter, as shown in Figure 3a. A dc-bus is added in Figure 3b, and each EV is connected to it via a bi-dc/dc converter. The dc-bus is then linked to the grid via a dc/ac inverter. However, the dc/ac inverter’s reliability is critical. If the dc/ac inverter fails, neither EV will be able to charge or discharge.

The sections that follow will concentrate on EV-UPS backup capacity evaluation. The calculation will be demonstrated using a single household EV UPS system, but the concept can also be applied to multiple-EV UPS systems.

3. Backup Capacity Calculation

The most important backup criteria in UPS systems are (1) the backup energy that UPSs can provide and (2) the backup time that UPSs can cover. The evaluation of these two criteria for EV-UPS systems, however, differs because the EV-UPS systems have different features.

(1)

The EV-UPS system’s battery is mobile, and the system can only support the grid when the EV is plugged in.

(2)

When the grid fails, the EV battery is not always full, and the stored energy is dependent on the EV mobility pattern and charging scheduling.

Using a single household EV system as an example, Figure 4 depicts a typical EV mobility pattern in which the EV is only connected to the grid during home charging (after t_HA and before t_HD). The following will calculate the backup energy and backup time that the EV-UPS system can provide based on the EV mobility pattern.

The backup energy E_BU and backup time T_BU that the EV-UPS can provide vary depending on the grid failure time. Figure 5 depicts four cases based on different grid failure times t_f. The duration of the grid’s outage is assumed here as T_D.

3.1. Case A (t_f < t_HA−T_D)

In Case A, the EV is disconnected from the grid for the duration of T_D after the grid fails. As a result, the EV battery’s stored energy cannot be discharged to the grid. Both the backup energy E_BU and backup time T_BU are zero.

$$\left\{\begin{array}{c}{E}_{BU}\left(t_f\right)=0\\ T_{BU}\left(t_f\right)=0\end{array}\right.\hspace{1em}(Case A)$$

(1)

3.2. Case C (t_HA ≤ t_f ≤ t_HD−T_D)

Cases B and D are special cases of Case C, which is examined first. Five parameters are first defined in Figure 6 to describe various situations in Case C. Figure 6 shows the charging time t_chg which is from the energy E(t_f) to the fully charged EV. t_dis is the time required to discharge the energy E(t_f) to the allowed minimum energy E_min. The EV charging time from the minimum charge to the full charge is represented by t_{chg_emp}. If the energy E(t_f) can withstand a continuous discharging of T_D, the charging time to fully charge the EV after this discharging is t_{chg_Td}. The remaining time to t_HD after T_D is denoted by t_left. It is worth noting that the discharging rate is not constant in practice, and changes in real time.

The values of the five above parameters are calculated for various grid failing times t_f. Then, using the relationship between these five parameters, five subcases for Case C are obtained, as shown in Figure 7.

Here, two assumptions are made.

(1)

The EV battery should be fully charged before departure to ensure the daily trip requirement. This strategy is commonly used in practice and is known as the full charge before departure (FCBD) strategy in this context.

(2)

During the power outage, the EV cannot be charged.

In Case C1, t_chg is greater than t_left. This means that the EV cannot discharge energy during the power outage period T_D in order to seek full charge before departure. As a result, as shown in (2), the backup energy E_BU is zero in this case. In contrast, t_chg is less than t_left in other cases (C2~C5). This means that in Cases C2~C5, the EV can discharge energy during T_D.

$$\left\{\begin{array}{c}{E}_{BU}\left(t_f\right)=0\\ T_{BU}\left(t_f\right)=0\end{array}\right.\hspace{1em}(Case C1)$$

(2)

In Cases C2 and C3, t_dis is greater than T_D, indicating that the EV has enough energy to discharge for a period of T_D. In Case C2, t_{chg_Td} is less than t_left, indicating that there is still enough time for the EV to be fully charged before departure after discharging for the duration of T_D. As a result, the EV can discharge continuously throughout the T_D. In Case C2, the backup energy E_BU and backup time T_BU are expressed as shown in (3).

$$\left\{\begin{array}{c}{E}_{BU}\left(t_f\right)={\int }_{t_f}^{t_f+T_D}{P}_{dis}\left(t\right)dt={\int }_{t_f}^{t_f+T_D}\frac{P_L\left(t\right)}{{\eta }_{dis}}dt\\ T_{BU}\left(t_f\right)=T_D\end{array}\right.\hspace{1em}(Case C2)$$

(3)

where P_dis is the discharging power of the EV battery, P_L is the load power, and η_dis is the discharging efficiency.

