1 Introduction

The increase in EVs and other DC loads has resulted in difficulty in meeting the demands for load diversity in and economy of AC micro-grid system. AC/DC hybrid micro-grid have gradually become one of the development paths of the micro-grid system owing to its advantages, such as access to various types of distributed power supply and economically increased DC load [1]. The optimal capacity allocation of micro-grid is a key aspect to be considered during its construction because it is closely related to economic benefits, reliability of the power supply, operation safety, and power quality of micro-grid.

At present, the research on micro-grid has been generally focused on operating and controlling AC/DC hybrid micro-grid. However, the effect of access to the hybrid micro-grid on the optimal allocation capacity of EVs has been disregarded. Previous studies have investigated the capacity allocation planning of AC/DC hybrid micro-grid under uncertain wind power, photovoltaic (PV), and load conditions [2, 3].

The economy and ability of self balancing have well been considered in optimal configuration of grid connected micro-grid [4,5,6]. And the relevant energy management strategy is proposed [7], aiming at the AC/DC micro-grid under the consideration of Optimization of power supply capacity.

The increasing number of EVs and uncertainty in terms of access quantity and time remain as challenges to the planning and intelligent scheduling of micro-grid. Given that energy storages mainly characterize EVs [8], reasonable planning and scheduling can reduce the number of energy storage devices and improve the economy of micro-grid on the basis of satisfying users’ normal transportation needs.

Although an optimal dispatching scheme for the access of EVs to micro-grid under the intelligent mode has been proposed [9]; the life cycle of each distributed generation in the micro-grid is neglected. The characteristics of the mobile energy storage of EVs have indicated that the engineering field has quantified the energy storage allocation capacity of micro-grid in relation to EVs [10]. In addition, the capacity allocation of a wind–solar complementary system for EV charging stations has been optimized and analyzed in a timely manner [11]. To reduce the cost of optimal allocation and load fluctuation, a multi-objective programming model of AC/DC hybrid micro-grid with the orderly charging of EVs under comprehensive constraints was established. In addition, the optimal capacity allocation of AC/DC hybrid micro-grid was explored [12]. The existing research on the optimal capacity allocation of micro-grid that simplifies EVs as controllable loads has mainly focused on the optimal capacity allocation of micro-grid caused by the orderly charging of EVs. At present, in the disordered charging mode without external interference, the daily charging load curve of EVs based on the travel habits and life rules of vehicle users is consistent with the load change of micro-grid [13], which increases the energy storage capacity configuration of micro-grid and increases the burden of micro-grid operation. However, only a few studies have been conducted on the effect of the orderly discharging of EVs and users’ satisfaction brought about by different charging and discharging modes on the capacity allocation of hybrid micro-grid.

Therefore, this study presents the capacity optimization of hybrid micro-grid in view of the PV/wind/storage hybrid AC/DC micro-grid and given the EV ordered charging/discharging and users’ satisfaction. The capacity optimization model of hybrid micro-grid is established on the basis of orderly charging/discharging of EVs and users’ satisfaction. The allocation program of the power supply capacity can be derived from different scenarios through the particle swarm optimization algorithm. By comparing different modes of charging/discharging EVs, this study analyzes the influence of AC/DC hybrid micro-grid on different charging/discharging modes and user satisfaction.

2 Ordered Discharge Model of EVs

This research focuses on the effects of the orderly charging/discharging of EVs on the optimal configuration of AC/DC hybrid micro-grid. Private EVs can be used as typical mobile energy storage device sowing to the short daily driving distances and long queues in charging piles.

2.1 Effective Discharge Duration

EVs are not constantly involved in charging/discharging while connected to charging piles, and a certain initial charge is required to participate in orderly discharging [14]. The starting charge of EVs is dependent on daily mileage and travel time. The probability density function \({\mathrm{f}}_{{\mathrm{L}}_{\mathrm{D}}}\left(\mathrm{x}\right)\) for the daily travel of EVs can be calculated as follows.

$$f_{{L_{D} }} (x) = \frac{1}{{\sqrt {2\pi } x\sigma_{D} }}\exp \left[ { - \frac{{(\ln x - \mu_{D} )^{2} }}{{2\sigma_{D}^{2} }}} \right],$$
(1)

where \(\mathrm{x}\) denotes the daily mileage, and \({\upmu }_{\mathrm{D}}\) is the expected daily driving mileage, and \({\upsigma }_{\mathrm{D}}\) refers to the standard deviation of daily mileage. The investigation of the US Department of Transportation 8 indicates that \({\upmu }_{\mathrm{D}}\) and \({\upsigma }_{\mathrm{D}}\) are evaluated at 3.2 and 0.88, respectively, whereas \(\mathrm{x}\) ranges from 0 to 200.

\({\mathrm{T}}_{\mathrm{s}}\) refers to the daily driving time of EVs, the probability density function of which can be calculated using Formula (2) as follows.

$$f_{{T_{d} }} (t) = \frac{1}{{\sqrt {2\pi } t\sigma_{D} }}\exp \left[ { - \frac{{(\ln t + \ln V_{s} - \mu_{D} )^{2} }}{{2\sigma_{D}^{2} }}} \right],$$
(2)

where \({\mathrm{V}}_{\mathrm{s}}\) is the average speed and t pertains to travel duration. In addition, t should be within specific limits as follows:

$$0 < t \le \frac{200}{{V_{s} }},$$
(3)

Probability function \({\mathrm{f}}_{{\mathrm{T}}_{\mathrm{d}}}\left(\mathrm{x}\right)\) of the effective discharge duration of EV \({\mathrm{T}}_{\mathrm{d}}\) can be calculated using Formula (4) as follows.

$$ \begin{aligned} & f_{{T_{s} }} (t) = \frac{{P_{d} }}{{\sqrt {2\pi } (0.8C_{b} - t \times P_{d} )\sigma_{D} }}\exp \\ &\left[ { - \frac{{\left[ {\ln 0.8C_{b} - t \times P_{d} ) - \ln 0.15_{s} - \mu_{D} } \right]^{2} }}{{2\sigma_{D}^{2} }}} \right],\end{aligned} $$
(4)

where the selection of \({\upmu }_{\mathrm{D}}\) and \({\upsigma }_{\mathrm{D}}\) can refer to Formula (1) and t is the discharge time of EVs to micro-grid. The selection oft should be within specific limits as follows.

$$\frac{{0.8C_{b} - 30}}{{P_{d} }} \le t < \frac{{0.8C_{b} }}{{P_{d} }}.$$
(5)

2.2 Time of Discharge

In terms of the orderly charging of EVs, starting time refers to the peak and valley price periods of the power supply system. When the discharge time is less than the peak price period based on retaining daily driving power consumption, users can start discharging any time within the peak price range that meets the full discharge time. When the time consumption of discharge is more than the peak price time interval, the start time of discharging will be selected at the initiation time of peak price. The time period beyond the peak price interval will be calculated according to the level or valley price time period. Formula (6) can be used to calculate the ordered discharge time \({\mathrm{t}}_{\mathrm{f}}\) as follows.

$$t_{f} = \left( \begin{gathered} t_{ps} + k_{c} \times (t_{pe} - T_{d} - t_{ps} ),\begin{array}{*{20}c} {} & {0 \le T_{d} \le (t_{pe} - t_{ps} )} \\ \end{array} \hfill \\ \begin{array}{*{20}c} {} & {t_{ps} \begin{array}{*{20}c} {\begin{array}{*{20}c} {\begin{array}{*{20}c} {} & {} \\ \end{array} } & {} & {} \\ \end{array} } & {} & {} & {T_{dc} > (t_{pe} - t_{ps} )} \\ \end{array} } \\ \end{array} \hfill \\ \end{gathered} \right.,$$
(6)

where \({\mathrm{T}}_{\mathrm{d}}\) denotes the length of time required, \({\mathrm{t}}_{\mathrm{ps}}\) is the start time of EVs in the peak period of electricity discharge, \({\mathrm{t}}_{\mathrm{pe}}\) refers to the completion time of discharge, and \({\mathrm{k}}_{\mathrm{c}}\) is a coefficient with values ranging from 0 to 1.

3 Optimal Capacity Allocation Model for AC/DC Hybrid Micro-grid Containing EVs

Various distributed generators and energy storage devices are connected to DC and AC buses, respectively, during the normal operation of hybrid micro-grid, thereby reducing power loss compared with traditional AC micro-grid. Moreover, the economy of hybrid micro-grid and user satisfaction should be improved, and power loss caused by power exchange between the AC and DC sides of hybrid micro-grid should also be reduced during the optimal capacity allocation of AC/DC hybrid micro-grid.