In Case C3, t_{chg_Td} is greater than t_left. This means that if the discharging lasts the duration of T_D, the EV battery will not be fully charged before departure. As a result, the EV is only permitted to discharge for a portion of the T_D. Figure 7c shows the backup energy E_BU and backup time T_BU in Case C3 in (4).

$$\left\{\begin{array}{c}{E}_{BU}\left(t_f\right)=P_{chg}{t}_{left}-\left(E_{full}-E\left(t_f\right)\right)\\ {{\int }_{t_f}^{t_f+t_{C3}}\frac{P_L\left(t\right)}{{\eta }_{dis}}dt=E}_{BU}\left(t_f\right)\\ T_{BU}\left(t_f\right)=t_{C3}\end{array}\right.(Case C3)$$

(4)

where P_chg is the EV charging power.

In Cases C4 and C5, t_dis is less than T_D, implying that the energy stored in the EV can be fully discharged during T_D. In Case C4, t_{chg_emp} is less than t_left, indicating that there is sufficient time for the EV battery to be fully charged after being fully discharged during T_D. As a result, the stored energy can be fully released. The associated backup energy E_BU and backup time T_BU are shown in (5).

$$\left\{\begin{array}{c}{E}_{BU}\left(t_f\right)=E\left(t_f\right)-E_{min}\\ T_{BU}\left(t_f\right)=t_{dis}\end{array}\right.\hspace{1em}(Case C4)$$

(5)

where E_min is the allowed minimum energy, which is normally set by EV manufacturers.

In Case C5, t_{chg_emp} is greater than t_left, which indicates that there is insufficient time for the EV battery to be fully charged after being fully discharged during T_D. As a result, the EV is only permitted to discharge a portion of the stored energy. The backup energy E_BU and backup time T_BU for Case C5 are shown in (6) based on Figure 7e.

$$\left\{\begin{array}{c}{E}_{BU}\left(t_f\right)=P_{chg}{t}_{left}-\left(E_{full}-E\left(t_f\right)\right)\\ {{\int }_{t_f}^{t_f+t_{C5}}\frac{P_L\left(t\right)}{{\eta }_{dis}}dt=E}_{BU}\left(t_f\right)\\ T_{BU}\left(t_f\right)=t_{C5}\end{array}\right.\hspace{1em}(Case C5)$$

(6)

The expression of E_BU for Case C is shown in (7) by combining (1)–(6). Similarly, the T_BU expression for Case C can be obtained.

$$E_{BU}\left(t_f\right)=\left\{\begin{array}{ll}0& \left(C1\right)\\ {\int }_{t_f}^{t_f+T_D}\frac{P_L\left(t\right)}{{\eta }_{dis}}dt& \left(C2\right)\\ E\left(t_f\right)-E_{min}& \left(C4\right)\\ P_{chg}{t}_{left}-\left(E_{full}-E\left(t_f\right)\right)& (C3,C5)\end{array}\right.$$

(7)

3.3. Case B (t_HA−T_D ≤ t_f < t_HA)

Case B is a subset of Case C. As shown in Figure 5, the EV in Case B is not connected to the grid until the time of t_HA, which is unlikely in Case C. As a result, the starting time for providing backup power in Case B is t_HA rather than t_f. Using the same method as in Case C, redefine the parameters in Figure 6, as shown in Figure 8.

Recalculate these five parameters to obtain five subcases for Case B. Equation (8) expresses the corresponding expression for E_BU in Case B. The expression for T_BU can be obtained in the same way.

$$E_{BU}\left(t_f\right)=\left\{\begin{array}{ll}0& \left(B1\right)\\ {\int }_{t_{HA}}^{t_f+T_D}\frac{P_L\left(t\right)}{{\eta }_{dis}}dt& \left(B2\right)\\ E\left(t_{HA}\right)-E_{min}& \left(B4\right)\\ P_{chg}{t}_{left}-\left(E_{full}-E\left(t_{HA}\right)\right)& (B3,B5)\end{array}\right.$$

(8)

3.4. Case D (t_HD−T_D < t_f ≤ t_HD)

Case D is also a subset of Case C. The duration from the grid failure to the EV departure is less than T_D in this case, as shown in Figure 5, indicating that the power outage lasts until the EV departure. In order to fully charge before departure, the EV cannot discharge backup energy (see Figure 9). As a result, as shown in (9), E_BU and T_BU are both zero.

$$\left\{\begin{array}{c}{E}_{BU}\left(t_f\right)=0\\ T_{BU}\left(t_f\right)=0\end{array}\right.\hspace{1em}(Case D)$$

(9)

As a result, the backup energy E_BU and backup time T_BU can be calculated for various scenarios. Another criterion, the load downtime percentage ${\chi }_{DT}$, is also introduced here. The load downtime percentage over the grid outage duration can be calculated using the backup time T_BU, as described in (10). The downtime percentage of the load ${\chi }_{DT}$ can be reduced by increasing the backup time T_BU from (10). The downtime percentage can also indicate load reliability.

$${\chi }_{DT}\left(t_f\right)=(1-\frac{T_{BU}\left(t_f\right)}{T_D})\times 100\%$$

(10)

4. Impact of System Parameters on Backup Capacity

Based on the previous section, this section will present case studies and calculate the backup energy and backup time, as well as the load downtime percentages, for various grid failure times. As mentioned in the previous section, these backup performance criteria ($E_{BU}$, $T_{BU}$, and ${\chi }_{DT}$) are closely related to a number of system operating parameters: (1) load power P_L, (2) EV travel pattern parameters (e.g., t_HD, t_HA, and E(t_HA)), and (3) grid outage duration T_D. As a result, the impact of these parameters will be examined as well. The following is the methodology used in this case. To begin, obtain system parameters such as charging power P_chg, discharging power P_dis, travel distance L, home departure time t_HD, home arrival time t_HA, and power outage duration T_D. Then, determine which case with these parameters is located, and the detailed analysis is provided in Section 2. The backup energy E_BU and backup time T_BU can then be calculated using the equations in Section 2 for various cases. Finally, with (10), the load downtime percentage ${\chi }_{DT}$ is calculated.

4.1. Constant Maximum Load

To begin, the load is assumed to be constant.

Table 1. System parameters.

Item	Parameter	Item	Parameter
Electric vehicle	Nissan Leaf	Charging power Pchg	6.6 kW
Discharging power Pdis	6.6 kW	Travel distance L	25 mile
Home departure time tHD	08:00 h	Home arrival time tHA	18:00 h
EV full energy Efull	40 kWh	EV minimum energy Emin	0.2 × 40 kWh
Power outage duration TD	1 h	Efficiency ηdis	0.95
Household load PL	6.6 kW × ηdis	Number of EVs per household	1

shows the parameters for the case study assuming that the load is the maximum power of the EV-UPS system.

Given an EV battery energy consumption rate of 40 kWh per 150 miles, the EV remaining energy when returning home is as shown in (11).

$$E(t_{HA})=(1-\frac{L}{150})\times E_{full}$$

(11)

where L is the traveling distance.

Obtain the system parameters at the time of the grid failure for various grid failure times. Then, determine which case the system is in and apply the parameters to the corresponding expression to obtain the backup energy (E_BU) and backup time (T_BU).

The case study results are shown in Figure 10 based on Table 1 and the analysis in Section 2. According to Figure 10a, the EV-UPS is often used in Case C, where the backup energy can reach 6.6 kWh, when the grid fails during the home charging time (after t_HA and before t_HD). The associated backup time can reach an hour according to Figure 10b. As a result, the EV-UPS can completely cover the grid loss and reduce the load downtime to zero, as shown in Figure 10c. Additionally, Figure 10a shows that the EV-UPS is primarily in Case A when the grid fails during non-charging time, and the backup energy and backup time are both zero. Therefore, as illustrated in Figure 10c, the load downtime percentage can reach 100%.