3.1 Objective Function

3.1.1 Economic Cost

The economic costs of AC/DC hybrid micro-grid comprise the costs of the initial equipment investment, operation and maintenance, charging/discharging of EVs, power interaction cost between micro-grid and power distribution networks, and residual cost of the power system after the entire life cycle. Life cycle cost is typically expressed as in Formula (7).

$$C_{Total} = C_{s} + C_{y} + C_{d} + C_{j} - C_{r}$$
(7)

where \({\mathrm{C}}_{\mathrm{Total}}\) is the economic cost of the total life cycle of hybrid micro-grid, \({\mathrm{C}}_{\mathrm{s}}\) is the initial equipment cost of micro-grid, \({\mathrm{C}}_{\mathrm{y}}\) denotes the operation and maintenance cost of micro-grid, \({\mathrm{C}}_{\mathrm{d}}\) pertains to the charging/discharging costs of EVs, \({\mathrm{C}}_{\mathrm{j}}\) is the cost of electric power interaction between hybrid micro-grid and distribution power network, and \({\mathrm{C}}_{\mathrm{r}}\) is the residual value of the hybrid micro-grid system after the total life cycle.

3.1.1.1 Cost of the Initial Equipment Investment

The cost of the initial equipment investment \({\mathrm{C}}_{\mathrm{s}}\) comprises the cost of the initial operation of various distributed generators and converters. Compared with centralized power generation, the high cost of initial investment has become the main constraint factor. However, the constraints are expected to be alleviated with the development of science and technology. The initial investment cost of hybrid micro-grid equipment is calculated using the equivalent annual method [15], which is shown as in Formula (8) as follows.

$$C_{s} = \sum\limits_{i = 1}^{N} {K_{i} } C_{i} \frac{{r(1 + r)^{{Y_{i} }} }}{{(1 + r)^{{Y_{i} }} - 1}},$$
(8)

where \(\mathrm{N}\) is the species number of power sources in the hybrid micro-grid systems. \({\mathrm{K}}_{\mathrm{i}}\) denotes the number of \(\mathrm{i}\)-type distributed power supply, and \({\mathrm{C}}_{\mathrm{i}}\) refers to the cost of the \(\mathrm{i}\)-type distributed power supply investment in the initial stage of hybrid micro-grid construction. \({\mathrm{Y}}_{\mathrm{i}}\) stands for the service life of the \(\mathrm{i}\)-type distributed power generation, and \(\mathrm{r}\) is the discount rate, which is takes a value of 8.10. In this study, wind power, PV, and storage battery are selected for hybrid micro-grid distributed generation.

3.1.1.2 Operation and Maintenance Cost of Hybrid Micro-grid

The entire lifecycle of hybrid micro-grid is typically planned for 20 years. Apart from storage battery, which requires replacement within the 20 years because of frequent charging/discharging, the life cycle of other power sources is beyond the planning period. The operation cost of micro-grid is mainly related to transmission power, such as the generation operation cost of distributed generation and operation cost of storage battery, which is shown in Formula (9) as follows.

$$C_{y} = C_{z} + \sum\limits_{i = 1}^{N} {\sum\limits_{j = 1}^{{K_{i} }} {\sum\limits_{t = 1}^{T} {k_{i} } P_{ibt} } } ,$$
(9)

where \({C}_{z}\) is the replacement cost of batteries, and \(T\) is the total operation time of hybrid micro-grid during the life cycle. The \({k}_{i}\) represents the operating factor of the \(i\)-type hybrid micro-grid equipment, and \({P}_{ibt}\) is the output power value of unit \(b\) of class \(i\) equipment of the system at time t.

3.1.1.3 Interaction Cost of the Hybrid Micro-grid and Power Distribution Networks

The interaction cost of the hybrid micro-grid and power distribution networks comprises the cost of purchasing electricity from power distribution networks and revenue from selling electricity to power distribution networks, which is shown in Formula (10) as follows.

$$C_{j} = \sum\limits_{t = 1}^{T} {\left( {k_{bt} P_{bt} - k_{st} P_{st} } \right)} ,$$
(10)

where \({P}_{bt}\) and \({P}_{st}\) refer to the power of hybrid micro-grid that purchase electricity from power distribution networks and sell electricity to power distribution networks, respectively, at time t.\({k}_{bt}\) and \({k}_{st}\) denote the prices of purchasing and selling electricity from power distribution networks, respectively, at time t.