4.1.1. Uncertainty of Daily Traveling Parameters

The EV traveling parameters (e.g., t_HD, t_HA, and E(t_HA)) are fixed in the preceding case study. A Monte Carlo simulation is performed to account for the uncertainty of the daily travel parameters. The average daily trip distance is assumed to be a lognormal distribution with a standard deviation of 0.5. Equation (12) depicts the relevant probability density distribution.

$$f_D\left(L\right)=\frac{1}{\sqrt{2\pi }{\sigma }_{D}L}{e}^{\left[-\frac{{\left(lnL-{\mu }_D\right)}^2}{2{\sigma }_D^2}\right]}$$

(12)

where ${\mu }_D$ = 3.22 and ${\sigma }_D$ = 0.5.

The EV home arrival time and home departure time are assumed to be normal distributions, and the related probability density functions are illustrated in (13) and (14), where ${\sigma }_{HA}$ is 3.4 and ${\sigma }_{HD}$ is 3.24.

$$f_{HA}\left(t_{HA}\right)=\left\{\begin{array}{c}\frac{1}{\sqrt{2\pi }{\sigma }_{HA}}{e}^{\left[-\frac{{\left(t_{HA}-{\mu }_{HA}\right)}^2}{2{\sigma }_{HA}^2}\right]},{\mu }_{HA}-12<t_{HA}\le 24\\ \frac{1}{{\sqrt{2\pi }\sigma }_{HA}}{e}^{\left[-\frac{{\left(t_{HA}+24-{\mu }_{HA}\right)}^2}{2{\sigma }_{HA}^2}\right]},0<t_{HA}\le {\mu }_{HA}-12\end{array}\right.$$

(13)

$$f_{HD}\left(t_{HD}\right)=\left\{\begin{array}{c}\frac{1}{{\sqrt{2\pi }\sigma }_{HD}}{e}^{\left[-\frac{{\left(t_{HD}-{\mu }_{HD}\right)}^2}{2{\sigma }_{HD}^2}\right]},0<t_{HD}\le 12+{\mathsf{\mu }}_{\mathrm{H}\mathrm{D}}\\ \frac{1}{\sqrt{2\pi }{\sigma }_{HD}}{e}^{\left[-\frac{{\left(t_{HD}-24-{\mu }_{HD}\right)}^2}{2{\sigma }_{HD}^2}\right]},12+{\mathsf{\mu }}_{\mathrm{H}\mathrm{D}}<t_{HD}\le 24\end{array}\right.$$

(14)

where ${\mu }_{HA}$ = 18, ${\mu }_{HD}=$8, ${\sigma }_{HA}$ = 3.4, and ${\sigma }_{HD}$ = 3.24.

The probability density functions fD, fHA, and fHD are plotted as shown in Figure 11.

The Monte Carlo simulation is run for 10,000 times. The expected backup energy ($\overline{E_{BU}}$), expected backup time ($\overline{T_{BU}}$), and expected load downtime percentage ($\overline{{\chi }_{DT}}$) for these ten thousand tests can then be computed using (15).

$$\left\{\begin{array}{c}\overline{E_{BU}}\left(t_f\right)=\frac{1}{N}\sum _{i=1}^{10000}{E}_{BU}\left(t_f,i\right)\\ \overline{T_{BU}}\left(t_f\right)=\frac{1}{N}\sum _{i=1}^{10000}{T}_{BU}\left(t_f,i\right)\\ \overline{{\chi }_{DT}}\left(t_f\right)=(1-\frac{\overline{T_{BU}}\left(t_f\right)}{T_D})\times 100\%\end{array}\right.$$

(15)

where $E_{BU}\left(t_f,i\right)$ and $T_{BU}\left(t_f,i\right)$ are the backup energy and time for the ith time of the Monte Carlo simulation, respectively; N denotes the number of tests.

Figure 12 shows the findings of $\overline{T_{BU}}$ and $\overline{{\chi }_{DT}}$ for the case study. According to Figure 12, when the grid fails during the day, the backup period that the EV-UPS can provide is quite short, resulting in a higher proportion of load downtime. The main reason for this is that the likelihood of the EV being connected to the grid is low throughout the day. When the grid fails during the night, the probability of EVs connected to the grid is greater, resulting in longer backup time and a lower percentage of load downtime. The proportion of load outage can be brought below 20%, particularly if the grid breakdown happens between 00:00 and 04:00. Thus, the EV-UPS system can significantly improve load dependability.

4.1.2. Different Grid Outage Duration T_D

In the analysis above, the grid outage length T_D is fixed as one hour. Figure 13 shows the outcomes using the same methodology for various grid outage lengths. According to Figure 13a, the backup time ($\overline{T_{BU}}$) normally increases as the grid outage length increases. In contrast, if T_D exceeds 5 h and the grid failure occurs at night (i.e., after 18:00), the backup duration actually reduces as T_D rises. An electric vehicle (EV) will not have enough time to recharge after discharging to support the grid if the duration of the power loss is too long. As a result, to ensure full charge before departure, the EV-UPS chooses to provide less backup energy to the grid, resulting in a decrease in backup time, as shown in Figure 13a. According to Figure 13b, the load downtime percentage increases as the T_D increases, resulting in lower load reliability. Especially if the T_D is 8 h, the load downtime percentage is greater than 60%, implying that the load downtime lasts longer than 4.8 h.

The results of $\overline{{\chi }_{DT}}$ for various T_D can also be plotted in 3D, as shown in Figure 14. The color in the figure represents the value of $\overline{{\chi }_{DT}}$. According to the graph, as T_D increases, so does the range of the red area. This means that as T_D increases, so does the percentage of load downtime. When T_D is low, the blue area’s range is relatively large, indicating that the corresponding load downtime percentage is low and load reliability is high. Furthermore, the red area is closer to the center of the t_f-axis, indicating that the load downtime percentage is higher if the grid failure occurs during the day.

4.2. Variable Load Condition

Figure 15 depicts a daily typical household load with varying values for load power over time. Refrigeration, heating and cooling, lighting, cooking, and washing and drying are the most common types of appliances. It should also be noted that the load power after work is relatively high, especially between 18:00 and 22:00. It is worth noting that the peculiarities of a particular household’s consumption cyclogram are not taken into account.

The results of $\overline{E_{BU}}$ and $\overline{T_{BU}}$ for the typical household load in Figure 15 are obtained using the same method as for the constant load conditions, and are shown in Figure 16. It is worth noting that the grid failure duration is set to one hour. According to Figure 16, when the grid fails during the day, the backup time and energy are both relatively low. When the grid fails during the night, the backup time and energy are relatively long. The backup energy is highest between 18:00 and 22:00, because the load power is high during this time period.

Figure 17 displays the results of $\overline{T_{BU}}$ for various grid outage durations T_D. The color in the graph represents the value of $\overline{T_{BU}}$. Figure 17 shows that as the grid outage duration T_D increases, the color begins to turn yellow, indicating that the backup time $\overline{T_{BU}}$ increases. Moreover, when the grid fails during the day, the blue color appears more frequently, indicating that the corresponding backup time is short.

The results of $\overline{{\chi }_{DT}}$ for various T_D can also be plotted in 3D, as shown in Figure 18. The color in the figure represents the value of $\overline{{\chi }_{DT}}$. According to the graph, as T_D increases, so does the range of the red area. This means that as T_D increases, so does the percentage of load downtime. When T_D is low, the blue area’s range is relatively large, indicating that the corresponding load downtime is low and the load reliability is high.

Figure 18 shows that the red area remains large, and thus, the load downtime percentage remains high. An improvement strategy is investigated in the following section to further reduce load downtime and increase load reliability.