3.1.1.4 Cost of EV Ordered Charging/Discharging

The charging/discharging time of EVs can be adjusted according to the peak and valley prices. Charging during valley price scan lower the cost of charging, whereas discharging during peak period scan make maximize revenue. The cost of charging/discharging can be calculated using Formula (11) as follows.

$$C_{d} = \sum\limits_{i = 1}^{n} {\sum\limits_{t = 1}^{T} {(k_{ft} } } P_{ft,i} - k_{ct} P_{ct,i} ) + C_{b} ,$$
(11)

where \(n\) is the number of EVs participating intheorderly charging/discharging in micro-grid; \({ k}_{ft}\) and \({k}_{ct}\) are the electrovalence values of the orderly discharging/charging of EVs at time t, respectively [16]; \({P}_{ft,i}\) and \({P}_{ct,i}\) pertain to the power of \(i\) EV discharging to hybrid micro-grid and charging from micro-grid at time t, respectively; and \({C}_{b}\) denotes the subsidy of the participating EV users, who will be subsidized accordingly for battery consumption and for participating in repeated and orderly charging/discharging, which reduces service life.

$$k_{ft} = \left\{ \begin{gathered} k_{p} \begin{array}{*{20}c} {} & {t_{ps} \le t \le t_{pe} } \\ \end{array} \hfill \\ k_{c} \begin{array}{*{20}c} {} & {t_{cs} \le t \le t_{ce} } \\ \end{array} \hfill \\ k_{n} \begin{array}{*{20}c} {} & {other} \\ \end{array} \hfill \\ \end{gathered} \right.,$$
(12)

where \({k}_{ct}\) refers to the charging price, which is similar to \({k}_{ft}\) and can be calculated according to charging time located in the different time zones of the peak and valley electricity prices. User subsidy \({C}_{b}\) can be calculated using Formula (13) as follows.

$$C_{b} = pk_{t} T_{d} .$$
(13)

where \(p\) is the subsidy coefficient and takes a value of 0.4 in the present study [17] kt is the average electricity price within the discharge period, and \({T}_{d}\) refers to the discharge duration.

3.1.2 Loss of Converter Transformers

In contrast to traditional AC micro-grid, distributed generators and loads are connected to the AC and DC buses of AC/DC hybrid micro-grid, respectively. PV, energy storage, and DC loads, such as EVs, are connected to DC buses. By contrast, wind power and AC loads are connected to AC buses, thereby reducing converter losses. The loss of converter transformers \({P}_{ls}\) is calculated using Formula (14) as follows.

$$P_{ls} = (1 - \sigma )P_{tr} ,$$
(14)

where \({P}_{tr}\) is the converter power between different buses in hybrid micro-grid and \(\upsigma\) stands for converter efficiency.

3.1.3 Satisfaction of EV Users

Vehicle usage habits will be optimized and adjusted in an orderly manner during the optimization of the allocation of load resources, which will reduce users’ experience to a certain extent. User satisfaction reflects the quality of the vehicle users’ experience, which is quantified by the cost of charging/discharging and difference between charging/discharging schemes, as shown in Formula (15).

$$U_{sat} = \sum\limits_{i = 1}^{n} {\sum\limits_{t = 1}^{T} {(k_{t} } } P_{t} - k_{ct} P_{ct,i} ) - C_{j} ,$$
(15)

Although the difference between orderly and disorderly charging/discharging time distribution is reduced (i.e., the time selection of orderly charging/discharging is similar to the users’ original habits), users’ satisfaction will be increased. By contrast, user’ satisfaction will be reduced when the time distribution of orderly charging/discharging deviates from the time probability distribution of disorderly charging/discharging.

3.2 Operation Constraint Condition of the AC/DC Hybrid Micro-grid

3.2.1 Output Power Constraints of the Distributed Generation

The output power constraints of wind power and PV are shown in Formula (16) as follows.

$$\left\{ \begin{gathered} 0 \le P_{wt} \le P_{wtm} \hfill \\ 0 \le P_{pv} \le P_{pvm} \hfill \\ \end{gathered} \right.,$$
(16)

where \({P}_{wtm}\) and \({P}_{pvm}\) are the maximum output power of wind power and PV, respectively.

3.2.2 Constraints of Storage Battery

The capacity and operating constraints of storage battery are shown in Formula (17) as follows.

$$\left\{ \begin{gathered} SOC_{\min } \le SOC \le SOC_{\max } \hfill \\ P_{in} \le P_{c\max } \hfill \\ P_{out} \le P_{d\max } \hfill \\ \end{gathered} \right.$$
(17)

where \({SOV}_{min}\) and \({SOV}_{max}\) are the maximum and minimum limits, respectively, of the charge capacity of batteries; and \({P}_{cmax}\) and \({P}_{dmax}\) denote the maximum limit of battery charging/discharging power, respectively.