5. Improvement of Backup Capacity

5.1. Concept of the Improved Strategy

Figure 19a depicts the previous FCBD strategy concept. According to the above analysis, backup capability is relatively low. The main reason is that EVs attempt to be fully charged before departure, limiting the amount of backup energy available. Another disadvantage of the previous strategy is that the duration of the grid outage must be known in advance in order to implement the algorithm. However, the length of a grid outage is difficult to predict in practice.

As a result, an improved strategy is proposed in Figure 19b. Even when the grid is normal, EVs try to be fully charged before leaving. During the duration of the grid outage, however, the battery energy requirement is modified to maintain only above the minimum energy E_min plus the next trip energy requirement E_trip. More energy can thus be released during the power outage. Furthermore, the next trip will be unaffected. It should be noted that the value of E_trip can utilize the data from the previous trip. Another advantage of this strategy is that the duration of the grid outage is not required by the algorithm.

Furthermore, the load can be reduced during the duration of the grid outage, as shown in Figure 19c, by only powering the essentials, such as cooking, lighting, and heating and cooling. As a result, during the grid outage, power cannot be used for washing and drying or refrigeration. This way, backup capacity can be increased even further. Here is a solution for implementation. When the power outage occurs, the control system can automatically turn off the power for the washing, drying, and refrigeration. During a grid outage, power is cut off for washing and drying as well as refrigeration. When the grid recovers, the control system can automatically activate the power breaker for the washing and drying and refrigeration systems.

The block scheme for both strategies is presented in Figure 20.

5.2. Backup Capacity Calculation

The backup capacity using the improved strategy can be calculated using the same method as in Section 2. Similarly, four cases are presented based on various grid failure times t_f (see Figure 5). Using Case C as an example, three subcases can be obtained, as shown in Figure 21.

In Case C1, E(t_f) is less than E_min plus E_trip. Therefore, the EV cannot release the backup energy. E_BU and T_BU are both zero in this case, as shown in (16).

$$\left\{\begin{array}{c}{E}_{BU}\left(t_f\right)=0\\ T_{BU}\left(t_f\right)=0\end{array}\right.\mathrm{\hspace{1em}}(Case\mathrm{ }C1)$$

(16)

In Cases C2 and C3, E(t_f) equals E_min plus E_trip, allowing the stored energy to be released for backup. In Case C2, the stored energy cannot last the entire duration of T_D. As a result, the EV energy reaches its limit in the middle of the T_D. In (17), the backup energy E_BU and backup time t_BU in Case C2 are as shown in Figure 21b.

$$\left\{\begin{array}{c}{E}_{BU}\left(t_f\right)=E\left(t_f\right)-\left(E_{min}+E_{trip}\right)\\ E_{BU}\left(t_f\right)={\int }_{t_f}^{t_f+T_{C2}}\frac{P_L\left(t\right)}{{\eta }_{dis}}dt\\ T_{BU}\left(t_f\right)=T_{C2}\end{array}\right.\mathrm{\hspace{1em}}(Case\mathrm{ }C2)$$

(17)

In Case C3, the stored energy can last the entire duration of T_D. As a result, the EV can discharge continuously throughout the T_D. In Case C3, the backup energy E_BU and backup time T_BU are expressed as shown in (18).

$$\left\{\begin{array}{c}{E}_{BU}\left(t_f\right)={\int }_{t_f}^{t_f+T_D}\frac{P_L\left(t\right)}{{\eta }_{dis}}dt\\ T_{BU}\left(t_f\right)=T_D\end{array}\right.\mathrm{\hspace{1em}}(Case\mathrm{ }C3)$$

(18)

The backup energy E_BU and backup time T_BU for other cases can be calculated using the same method, which will not be discussed further here.

5.3. Backup Capacity Results

Figure 22 shows the results of the backup time ($\overline{T_{BU}}$) using the previous strategy and the improved strategy, with the grid failure duration set to 8 h. Figure 22 shows that the improved strategy significantly increases backup time. With the improved strategy, backup time can be increased by two hours when the grid fails during the night. However, if the grid fails during the day, the backup time is nearly identical to that of the old strategy.