3.2.3 Power Constraints of EVs

$$\left\{ \begin{gathered} S_{EV\min } \le S_{EV} \le S_{EV\max } \hfill \\ 0 \le P_{EVc} \le P_{EVc\max } \hfill \\ 0 \le P_{EVd} \le P_{EVd\max } \hfill \\ \end{gathered} \right.,$$
(18)

where \({S}_{EVmin}\) and \({S}_{EVmax}\) are the minimum and maximum charge capacities, respectively, of EVs; and \({P}_{EVcmax}\) and \({P}_{EVdmax}\) are the maximum power of charging/discharging, respectively, for EVs.

3.2.4 Interactive Power Constraints in Power Distribution Networks

A power distribution network will be extremely affected when interactive power between hybrid micro-grid and distribution network increase. Therefore, the power constraints on hybrid micro-grid are formulated as Formula (19) as follows.

$$P_{sold} \le P_{sold\max } ,$$
(19)

where \({P}_{soldmax}\) is the maximum power transfer from hybrid micro-grid tothedistribution network.

4 Results and Discussion

4.1 Example

This study proposes an AC/DC hybrid micro-grid capacity allocation model on the basis of an actual power grid situation in a certain area in Inner Mongolia. In particular, this research investigates the optimal capacity allocation of hybrid micro-grid with EVs [18]. An AC/DC hybrid micro-grid comprises wind power, PV, storage battery, and other distributed power sources, and loads, such as EVs and other forms. The relevant economic parameters of AC/DC hybrid micro-grid are provided in Table 1.

Table 1 Economic parameters of hybrid micro-grid systems
Full size table

The light resources are illustrated in Fig. 1. The average annual wind speed in a region is approximately 6.7 m/s. The average daily irradiation intensity is approximately 4.55 (kW h)/(m2 d). The state of charge (SOC) of battery ranges from 0.5 to 0.95 [19, 20], and the initial SOC of storage batteries take a value of 0.8. The maximum loads in summer and winter are approximately 390 kW and 300 kW, respectively. The number of EVs is set to 300. Table 2 presents other parameters [21, 22].

Fig. 1
figure 1

Irradiance curve in certain areas

Full size image
Table 2 Parameter setting of EV
Full size table

4.2 Scenarios Analysis

The optimal capacity allocation of AC/DC hybrid micro-grid is investigated under the following scenarios: ① disorderly charging, ② orderly charging/discharging scenarios, and ③ satisfaction of EV users.

This study highlights the charging/discharging status of EVs within 24 h, and typical days in the summer and winter seasons are selected. In addition, this study identifies and analyzes the influence of orderly charging/discharging of EVs on the optimal capacity allocation of hybrid micro-grid. Figure 2 depicts the load curves of certain areas in the summer and winter. The maximum and second load peak occurred at 8 pm and 1 pm, respectively, whereas the minimum load occurred at 4 am. In the summer, the gap between peak and trough loads is large with large fluctuations. By contrast, load fluctuation is relatively gentle during the winter.

Fig. 2
figure 2

Load curve of typical days in the summer and winter in certain areas

Full size image

Table 3 presents the results of the optimal capacity allocation for hybrid micro-grid across scenarios.

Table 3 Capacity optimization of hybrid micro-grid across scenarios
Full size table

4.2.1 Optimal Capacity Configuration Analysis of Hybrid micro-grid in EV Sunder Disorderely Charging Scenario

The optimal capacity allocation results of AC/DC hybrid micro-grid in the disorderly charging scenario are listed in scenario 1 of Table 3. A total of 14 wind turbines, 385 KW PVs, and 923 energy storage batteries are included. During the operation life cycle of hybrid micro-grid, the initial installation cost of micro-grid can reach RMB 13,304,000, whereas the operation and maintenance cost can reach RMB 70,100.

EVs are randomly and disorderly charged without the guidance of market time-sharing price. Figure 3 demonstrates the charging power expectation, in which the fluctuation of power expectation of EVs is evident, thereby increasing the gap between the peak and valley of the load curve.

Fig. 3
figure 3

Expected disorderly charging of EVs

Full size image

Figure 4 shows that the peak load of a system increases in the case of disorderly charging of EVs, thereby aggravating the load fluctuation of hybrid micro-grid. The energy storage capacity should increase under circumstances where wind power and photovoltaic capacity remain unchanged, thereby increasing the economic cost.

Fig. 4
figure 4

Load power curve of EVs in disorderly charging mode

Full size image

4.2.2 Optimal Capacity Configuration Analysis of Hybrid Micro-grid in Orderly Charging/Discharging Scenario of EVs

Figure 5 presents the power expectation of EVs in the case of sequential charging/discharging.

Fig. 5
figure 5

Expectation of EV charging in orderly mode

Full size image

In the orderly charging scenario, EV owners can be guided in orderly charging according to the peak and valley price periods and time required for charging. The load can be transferred by changing the original disorderly charging mode of EVs. Table 4 lists the peak–valley time-of-use electricity prices.

Table 4 Peak–valley time-of-use of electricity prices
Full size table

In particular, the peak price period ranges from 11 am to 2 pm and from 7 to 11 pm, whereas the valley price period ranges from 12 to 7 am, and the remainder is considered a normal price period.

Figure 6 shows that the maximum load is reduced by 11%, as guided by peak and valley electricity prices, which play the role of filling valleys and cutting peaks during the peak and valley price periods. In the orderly charging/discharging scenario of EVs, the optimal capacity configuration of hybrid micro-grid is shown in scenario 2 of Table 3. A total of 14 wind turbines, 279-KW PVs ,and 680 energy storage batteries are included, and the installation cost of hybrid micro-grid can reach RMB 11.74 million. The operation cost is RMB 0.068 million, which indicates that the economic cost of hybrid micro-grid in the orderly charging/discharging scenario is reduced by 15% compared with the disorderly charging/discharging scenario of EVs.

Fig. 6
figure 6

Expectation of EV charging in the orderly mode

Full size image

4.2.3 Capacity Optimization Analysis of Hybrid Micro-grid Considering Satisfaction of Elecrivc Vehicle Users

A certain proportion of EV owners are encouraged to implement orderly charging/discharging combined with peak and valley electricity prices to promote their prices in the power market. However, a percentage of car owners maintain the original disordered charging/discharging mode. The enthusiasm of EV owners to participate in orderly charging can be enhanced by improving users’ satisfaction of EVs. This endeavor can increase the proportion of users participating in orderly charging/discharging and extend the effect of EV mobile energy storage on peak load shifting.

Scenario 3 in Table 3 depicts the optimal capacity allocation of hybrid micro-grid that considers the satisfaction of EV owners based on orderly charging/discharging of EVs. A total of 14 wind turbines, 256-KW PVs, and 623 energy storage batteries are included, and the installation and operation costs of hybrid micro-grid can reach RMB 10.73 and 0.065 million, respectively. The AC and DC bus power of hybrid micro-grid and converter capacity should be increased to meet the peak load supply because of the reduction in distributed power supply capacity. The economic cost of hybrid micro-grid under the user satisfaction scenario is reduced by 18.3% compared with the disorderly charging/discharging of EVs.

Figure 7 presents the orderly charging/discharging in the winter and summer, respectively. The number of EV users participating in orderly charging/discharging increases with the improvement of user satisfaction.

Fig. 7
figure 7

Load power curve in the summer and winter according to user satisfaction

Full size image

The economy of capacity allocation of hybrid micro-grid is improved with the reduction in peak load and smoothing of the load curve. By contrast, the economy of the capacity allocation of hybrid micro-grid will be decreased in the orderly charging/discharging of EV sowing to the low level of satisfaction of users and less number of users participating in orderly charging/discharging.

5 Conclusion

This study investigates the multi-objective capacity optimal allocation of AC/DC hybrid micro-grid for EVs under three scenarios. The influence of the different charging/discharging modes of EVs on the optimal capacity allocation of micro-grid is verified, and the influence of user satisfaction on the optimal capacity allocation of hybrid micro-grid is further considered. The main contributions of this research are as follows.

  1. (1)

    The peak load of hybrid micro-grid can be reduced, and the load curve can be alleviated through orderly charging/discharging of EVs. Compared with disordered charging/discharging, the installation and operation costs of the distributed generation of hybrid micro-grid are reduced, and the economy of capacity allocation of AC/DC hybrid micro-grid is increased.

  2. (2)

    The number of EV users participating in orderly charging/discharging is increased with the improvement in users’ satisfaction. The economy of capacity allocation of hybrid micro-grid is improved, and the effect of cutting peak and smoothing curve on orderly charging/discharging of EVs is notable.

This study considered the orderly charging/discharging of EVs and user satisfaction. However, future studies can explore the effects of the capacity allocation of hybrid micro-grid on EVs, particularly given the demand side responses.