Figure 23 depicts the results of $\overline{{\chi }_{DT}}$ for various T_D after using the improved strategy. The color in the figure represents the value of $\overline{{\chi }_{DT}}$. When compared to the previous strategy’s results (see Figure 18), the red area is reduced to yellow. This means that the improved strategy reduces load downtime by approximately 20%. In addition, the improved strategy expands the blue area. As a result of the improved strategy, load downtime is reduced and load reliability is increased.

6. Experimental Verifications

The setup for a 5 kW EV-UPS experimental platform is shown in Figure 24a, where the battery is used to simulate the EV. Figure 24b depicts the system’s topology as well. Every five minutes, the system’s data are sent to users via Ethernet cable.

The parameters of the system are presented in

Table 2. Parameters of the system.

Item	Value
Battery voltage range	350~450 V
Battery capacity	9.8 kWh
EV minimum energy Emin	0.2 × 9.8 kWh
Maximum input current	17.5 A
Charging power	5 kW
Nominal grid voltage (L-L)	240 V
Nominal grid frequency	50 Hz
Maximum continuous ac current	21 A @ 240 V
Load power	1 kW
Home arrival time tHA	18:00 h
Home departure time tHD	08:00 h
Battery SOC when arriving home	0.85

.

In the first case, the grid outage lasts three hours. Furthermore, the grid failure is assumed to begin at 05:00 and last until the departure at 08:00. Figure 25 and Figure 26 show the experimental results after using the old strategy and the improved strategy, respectively. It is worth noting that the data are collected every 5 min and then plotted using MATLAB. According to the data, when the EV arrives home at 18:00 h, the battery begins to charge itself, and the battery is fully charged before the grid goes down. If the old strategy is used (see Figure 25), the battery will be unable to discharge energy in order to ensure full charge before departure. As a result, the backup time is 0 and the load downtime percentage is 100%. If the improved strategy is used, the battery can discharge energy to support the load after the grid fails, and the discharging time can be extended to three hours. As a result, the duration of the grid outage can be fully covered, and the load downtime percentage is 0%. Furthermore, before departure, the battery SOC is 0.65. As a result, the trip requirement can also be met.

The grid outage duration is set to 5 h in the second case. It is assumed that the grid failure begins at 02:30 and ends at 07:30. Figure 27 and Figure 28 show the experimental results after using the old strategy and the improved strategy, respectively. According to the data, when the EV arrives home at 18:00 h, the battery begins to charge itself, and the battery is fully charged before the grid goes down. The battery can discharge and support the load for 2.5 h if the old strategy is used (see Figure 27). The full charge can thus be guaranteed prior to departure. As a result, the backup time is 2.5 h and the load downtime is 50%. If the improved strategy is used, the charging time can be increased to five hours. As a result, the duration of the grid outage can be fully covered, and the load downtime percentage is 0%. Moreover, before departure, the battery SOC is 0.65, and the trip requirement can be met.

Figure 29 depicts the backup time results for the two preceding cases. It can be seen that the improved strategy significantly increases backup time.

7. Conclusions

The use of EVs as UPSs for households, particularly in rural areas, can greatly improve the reliability of household power. The UPS architectures for single and multiple EVs are presented first. The methodology for calculating backup capacity for EV-UPS systems is then presented based on the EV mobility pattern, and four cases based on different grid failure times are detailed. According to the calculations, if the grid fails during charging, the EV-UPS can completely cover the outage. A Monte Carlo simulation is also run to account for the uncertainty of the daily travel parameters. The duration of the power outage is also considered. The percentage of load downtime increases with the duration of the power outage, resulting in lower load reliability. An improved strategy is proposed to increase backup capacity even further. The battery energy requirement is changed during the grid outage to maintain only above the minimum energy E_min plus the next trip energy requirement E_trip. More energy can thus be released during the power outage. Furthermore, the next trip will be unaffected. Furthermore, during a grid outage, the load can be reduced by only using power for the essentials. In the case study, the improved strategy can increase backup time by two hours. Finally, a 5 kW EV-UPS testing platform is constructed. The experimental results show that the improved strategy significantly improves backup time.